nlsystemfit: Nonlinear Equation System Estimation

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/nlsystemfit.r

Description

Fits a set of structural nonlinear equations using Ordinary Least Squares (OLS), Seemingly Unrelated Regression (SUR), Two-Stage Least Squares (2SLS), Three-Stage Least Squares (3SLS).

Usage

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 nlsystemfit( method="OLS", eqns, startvals,
                     eqnlabels=c(as.character(1:length(eqns))), inst=NULL,
                     data=list(), solvtol=.Machine$double.eps,
                     maxiter=1000, ... )

Arguments

method

the estimation method, one of "OLS", "SUR", "2SLS", "3SLS".

eqns

a list of structural equations to be estimated.

startvals

a list of starting values for the coefficients.

eqnlabels

an optional list of character vectors of names for the equation labels.

inst

one-sided model formula specifying instrumental variables or a list of one-sided model formulas if different instruments should be used for the different equations (only needed for 2SLS, 3SLS and GMM estimations).

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment from which nlsystemfit is called.

solvtol

tolerance for detecting linear dependencies in the columns of X in the qr function calls.

maxiter

the maximum number of iterations for the nlm function.

...

arguments passed to nlm.

Details

The nlsystemfit function relies on nlm to perform the minimization of the objective functions and the qr set of functions.

A system of nonlinear equations can be written as:

ε_{t} = q( y_t, x_t, θ )

z_{t} = Z( x_t )

where ε_{t} are the residuals from the y observations and the function evaluated at the coefficient estimates.

The objective functions for the methods are:

Method Instruments Objective Function Covariance of θ
OLS no r'r (X(diag(S)^{-1}\bigotimes I)X)^{-1}
SUR no r'(diag(S)_{OLS}^{-1}\bigotimes I)r (X(S^{-1}\bigotimes I)X)^{-1}
2SLS yes r'(I \bigotimes W)r (X(diag(S)^{-1}\bigotimes I)X)^{-1}
3SLS yes r'(S_{2SLS}^{-1} \bigotimes W)r (X(diag(S)^{-1}\bigotimes W)X)^{-1}

where, r is a column vector for the residuals for each equation, S is variance-covariance matrix between the equations (\hat{σ}_{ij} = (\hat{e}_i' \hat{e}_j) / √{(T - k_i)*(T - k_j)}), X is matrix of the partial derivates with respect to the coefficients, W is a matrix of the instrument variables Z(Z'Z)^{-1}Z, Z is a matrix of the instrument variables, and I is an nxn identity matrix.

The SUR and 3SLS methods requires two solutions. The first solution for the SUR is an OLS solution to obtain the variance-covariance matrix. The 3SLS uses the variance-covatiance from a 2SLS solution, then fits all the equations simultaneously.

The user should be aware that the function is VERY sensative to the starting values and the nlm function may not converge. The nlm function will be called with the typsize argument set the absolute values of the starting values for the OLS and 2SLS methods. For the SUR and 3SLS methods, the typsize argument is set to the absolute values of the resulting OLS and 2SLS coefficient estimates from the nlm result structre. In addition, the starting values for the SUR and 3SLS methods are obtained from the OLS and 2SLS coefficient estimates to shorten the number of iterations. The number of iterations reported in the summary are only those used in the last call to nlm, thus the number of iterations in the OLS portion of the SUR fit and the 2SLS portion of the 3SLS fit are not included.

Value

nlsystemfit returns a list of the class nlsystemfit.system and contains all results that belong to the whole system. This list contains one special object: "eq". It is a list and contains one object for each estimated equation. These objects are of the class nlsystemfit.equation and contain the results that belong only to the regarding equation.

The objects of the class nlsystemfit.system and nlsystemfit.equation have the following components (the elements of the latter are marked with an asterisk (*)):

eq

a list object that contains a list object for each equation.

method

estimation method.

resids

an n \times g matrix of the residuals.

g

number of equations.

n

total number of observations.

k

total number of coefficients.

b

vector of all estimated coefficients.

se

estimated standard errors of b.

t

t values for b.

p

p values for b.

bcov

estimated covariance matrix of b.

rcov

estimated residual covariance matrix.

drcov

determinant of rcov.

rcovest

residual covariance matrix used for estimation (only SUR and 3SLS).

rcor

estimated residual correlation matrix.

nlmest

results from the nlm function call

solvetol

tolerance level when inverting a matrix or calculating a determinant.

## elements of the class nlsystemfit.eq

eq

a list that contains the results that belong to the individual equations.

eqnlabel*

the equation label of the ith equation (from the labels list).

formula*

model formula of the ith equation.

n*

number of observations of the ith equation.

k*

number of coefficients/regressors in the ith equation.

df*

degrees of freedom of the ith equation.

b*

estimated coefficients of the ith equation.

se*

estimated standard errors of b.

t*

t values for b.

p*

p values for b.

covb*

estimated covariance matrix of b.

predicted*

vector of predicted values of the ith equation.

residuals*

vector of residuals of the ith equation.

ssr*

sum of squared residuals of the ith equation.

mse*

estimated variance of the residuals (mean of squared errors) of the ith equation.

s2*

estimated variance of the residuals (\hat{σ}^2) of the ith equation.

rmse*

estimated standard error of the residulas (square root of mse) of the ith equation.

s*

estimated standard error of the residuals (\hat{σ}) of the ith equation.

r2*

R-squared (coefficient of determination).

adjr2*

adjusted R-squared value.

Author(s)

Jeff D. Hamann [email protected]

References

Gallant, R. H. (1987) Nonlinear Equation Estimation, John Wiley and Sons, 610 pp.

SAS Institute (1999) SAS/ETS User's Guide, Version 8, Cary NC: SAS Institute 1546 pp.

See Also

systemfit, nlm, and qr

Examples

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library( systemfit )
data( ppine )

hg.formula <- hg ~ exp( h0 + h1*log(tht) + h2*tht^2 + h3*elev + h4*cr)
dg.formula <- dg ~ exp( d0 + d1*log(dbh) + d2*hg + d3*cr + d4*ba  )
labels <- list( "height.growth", "diameter.growth" )
inst <- ~ tht + dbh + elev + cr + ba
start.values <- c(h0=-0.5, h1=0.5, h2=-0.001, h3=0.0001, h4=0.08,
                  d0=-0.5, d1=0.009, d2=0.25, d3=0.005, d4=-0.02 )
model <- list( hg.formula, dg.formula )

model.ols <- nlsystemfit( "OLS", model, start.values, data=ppine, eqnlabels=labels )
print( model.ols )

model.sur <- nlsystemfit( "SUR", model, start.values, data=ppine, eqnlabels=labels )
print( model.sur )

model.2sls <- nlsystemfit( "2SLS", model, start.values, data=ppine,
   eqnlabels=labels, inst=inst )
print( model.2sls )

model.3sls <- nlsystemfit( "3SLS", model, start.values, data=ppine,
                                    eqnlabels=labels, inst=inst )
print( model.3sls )

Example output

Loading required package: Matrix
Loading required package: car
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric


Please cite the 'systemfit' package as:
Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/.

If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site:
https://r-forge.r-project.org/projects/systemfit/
Warning messages:
1: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
2: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
$eq
$eq[[1]]
$method
[1] "OLS"

$i
[1] 1

$eqnlabel
[1] "height.growth"

$formula
hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

$b
           h0            h1            h2            h3            h4 
-0.5125587078  0.4207532666 -0.0001122495  0.0001536430  0.0845993400 

$se
               h0
[1,] 4.702938e-01
[2,] 2.081047e-01
[3,] 3.007921e-04
[4,] 2.226427e-05
[5,] 1.464941e-02

$t
             h0
[1,] -1.0898692
[2,]  2.0218348
[3,] -0.3731798
[4,]  6.9008803
[5,]  5.7749311

$p
               h0
[1,] 2.773993e-01
[2,] 4.484944e-02
[3,] 7.095055e-01
[4,] 1.124631e-10
[5,] 3.863849e-08

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
           [,1]
  [1,] 4.041648
  [2,] 4.541192
  [3,] 5.934397
  [4,] 5.875073
  [5,] 5.380850
  [6,] 4.869519
  [7,] 5.403979
  [8,] 4.593062
  [9,] 4.348993
 [10,] 5.438162
 [11,] 3.698608
 [12,] 2.832854
 [13,] 3.831431
 [14,] 5.299353
 [15,] 5.107354
 [16,] 4.763969
 [17,] 4.788288
 [18,] 7.271637
 [19,] 3.713791
 [20,] 4.320094
 [21,] 3.440131
 [22,] 6.681025
 [23,] 6.286435
 [24,] 5.211018
 [25,] 5.403979
 [26,] 5.211003
 [27,] 6.316420
 [28,] 6.906078
 [29,] 7.500303
 [30,] 4.970492
 [31,] 3.456607
 [32,] 5.133737
 [33,] 6.125762
 [34,] 4.086478
 [35,] 3.817085
 [36,] 5.471742
 [37,] 6.620397
 [38,] 6.146661
 [39,] 5.853734
 [40,] 6.244834
 [41,] 5.671051
 [42,] 5.237907
 [43,] 4.541141
 [44,] 6.304540
 [45,] 6.052145
 [46,] 5.391903
 [47,] 5.418815
 [48,] 5.926131
 [49,] 6.504803
 [50,] 5.164399
 [51,] 4.603851
 [52,] 6.297018
 [53,] 7.500782
 [54,] 4.609224
 [55,] 5.418815
 [56,] 5.406913
 [57,] 3.551454
 [58,] 3.824503
 [59,] 6.134112
 [60,] 6.645063
 [61,] 5.652614
 [62,] 5.659040
 [63,] 5.121548
 [64,] 6.222652
 [65,] 6.026606
 [66,] 6.368778
 [67,] 5.243357
 [68,] 5.483015
 [69,] 4.081686
 [70,] 6.260166
 [71,] 6.403707
 [72,] 6.175104
 [73,] 7.472574
 [74,] 6.235231
 [75,] 6.621119
 [76,] 6.080894
 [77,] 5.933956
 [78,] 5.015783
 [79,] 4.663540
 [80,] 7.385112
 [81,] 4.258321
 [82,] 4.067453
 [83,] 4.222441
 [84,] 3.751550
 [85,] 2.974481
 [86,] 4.559949
 [87,] 3.630734
 [88,] 4.215736
 [89,] 4.025814
 [90,] 3.565180
 [91,] 4.420640
 [92,] 4.085813
 [93,] 4.005981
 [94,] 4.509803
 [95,] 3.472775
 [96,] 3.665775
 [97,] 3.259613
 [98,] 3.368408
 [99,] 3.263850
[100,] 3.333685
[101,] 3.786635
[102,] 4.155387
[103,] 2.980494
[104,] 3.119646
[105,] 3.958657
[106,] 3.818303
[107,] 3.751550
[108,] 4.341037
[109,] 4.025814
[110,] 3.447226
[111,] 4.015277
[112,] 4.534577
[113,] 3.754373
[114,] 5.026704
[115,] 3.368408
[116,] 3.949021
[117,] 4.663679
[118,] 3.665316
[119,] 3.925762
[120,] 4.323104
[121,] 4.621358
[122,] 3.510452
[123,] 4.561191
[124,] 4.587547
[125,] 5.102449
[126,] 5.569115
[127,] 5.423036
[128,] 4.022256
[129,] 5.363876
[130,] 4.949033
[131,] 4.600287
[132,] 4.130406
[133,] 5.317830
[134,] 4.999044
[135,] 5.171810
[136,] 5.162217
[137,] 5.046124
[138,] 4.923601
[139,] 4.533648
[140,] 4.152380
[141,] 4.591826
[142,] 4.411167
[143,] 4.533648
[144,] 4.454235
[145,] 4.954010
[146,] 3.755485
[147,] 4.076642
[148,] 4.405621
[149,] 4.174439
[150,] 3.968077
[151,] 4.632855
[152,] 4.394421
[153,] 4.763781
[154,] 4.130760
[155,] 4.499987
[156,] 4.432987
[157,] 3.747908
[158,] 4.416676
[159,] 4.565665
[160,] 4.011625
[161,] 4.000857
[162,] 3.856709
[163,] 4.413876
[164,] 4.448976
[165,] 5.417853
[166,] 4.608918

$residuals
              [,1]
  [1,] -0.54164797
  [2,] -0.54119150
  [3,]  2.76560339
  [4,]  1.22492746
  [5,]  0.71915007
  [6,]  0.83048143
  [7,] -1.30397901
  [8,]  0.20693830
  [9,] -0.44899349
 [10,] -0.73816187
 [11,]  0.30139171
 [12,] -0.33285389
 [13,] -0.23143136
 [14,]  0.50064676
 [15,] -0.50735358
 [16,] -0.66396888
 [17,]  0.31171203
 [18,] -0.07163698
 [19,] -0.11379098
 [20,] -0.62009428
 [21,]  1.05986853
 [22,]  0.61897528
 [23,]  1.01356464
 [24,] -0.41101774
 [25,]  0.39602099
 [26,]  0.08899743
 [27,]  0.38357963
 [28,] -0.70607774
 [29,] -0.80030312
 [30,] -0.37049201
 [31,]  0.84339310
 [32,] -0.93373732
 [33,]  2.67423847
 [34,] -0.98647757
 [35,] -0.41708519
 [36,] -0.17174163
 [37,]  0.07960322
 [38,]  0.55333893
 [39,] -0.15373389
 [40,]  0.25516592
 [41,]  0.32894867
 [42,]  0.96209256
 [43,]  0.25885912
 [44,] -2.10453999
 [45,]  3.04785492
 [46,] -2.69190306
 [47,] -0.71881506
 [48,]  1.37386937
 [49,] -0.30480285
 [50,]  1.23560147
 [51,]  1.39614898
 [52,]  1.60298197
 [53,] -1.50078164
 [54,] -0.80922411
 [55,] -1.11881506
 [56,]  1.39308696
 [57,]  0.14854580
 [58,] -0.62450301
 [59,] -1.33411231
 [60,] -1.14506269
 [61,] -1.65261378
 [62,]  0.94096040
 [63,]  2.97845161
 [64,]  1.47734799
 [65,]  1.07339397
 [66,]  0.53122198
 [67,] -1.84335685
 [68,]  1.61698513
 [69,] -0.28168630
 [70,]  1.93983379
 [71,]  1.99629322
 [72,]  1.32489629
 [73,] -1.47257354
 [74,] -1.03523104
 [75,] -0.22111876
 [76,] -0.58089369
 [77,] -0.13395627
 [78,]  0.08421721
 [79,] -1.06354034
 [80,] -1.88511183
 [81,] -0.65832147
 [82,] -0.76745321
 [83,] -0.82244069
 [84,]  0.04845002
 [85,]  1.22551945
 [86,]  0.24005109
 [87,] -0.43073444
 [88,] -0.41573621
 [89,]  0.17418642
 [90,]  0.13481964
 [91,] -0.42063962
 [92,]  0.11418709
 [93,] -0.90598070
 [94,]  2.19019697
 [95,]  0.42722464
 [96,]  1.33422544
 [97,]  0.44038677
 [98,]  0.53159172
 [99,]  0.43615026
[100,]  0.26631542
[101,] -0.28663506
[102,] -0.05538669
[103,] -0.18049388
[104,] -0.21964591
[105,] -0.85865719
[106,] -0.51830325
[107,] -0.55154998
[108,] -1.84103706
[109,]  2.17418642
[110,]  2.55277437
[111,]  0.58472318
[112,]  0.46542283
[113,] -0.55437328
[114,]  1.57329579
[115,]  0.13159172
[116,]  1.35097887
[117,] -0.16367910
[118,]  0.63468385
[119,]  1.77423839
[120,]  0.67689554
[121,]  1.77864215
[122,]  2.38954795
[123,]  0.03880923
[124,] -0.08754732
[125,] -1.00244915
[126,] -2.16911485
[127,] -1.62303591
[128,] -0.62225618
[129,] -0.36387586
[130,] -0.54903280
[131,] -1.10028735
[132,]  3.76959378
[133,] -0.31783049
[134,] -1.59904391
[135,]  1.52818985
[136,]  1.83778289
[137,]  0.05387606
[138,] -0.92360083
[139,] -1.33364825
[140,]  1.64762027
[141,] -0.69182624
[142,] -0.21116697
[143,] -0.23364825
[144,] -0.05423487
[145,]  0.84598976
[146,] -3.45548526
[147,] -0.87664233
[148,]  0.69437855
[149,] -0.17443877
[150,] -2.66807681
[151,]  0.06714464
[152,] -1.09442099
[153,] -0.76378092
[154,] -1.03075987
[155,] -1.49998738
[156,] -3.03298731
[157,] -1.74790763
[158,] -1.81667619
[159,]  3.23433468
[160,] -0.21162528
[161,]  0.59914299
[162,] -1.35670858
[163,] -1.11387643
[164,]  0.05102376
[165,]  1.08214719
[166,] -2.70891782

$ssr
[1] 259.4263

$mse
[1] 1.611343

$s2
[1] 1.611343

$rmse
[1] 1.269387

$s
[1] 1.269387

$covb
              h0            h1            h2            h3            h4
h0  2.211762e-01 -9.443516e-02  1.252400e-04  1.618822e-06 -3.269671e-04
h1 -9.443516e-02  4.330755e-02 -5.967376e-05 -1.494795e-06 -4.646789e-04
h2  1.252400e-04 -5.967376e-05  9.047591e-08  2.264834e-09  8.336480e-07
h3  1.618822e-06 -1.494795e-06  2.264834e-09  4.956976e-10  3.638582e-08
h4 -3.269671e-04 -4.646789e-04  8.336480e-07  3.638582e-08  2.146052e-04

$r2
          [,1]
[1,] 0.4053022

$adjr2
          [,1]
[1,] 0.3905271

attr(,"class")
[1] "nlsystemfit.equation"

$eq[[2]]
$method
[1] "OLS"

$i
[1] 2

$eqnlabel
[1] "diameter.growth"

$formula
dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

$b
         d0          d1          d2          d3          d4 
-0.26606900  0.17040388  0.12485318  0.01987066 -0.01495275 

$se
              d0
[1,] 0.110459505
[2,] 0.055618909
[3,] 0.012865988
[4,] 0.014037757
[5,] 0.001011669

$t
             d0
[1,]  -2.408747
[2,]   3.063776
[3,]   9.704127
[4,]   1.415515
[5,] -14.780279

$p
              d0
[1,] 0.017136505
[2,] 0.002562918
[3,] 0.000000000
[4,] 0.158849035
[5,] 0.000000000

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
            [,1]
  [1,] 0.4393471
  [2,] 0.5066431
  [3,] 1.0531686
  [4,] 0.8405805
  [5,] 0.6977729
  [6,] 0.6560230
  [7,] 0.5659292
  [8,] 0.5815599
  [9,] 0.5231429
 [10,] 0.6433279
 [11,] 0.4903567
 [12,] 0.3305556
 [13,] 0.4765250
 [14,] 0.7522870
 [15,] 0.6188738
 [16,] 0.5471352
 [17,] 0.6382312
 [18,] 1.0109946
 [19,] 0.4610171
 [20,] 0.5143023
 [21,] 0.5278211
 [22,] 1.1687296
 [23,] 1.1329300
 [24,] 0.7465218
 [25,] 0.8857339
 [26,] 0.8195207
 [27,] 1.0706179
 [28,] 1.0295509
 [29,] 1.1489618
 [30,] 0.9043208
 [31,] 0.7438742
 [32,] 0.9069565
 [33,] 1.8375230
 [34,] 0.8082315
 [35,] 0.8321314
 [36,] 1.3041848
 [37,] 1.5106851
 [38,] 1.5764882
 [39,] 1.3791585
 [40,] 1.5242287
 [41,] 1.3906593
 [42,] 0.2572936
 [43,] 0.2027282
 [44,] 0.2206388
 [45,] 1.4662985
 [46,] 0.6425009
 [47,] 0.8083571
 [48,] 1.1781968
 [49,] 1.1068481
 [50,] 0.9922767
 [51,] 0.9111323
 [52,] 1.3047381
 [53,] 1.3851815
 [54,] 0.8282641
 [55,] 0.9726292
 [56,] 1.3568097
 [57,] 0.7908255
 [58,] 0.7571823
 [59,] 1.0772544
 [60,] 1.2179820
 [61,] 0.9792653
 [62,] 1.3281605
 [63,] 1.9308232
 [64,] 1.9970709
 [65,] 1.7872136
 [66,] 1.8001708
 [67,] 1.0790447
 [68,] 1.7208757
 [69,] 0.9312597
 [70,] 2.0542547
 [71,] 2.0751982
 [72,] 2.1461564
 [73,] 2.0794669
 [74,] 1.6135440
 [75,] 1.9319588
 [76,] 1.6835970
 [77,] 1.6995961
 [78,] 1.4929076
 [79,] 1.1533962
 [80,] 1.8132348
 [81,] 0.7725164
 [82,] 0.7101188
 [83,] 0.7703754
 [84,] 0.7597352
 [85,] 0.7271292
 [86,] 0.9648963
 [87,] 0.6910329
 [88,] 0.8025053
 [89,] 0.7986408
 [90,] 0.7466833
 [91,] 0.8120765
 [92,] 0.8270036
 [93,] 0.7556481
 [94,] 1.4680116
 [95,] 0.8885839
 [96,] 1.0398567
 [97,] 0.8403262
 [98,] 0.9149899
 [99,] 0.8245972
[100,] 0.8780466
[101,] 0.9446650
[102,] 1.0701835
[103,] 0.7438266
[104,] 0.7910138
[105,] 0.8926600
[106,] 0.9213682
[107,] 0.8718204
[108,] 0.8496518
[109,] 1.6189385
[110,] 1.4772235
[111,] 1.4080776
[112,] 1.4827277
[113,] 1.1056738
[114,] 2.0791589
[115,] 1.1640687
[116,] 1.5933211
[117,] 1.5589993
[118,] 1.3684031
[119,] 1.6624784
[120,] 1.6339925
[121,] 1.9582513
[122,] 1.6709787
[123,] 0.3010300
[124,] 0.3020485
[125,] 0.3004117
[126,] 0.2817086
[127,] 0.2932089
[128,] 0.2365907
[129,] 0.4226749
[130,] 0.3811903
[131,] 0.3422171
[132,] 0.5423089
[133,] 0.4326272
[134,] 0.2961452
[135,] 0.5185397
[136,] 0.5574486
[137,] 0.4246441
[138,] 0.6044336
[139,] 0.5362169
[140,] 0.7149184
[141,] 0.5851896
[142,] 0.5824012
[143,] 0.6044896
[144,] 0.6228854
[145,] 0.7880234
[146,] 0.5606723
[147,] 0.8271928
[148,] 1.0939221
[149,] 0.9434363
[150,] 0.6209407
[151,] 1.1320282
[152,] 0.8778344
[153,] 0.9816847
[154,] 0.8114285
[155,] 0.8640244
[156,] 0.7017111
[157,] 0.8876009
[158,] 1.0595341
[159,] 2.0280320
[160,] 1.1636495
[161,] 1.2971691
[162,] 0.9396694
[163,] 1.0987595
[164,] 1.3067846
[165,] 1.8484611
[166,] 0.9324321

$residuals
                [,1]
  [1,] -0.2393471181
  [2,] -0.0066431130
  [3,]  0.0468313623
  [4,]  0.0594194782
  [5,] -0.1977729088
  [6,] -0.0560229533
  [7,] -0.1659291556
  [8,]  0.1184401383
  [9,] -0.0231428847
 [10,]  0.0566721304
 [11,]  0.0096432850
 [12,] -0.0305556041
 [13,] -0.3765249717
 [14,]  0.0477130469
 [15,] -0.3188737587
 [16,] -0.2471351909
 [17,]  0.0617688063
 [18,]  0.4890053783
 [19,]  0.0389828750
 [20,]  0.1856977212
 [21,] -0.0278210746
 [22,]  0.0312703919
 [23,] -0.1329300077
 [24,] -0.2465218205
 [25,] -0.3857338941
 [26,] -0.2195207426
 [27,] -0.0706179201
 [28,]  0.1704491270
 [29,] -0.0489618304
 [30,] -0.3043208316
 [31,]  0.0561257790
 [32,] -0.0069565375
 [33,] -0.2375229666
 [34,]  0.2917685404
 [35,]  0.2678685684
 [36,]  0.0958151604
 [37,] -0.1106851189
 [38,] -0.0764882302
 [39,] -0.1791584710
 [40,] -0.1242287145
 [41,] -0.0906593384
 [42,]  0.3427064447
 [43,]  0.2972718487
 [44,]  0.4793611763
 [45,]  0.1337015130
 [46,]  0.0574990772
 [47,]  0.1916428869
 [48,]  0.4218031732
 [49,]  0.1931518856
 [50,] -0.0922767202
 [51,] -0.1111323320
 [52,] -0.2047380700
 [53,]  0.4148185076
 [54,]  0.2717359102
 [55,]  0.1273707634
 [56,]  0.4431902881
 [57,]  0.4091745018
 [58,]  0.6428177157
 [59,]  0.4227455994
 [60,]  0.6820180323
 [61,]  0.4207346985
 [62,] -0.2281605488
 [63,] -0.4308232211
 [64,] -0.2970709285
 [65,]  0.3127863609
 [66,] -0.4001707505
 [67,] -0.2790446648
 [68,]  0.5791243090
 [69,] -0.3312596990
 [70,]  0.6457453170
 [71,] -0.2751981804
 [72,] -0.2461564300
 [73,]  0.3205330860
 [74,] -0.0135440446
 [75,]  0.1680411980
 [76,]  0.3164030196
 [77,]  0.4004038881
 [78,] -0.0929075754
 [79,]  0.3466037893
 [80,] -0.2132348377
 [81,]  0.1274835507
 [82,] -0.2101187741
 [83,]  0.0296246029
 [84,]  0.1402647784
 [85,] -0.3271292299
 [86,] -0.4648962954
 [87,] -0.0910328856
 [88,] -0.0025052514
 [89,] -0.0986407764
 [90,] -0.3466832847
 [91,] -0.0120765225
 [92,] -0.2270035734
 [93,]  0.0443518627
 [94,] -0.2680116479
 [95,] -0.1885838810
 [96,]  0.0601432856
 [97,] -0.1403261946
 [98,] -0.0149898766
 [99,]  0.0754028096
[100,] -0.1780466379
[101,] -0.0446650497
[102,] -0.1701835321
[103,] -0.4438266258
[104,] -0.3910138189
[105,]  0.1073399860
[106,] -0.2213682406
[107,] -0.2718203581
[108,]  0.1503481838
[109,] -0.1189385012
[110,]  0.4227765302
[111,] -0.4080776170
[112,]  0.2172722879
[113,] -0.1056738225
[114,] -0.1791588827
[115,] -0.1640686944
[116,] -0.2933211437
[117,]  0.1410007279
[118,]  0.3315969343
[119,]  0.1375215571
[120,] -0.0339924604
[121,] -0.1582513498
[122,]  0.2290212923
[123,] -0.1010299601
[124,] -0.0020484534
[125,] -0.0004117494
[126,]  0.5182913598
[127,]  0.2067910863
[128,] -0.1365906943
[129,]  0.1773251036
[130,] -0.1811903213
[131,]  0.1577829449
[132,] -0.2423088759
[133,] -0.2326271703
[134,]  0.4038548313
[135,] -0.4185396938
[136,]  0.1425514024
[137,] -0.0246441342
[138,] -0.2044336486
[139,]  0.2637831238
[140,] -0.3149183503
[141,]  0.5148103825
[142,]  0.0175987531
[143,]  0.1955103586
[144,]  0.2771146215
[145,] -0.0880234143
[146,] -0.2606723456
[147,] -0.3271927952
[148,]  0.2060778852
[149,]  0.0565636563
[150,] -0.3209407062
[151,]  0.2679717833
[152,] -0.2778343860
[153,]  0.0183152714
[154,] -0.2114285040
[155,]  0.3359756276
[156,] -0.0017111492
[157,]  0.2123991107
[158,]  0.1404658865
[159,]  0.0719680346
[160,]  0.4363505261
[161,] -0.4971691168
[162,] -0.2396693854
[163,]  0.4012404813
[164,] -0.5067846120
[165,] -0.4484611436
[166,] -0.1324321313

$ssr
[1] 11.72535

$mse
[1] 0.07282824

$s2
[1] 0.07282824

$rmse
[1] 0.2698671

$s
[1] 0.2698671

$covb
              d0            d1            d2            d3            d4
d0  1.220130e-02 -1.863011e-03 -4.145993e-04 -9.987896e-04 -4.076565e-05
d1 -1.863011e-03  3.093463e-03 -3.144906e-04 -2.003628e-05 -1.242376e-06
d2 -4.145993e-04 -3.144906e-04  1.655336e-04 -2.744827e-05  5.420355e-07
d3 -9.987896e-04 -2.003628e-05 -2.744827e-05  1.970586e-04  9.029890e-07
d4 -4.076565e-05 -1.242376e-06  5.420355e-07  9.029890e-07  1.023474e-06

$r2
          [,1]
[1,] 0.7530833

$adjr2
          [,1]
[1,] 0.7469487

attr(,"class")
[1] "nlsystemfit.equation"


$resids
              [,1]          [,2]
  [1,] -0.54164797 -0.2393471181
  [2,] -0.54119150 -0.0066431130
  [3,]  2.76560339  0.0468313623
  [4,]  1.22492746  0.0594194782
  [5,]  0.71915007 -0.1977729088
  [6,]  0.83048143 -0.0560229533
  [7,] -1.30397901 -0.1659291556
  [8,]  0.20693830  0.1184401383
  [9,] -0.44899349 -0.0231428847
 [10,] -0.73816187  0.0566721304
 [11,]  0.30139171  0.0096432850
 [12,] -0.33285389 -0.0305556041
 [13,] -0.23143136 -0.3765249717
 [14,]  0.50064676  0.0477130469
 [15,] -0.50735358 -0.3188737587
 [16,] -0.66396888 -0.2471351909
 [17,]  0.31171203  0.0617688063
 [18,] -0.07163698  0.4890053783
 [19,] -0.11379098  0.0389828750
 [20,] -0.62009428  0.1856977212
 [21,]  1.05986853 -0.0278210746
 [22,]  0.61897528  0.0312703919
 [23,]  1.01356464 -0.1329300077
 [24,] -0.41101774 -0.2465218205
 [25,]  0.39602099 -0.3857338941
 [26,]  0.08899743 -0.2195207426
 [27,]  0.38357963 -0.0706179201
 [28,] -0.70607774  0.1704491270
 [29,] -0.80030312 -0.0489618304
 [30,] -0.37049201 -0.3043208316
 [31,]  0.84339310  0.0561257790
 [32,] -0.93373732 -0.0069565375
 [33,]  2.67423847 -0.2375229666
 [34,] -0.98647757  0.2917685404
 [35,] -0.41708519  0.2678685684
 [36,] -0.17174163  0.0958151604
 [37,]  0.07960322 -0.1106851189
 [38,]  0.55333893 -0.0764882302
 [39,] -0.15373389 -0.1791584710
 [40,]  0.25516592 -0.1242287145
 [41,]  0.32894867 -0.0906593384
 [42,]  0.96209256  0.3427064447
 [43,]  0.25885912  0.2972718487
 [44,] -2.10453999  0.4793611763
 [45,]  3.04785492  0.1337015130
 [46,] -2.69190306  0.0574990772
 [47,] -0.71881506  0.1916428869
 [48,]  1.37386937  0.4218031732
 [49,] -0.30480285  0.1931518856
 [50,]  1.23560147 -0.0922767202
 [51,]  1.39614898 -0.1111323320
 [52,]  1.60298197 -0.2047380700
 [53,] -1.50078164  0.4148185076
 [54,] -0.80922411  0.2717359102
 [55,] -1.11881506  0.1273707634
 [56,]  1.39308696  0.4431902881
 [57,]  0.14854580  0.4091745018
 [58,] -0.62450301  0.6428177157
 [59,] -1.33411231  0.4227455994
 [60,] -1.14506269  0.6820180323
 [61,] -1.65261378  0.4207346985
 [62,]  0.94096040 -0.2281605488
 [63,]  2.97845161 -0.4308232211
 [64,]  1.47734799 -0.2970709285
 [65,]  1.07339397  0.3127863609
 [66,]  0.53122198 -0.4001707505
 [67,] -1.84335685 -0.2790446648
 [68,]  1.61698513  0.5791243090
 [69,] -0.28168630 -0.3312596990
 [70,]  1.93983379  0.6457453170
 [71,]  1.99629322 -0.2751981804
 [72,]  1.32489629 -0.2461564300
 [73,] -1.47257354  0.3205330860
 [74,] -1.03523104 -0.0135440446
 [75,] -0.22111876  0.1680411980
 [76,] -0.58089369  0.3164030196
 [77,] -0.13395627  0.4004038881
 [78,]  0.08421721 -0.0929075754
 [79,] -1.06354034  0.3466037893
 [80,] -1.88511183 -0.2132348377
 [81,] -0.65832147  0.1274835507
 [82,] -0.76745321 -0.2101187741
 [83,] -0.82244069  0.0296246029
 [84,]  0.04845002  0.1402647784
 [85,]  1.22551945 -0.3271292299
 [86,]  0.24005109 -0.4648962954
 [87,] -0.43073444 -0.0910328856
 [88,] -0.41573621 -0.0025052514
 [89,]  0.17418642 -0.0986407764
 [90,]  0.13481964 -0.3466832847
 [91,] -0.42063962 -0.0120765225
 [92,]  0.11418709 -0.2270035734
 [93,] -0.90598070  0.0443518627
 [94,]  2.19019697 -0.2680116479
 [95,]  0.42722464 -0.1885838810
 [96,]  1.33422544  0.0601432856
 [97,]  0.44038677 -0.1403261946
 [98,]  0.53159172 -0.0149898766
 [99,]  0.43615026  0.0754028096
[100,]  0.26631542 -0.1780466379
[101,] -0.28663506 -0.0446650497
[102,] -0.05538669 -0.1701835321
[103,] -0.18049388 -0.4438266258
[104,] -0.21964591 -0.3910138189
[105,] -0.85865719  0.1073399860
[106,] -0.51830325 -0.2213682406
[107,] -0.55154998 -0.2718203581
[108,] -1.84103706  0.1503481838
[109,]  2.17418642 -0.1189385012
[110,]  2.55277437  0.4227765302
[111,]  0.58472318 -0.4080776170
[112,]  0.46542283  0.2172722879
[113,] -0.55437328 -0.1056738225
[114,]  1.57329579 -0.1791588827
[115,]  0.13159172 -0.1640686944
[116,]  1.35097887 -0.2933211437
[117,] -0.16367910  0.1410007279
[118,]  0.63468385  0.3315969343
[119,]  1.77423839  0.1375215571
[120,]  0.67689554 -0.0339924604
[121,]  1.77864215 -0.1582513498
[122,]  2.38954795  0.2290212923
[123,]  0.03880923 -0.1010299601
[124,] -0.08754732 -0.0020484534
[125,] -1.00244915 -0.0004117494
[126,] -2.16911485  0.5182913598
[127,] -1.62303591  0.2067910863
[128,] -0.62225618 -0.1365906943
[129,] -0.36387586  0.1773251036
[130,] -0.54903280 -0.1811903213
[131,] -1.10028735  0.1577829449
[132,]  3.76959378 -0.2423088759
[133,] -0.31783049 -0.2326271703
[134,] -1.59904391  0.4038548313
[135,]  1.52818985 -0.4185396938
[136,]  1.83778289  0.1425514024
[137,]  0.05387606 -0.0246441342
[138,] -0.92360083 -0.2044336486
[139,] -1.33364825  0.2637831238
[140,]  1.64762027 -0.3149183503
[141,] -0.69182624  0.5148103825
[142,] -0.21116697  0.0175987531
[143,] -0.23364825  0.1955103586
[144,] -0.05423487  0.2771146215
[145,]  0.84598976 -0.0880234143
[146,] -3.45548526 -0.2606723456
[147,] -0.87664233 -0.3271927952
[148,]  0.69437855  0.2060778852
[149,] -0.17443877  0.0565636563
[150,] -2.66807681 -0.3209407062
[151,]  0.06714464  0.2679717833
[152,] -1.09442099 -0.2778343860
[153,] -0.76378092  0.0183152714
[154,] -1.03075987 -0.2114285040
[155,] -1.49998738  0.3359756276
[156,] -3.03298731 -0.0017111492
[157,] -1.74790763  0.2123991107
[158,] -1.81667619  0.1404658865
[159,]  3.23433468  0.0719680346
[160,] -0.21162528  0.4363505261
[161,]  0.59914299 -0.4971691168
[162,] -1.35670858 -0.2396693854
[163,] -1.11387643  0.4012404813
[164,]  0.05102376 -0.5067846120
[165,]  1.08214719 -0.4484611436
[166,] -2.70891782 -0.1324321313

$method
[1] "OLS"

$n
[1] 332

$k
[1] 10

$b
           h0            h1            h2            h3            h4 
-0.5125587078  0.4207532666 -0.0001122495  0.0001536430  0.0845993400 
           d0            d1            d2            d3            d4 
-0.2660689962  0.1704038812  0.1248531830  0.0198706561 -0.0149527507 

$se
          h0           h1           h2           h3           h4           d0 
4.702938e-01 2.081047e-01 3.007921e-04 2.226427e-05 1.464941e-02 1.104595e-01 
          d1           d2           d3           d4 
5.561891e-02 1.286599e-02 1.403776e-02 1.011669e-03 

$t
         h0          h1          h2          h3          h4          d0 
 -1.0898692   2.0218348  -0.3731798   6.9008803   5.7749311  -2.4087469 
         d1          d2          d3          d4 
  3.0637761   9.7041271   1.4155150 -14.7802789 

$p
          h0           h1           h2           h3           h4           d0 
2.765857e-01 4.402012e-02 7.092602e-01 2.752776e-11 1.813498e-08 1.656864e-02 
          d1           d2           d3           d4 
2.370196e-03 0.000000e+00 1.578840e-01 0.000000e+00 

$solvtol
[1] 2.220446e-16

$covb
              h0            h1            h2            h3            h4
h0  2.211762e-01 -9.443516e-02  1.252400e-04  1.618822e-06 -3.269671e-04
h1 -9.443516e-02  4.330755e-02 -5.967376e-05 -1.494795e-06 -4.646789e-04
h2  1.252400e-04 -5.967376e-05  9.047591e-08  2.264834e-09  8.336480e-07
h3  1.618822e-06 -1.494795e-06  2.264834e-09  4.956976e-10  3.638582e-08
h4 -3.269671e-04 -4.646789e-04  8.336480e-07  3.638582e-08  2.146052e-04
d0  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d1  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d2  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d3  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
              d0            d1            d2            d3            d4
h0  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h1  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h2  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h3  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d0  1.220130e-02 -1.863011e-03 -4.145993e-04 -9.987896e-04 -4.076565e-05
d1 -1.863011e-03  3.093463e-03 -3.144906e-04 -2.003628e-05 -1.242376e-06
d2 -4.145993e-04 -3.144906e-04  1.655336e-04 -2.744827e-05  5.420355e-07
d3 -9.987896e-04 -2.003628e-05 -2.744827e-05  1.970586e-04  9.029890e-07
d4 -4.076565e-05 -1.242376e-06  5.420355e-07  9.029890e-07  1.023474e-06

$rcov
            [,1]        [,2]
[1,]  1.61134330 -0.05189704
[2,] -0.05189704  0.07282824

$rcor
           [,1]       [,2]
[1,]  1.0000000 -0.1515004
[2,] -0.1515004  1.0000000

$drcov
[1] 0.114658

$g
[1] 2

$nlmest
$nlmest$minimum
[1] 271.1516

$nlmest$estimate
 [1] -0.5125587078  0.4207532666 -0.0001122495  0.0001536430  0.0845993400
 [6] -0.2660689962  0.1704038812  0.1248531830  0.0198706561 -0.0149527507

$nlmest$gradient
 [1]  2.845601e-06  1.420859e-06  1.768007e-03  3.897520e-02  4.394103e-05
 [6] -7.489638e-06 -6.064031e-06 -3.041389e-05  1.567711e-05 -3.166653e-04

$nlmest$code
[1] 1

$nlmest$iterations
[1] 104


attr(,"class")
[1] "nlsystemfit.system"
Warning messages:
1: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
2: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
$eq
$eq[[1]]
$method
[1] "SUR"

$i
[1] 1

$eqnlabel
[1] "height.growth"

$formula
hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

$b
           h0            h1            h2            h3            h4 
-4.715774e-01  3.858819e-01 -5.628742e-05  1.637233e-04  8.579685e-02 

$se
               h0
[1,] 0.4625613594
[2,] 0.2041058227
[3,] 0.0002941711
[4,] 0.0000220272
[5,] 0.0147202403

$t
             h0
[1,] -1.0194916
[2,]  1.8905972
[3,] -0.1913424
[4,]  7.4327811
[5,]  5.8284954

$p
               h0
[1,] 3.094991e-01
[2,] 6.047476e-02
[3,] 8.484984e-01
[4,] 5.927259e-12
[5,] 2.966778e-08

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
           [,1]
  [1,] 4.073965
  [2,] 4.550076
  [3,] 5.951350
  [4,] 5.888354
  [5,] 5.385318
  [6,] 4.887930
  [7,] 5.408229
  [8,] 4.600018
  [9,] 4.366011
 [10,] 5.442177
 [11,] 3.724646
 [12,] 2.885204
 [13,] 3.850419
 [14,] 5.300711
 [15,] 5.117431
 [16,] 4.786811
 [17,] 4.789310
 [18,] 7.332698
 [19,] 3.739006
 [20,] 4.338449
 [21,] 3.457673
 [22,] 6.703092
 [23,] 6.303480
 [24,] 5.209984
 [25,] 5.408229
 [26,] 5.218360
 [27,] 6.334692
 [28,] 6.935730
 [29,] 7.601845
 [30,] 4.985053
 [31,] 3.496135
 [32,] 5.143062
 [33,] 6.160736
 [34,] 4.093227
 [35,] 3.836817
 [36,] 5.475633
 [37,] 6.641471
 [38,] 6.184311
 [39,] 5.919754
 [40,] 6.297497
 [41,] 5.676721
 [42,] 5.289744
 [43,] 4.571145
 [44,] 6.378662
 [45,] 6.109418
 [46,] 5.440155
 [47,] 5.466572
 [48,] 5.984781
 [49,] 6.567803
 [50,] 5.218345
 [51,] 4.652539
 [52,] 6.354929
 [53,] 7.588165
 [54,] 4.715911
 [55,] 5.466572
 [56,] 5.444440
 [57,] 3.598131
 [58,] 3.858752
 [59,] 6.212337
 [60,] 6.715138
 [61,] 5.717208
 [62,] 5.704536
 [63,] 5.157466
 [64,] 6.279838
 [65,] 6.079226
 [66,] 6.427898
 [67,] 5.278921
 [68,] 5.522630
 [69,] 4.153045
 [70,] 6.317654
 [71,] 6.463614
 [72,] 6.236082
 [73,] 7.576619
 [74,] 6.292505
 [75,] 6.689392
 [76,] 6.160620
 [77,] 6.018292
 [78,] 5.053013
 [79,] 4.691355
 [80,] 7.480754
 [81,] 4.213693
 [82,] 4.034690
 [83,] 4.160139
 [84,] 3.716088
 [85,] 2.932312
 [86,] 4.486987
 [87,] 3.582389
 [88,] 4.173669
 [89,] 3.973569
 [90,] 3.504173
 [91,] 4.366828
 [92,] 4.030283
 [93,] 3.938901
 [94,] 4.451419
 [95,] 3.434415
 [96,] 3.635993
 [97,] 3.216081
 [98,] 3.337044
 [99,] 3.261977
[100,] 3.326887
[101,] 3.729450
[102,] 4.096274
[103,] 2.956078
[104,] 3.085466
[105,] 3.893398
[106,] 3.759481
[107,] 3.716088
[108,] 4.291604
[109,] 3.973569
[110,] 3.410553
[111,] 3.947863
[112,] 4.474993
[113,] 3.698915
[114,] 4.963634
[115,] 3.337044
[116,] 3.884156
[117,] 4.589959
[118,] 3.614910
[119,] 3.879342
[120,] 4.250404
[121,] 4.547764
[122,] 3.469636
[123,] 4.545673
[124,] 4.576646
[125,] 5.122533
[126,] 5.602653
[127,] 5.421228
[128,] 3.984118
[129,] 5.352412
[130,] 4.935674
[131,] 4.591815
[132,] 4.102504
[133,] 5.300159
[134,] 4.981387
[135,] 5.216259
[136,] 5.202773
[137,] 5.051408
[138,] 4.906441
[139,] 4.513841
[140,] 4.107376
[141,] 4.581725
[142,] 4.377494
[143,] 4.513841
[144,] 4.424596
[145,] 4.941441
[146,] 3.717260
[147,] 4.040283
[148,] 4.371486
[149,] 4.152543
[150,] 3.923752
[151,] 4.631256
[152,] 4.359388
[153,] 4.729926
[154,] 4.085544
[155,] 4.475590
[156,] 4.401257
[157,] 3.701774
[158,] 4.383475
[159,] 4.550895
[160,] 3.972761
[161,] 3.961301
[162,] 3.815015
[163,] 4.369797
[164,] 4.418801
[165,] 5.415114
[166,] 4.567246

$residuals
               [,1]
  [1,] -0.573964520
  [2,] -0.550075608
  [3,]  2.748650175
  [4,]  1.211646123
  [5,]  0.714682136
  [6,]  0.812070203
  [7,] -1.308229266
  [8,]  0.199982229
  [9,] -0.466011426
 [10,] -0.742177382
 [11,]  0.275354355
 [12,] -0.385203859
 [13,] -0.250418794
 [14,]  0.499288710
 [15,] -0.517431118
 [16,] -0.686810689
 [17,]  0.310689763
 [18,] -0.132697694
 [19,] -0.139005831
 [20,] -0.638448813
 [21,]  1.042326850
 [22,]  0.596908070
 [23,]  0.996519991
 [24,] -0.409984447
 [25,]  0.391770734
 [26,]  0.081639596
 [27,]  0.365307634
 [28,] -0.735729938
 [29,] -0.901845288
 [30,] -0.385053316
 [31,]  0.803865012
 [32,] -0.943062425
 [33,]  2.639264437
 [34,] -0.993226784
 [35,] -0.436816594
 [36,] -0.175632634
 [37,]  0.058528850
 [38,]  0.515689471
 [39,] -0.219753700
 [40,]  0.202503093
 [41,]  0.323279304
 [42,]  0.910255652
 [43,]  0.228855240
 [44,] -2.178661776
 [45,]  2.990582239
 [46,] -2.740154630
 [47,] -0.766571910
 [48,]  1.315219383
 [49,] -0.367802974
 [50,]  1.181655118
 [51,]  1.347461370
 [52,]  1.545071219
 [53,] -1.588164969
 [54,] -0.915911159
 [55,] -1.166571910
 [56,]  1.355559879
 [57,]  0.101869371
 [58,] -0.658752323
 [59,] -1.412337002
 [60,] -1.215137529
 [61,] -1.717207735
 [62,]  0.895463554
 [63,]  2.942534224
 [64,]  1.420161599
 [65,]  1.020773629
 [66,]  0.472101710
 [67,] -1.878921151
 [68,]  1.577370165
 [69,] -0.353045380
 [70,]  1.882345768
 [71,]  1.936385811
 [72,]  1.263917761
 [73,] -1.576619467
 [74,] -1.092504532
 [75,] -0.289391729
 [76,] -0.660620425
 [77,] -0.218292447
 [78,]  0.046987087
 [79,] -1.091354779
 [80,] -1.980754068
 [81,] -0.613692717
 [82,] -0.734689642
 [83,] -0.760138596
 [84,]  0.083912237
 [85,]  1.267687943
 [86,]  0.313012577
 [87,] -0.382389465
 [88,] -0.373668647
 [89,]  0.226431048
 [90,]  0.195826511
 [91,] -0.366827939
 [92,]  0.169717330
 [93,] -0.838900993
 [94,]  2.248580623
 [95,]  0.465584915
 [96,]  1.364007061
 [97,]  0.483918831
 [98,]  0.562956014
 [99,]  0.438022822
[100,]  0.273112775
[101,] -0.229449619
[102,]  0.003725964
[103,] -0.156077810
[104,] -0.185465699
[105,] -0.793397665
[106,] -0.459481074
[107,] -0.516087763
[108,] -1.791604452
[109,]  2.226431048
[110,]  2.589446534
[111,]  0.652136703
[112,]  0.525006546
[113,] -0.498915475
[114,]  1.636365558
[115,]  0.162956014
[116,]  1.415844139
[117,] -0.089958613
[118,]  0.685090016
[119,]  1.820658024
[120,]  0.749595772
[121,]  1.852236368
[122,]  2.430364345
[123,]  0.054326520
[124,] -0.076645595
[125,] -1.022533241
[126,] -2.202652877
[127,] -1.621227899
[128,] -0.584117925
[129,] -0.352412387
[130,] -0.535674067
[131,] -1.091815139
[132,]  3.797496299
[133,] -0.300158936
[134,] -1.581387205
[135,]  1.483740595
[136,]  1.797226866
[137,]  0.048591866
[138,] -0.906440601
[139,] -1.313841465
[140,]  1.692624500
[141,] -0.681725356
[142,] -0.177494014
[143,] -0.213841465
[144,] -0.024595676
[145,]  0.858558615
[146,] -3.417260330
[147,] -0.840282784
[148,]  0.728514141
[149,] -0.152543454
[150,] -2.623752093
[151,]  0.068743551
[152,] -1.059387907
[153,] -0.729926416
[154,] -0.985544338
[155,] -1.475590485
[156,] -3.001257378
[157,] -1.701773635
[158,] -1.783475122
[159,]  3.249105309
[160,] -0.172761174
[161,]  0.638698669
[162,] -1.315015259
[163,] -1.069797461
[164,]  0.081199458
[165,]  1.084886269
[166,] -2.667245917

$ssr
[1] 259.7675

$mse
[1] 1.613463

$s2
[1] 1.613463

$rmse
[1] 1.270221

$s
[1] 1.270221

$covb
              h0            h1            h2            h3            h4
h0  2.139630e-01 -9.097014e-02  1.198172e-04  1.465294e-06 -3.664185e-04
h1 -9.097014e-02  4.165919e-02 -5.713139e-05 -1.417350e-06 -4.482972e-04
h2  1.198172e-04 -5.713139e-05  8.653665e-08  2.183748e-09  8.009434e-07
h3  1.465294e-06 -1.417350e-06  2.183748e-09  4.851974e-10  3.384438e-08
h4 -3.664185e-04 -4.482972e-04  8.009434e-07  3.384438e-08  2.166855e-04

$r2
          [,1]
[1,] 0.4045201

$adjr2
          [,1]
[1,] 0.3897255

attr(,"class")
[1] "nlsystemfit.equation"

$eq[[2]]
$method
[1] "SUR"

$i
[1] 2

$eqnlabel
[1] "diameter.growth"

$formula
dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

$b
        d0         d1         d2         d3         d4 
-0.3029064  0.1319401  0.1434493  0.0173655 -0.0149856 

$se
               d0
[1,] 0.1117442951
[2,] 0.0557143801
[3,] 0.0126573338
[4,] 0.0141514040
[5,] 0.0009995978

$t
             d0
[1,]  -2.710711
[2,]   2.368151
[3,]  11.333291
[4,]   1.227122
[5,] -14.991626

$p
             d0
[1,] 0.00744222
[2,] 0.01906404
[3,] 0.00000000
[4,] 0.22156795
[5,] 0.00000000

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
            [,1]
  [1,] 0.4382831
  [2,] 0.5009979
  [3,] 1.1021509
  [4,] 0.8588553
  [5,] 0.7095653
  [6,] 0.6639254
  [7,] 0.5494639
  [8,] 0.5787108
  [9,] 0.5190883
 [10,] 0.6337137
 [11,] 0.4950503
 [12,] 0.3393965
 [13,] 0.4752275
 [14,] 0.7516114
 [15,] 0.6121111
 [16,] 0.5435542
 [17,] 0.6404493
 [18,] 1.0148581
 [19,] 0.4632082
 [20,] 0.5075129
 [21,] 0.5354320
 [22,] 1.1891768
 [23,] 1.1585779
 [24,] 0.7432722
 [25,] 0.8908854
 [26,] 0.8194782
 [27,] 1.0782340
 [28,] 1.0239124
 [29,] 1.1410927
 [30,] 0.9060329
 [31,] 0.7649848
 [32,] 0.8912436
 [33,] 1.9093136
 [34,] 0.7930726
 [35,] 0.8226347
 [36,] 1.2782759
 [37,] 1.5353665
 [38,] 1.5806267
 [39,] 1.3573332
 [40,] 1.5255636
 [41,] 1.3881409
 [42,] 0.2649352
 [43,] 0.2055080
 [44,] 0.2150542
 [45,] 1.5821365
 [46,] 0.6178788
 [47,] 0.8104994
 [48,] 1.2277675
 [49,] 1.1111254
 [50,] 1.0285435
 [51,] 0.9430798
 [52,] 1.3665018
 [53,] 1.3827834
 [54,] 0.8344773
 [55,] 0.9654734
 [56,] 1.4015473
 [57,] 0.7950407
 [58,] 0.7509536
 [59,] 1.0739236
 [60,] 1.2203398
 [61,] 0.9589414
 [62,] 1.3684480
 [63,] 2.0417782
 [64,] 2.0651242
 [65,] 1.8389230
 [66,] 1.8356483
 [67,] 1.0443913
 [68,] 1.7823154
 [69,] 0.9494233
 [70,] 2.1607135
 [71,] 2.1982203
 [72,] 2.2253887
 [73,] 2.0325334
 [74,] 1.6055439
 [75,] 1.9523718
 [76,] 1.6860399
 [77,] 1.7224353
 [78,] 1.4987889
 [79,] 1.1419471
 [80,] 1.7857142
 [81,] 0.7520588
 [82,] 0.6947628
 [83,] 0.7419856
 [84,] 0.7479024
 [85,] 0.7322186
 [86,] 0.9430718
 [87,] 0.6744095
 [88,] 0.7818466
 [89,] 0.7920719
 [90,] 0.7315877
 [91,] 0.7964738
 [92,] 0.8137659
 [93,] 0.7193666
 [94,] 1.5021890
 [95,] 0.8898250
 [96,] 1.0601699
 [97,] 0.8425679
 [98,] 0.9102313
 [99,] 0.8390409
[100,] 0.8767396
[101,] 0.9216593
[102,] 1.0460932
[103,] 0.7398008
[104,] 0.7795234
[105,] 0.8657716
[106,] 0.8955928
[107,] 0.8557590
[108,] 0.8134474
[109,] 1.6598755
[110,] 1.5287922
[111,] 1.3797062
[112,] 1.4689381
[113,] 1.0716329
[114,] 2.1099159
[115,] 1.1578694
[116,] 1.6061301
[117,] 1.5242830
[118,] 1.3623658
[119,] 1.6945500
[120,] 1.6149605
[121,] 1.9876323
[122,] 1.7138487
[123,] 0.2951857
[124,] 0.2945775
[125,] 0.2884737
[126,] 0.2661522
[127,] 0.2797118
[128,] 0.2311309
[129,] 0.4157046
[130,] 0.3723899
[131,] 0.3277832
[132,] 0.5740213
[133,] 0.4232634
[134,] 0.2940170
[135,] 0.5262574
[136,] 0.5644466
[137,] 0.4183304
[138,] 0.5856230
[139,] 0.5131413
[140,] 0.7240640
[141,] 0.5673440
[142,] 0.5732380
[143,] 0.5927669
[144,] 0.6095313
[145,] 0.7823039
[146,] 0.5195237
[147,] 0.8056641
[148,] 1.0911266
[149,] 0.9223640
[150,] 0.5891870
[151,] 1.0996719
[152,] 0.8458756
[153,] 0.9549614
[154,] 0.7884829
[155,] 0.8239099
[156,] 0.6507366
[157,] 0.8452675
[158,] 0.9990409
[159,] 2.1063920
[160,] 1.1340198
[161,] 1.2805577
[162,] 0.9061100
[163,] 1.0638689
[164,] 1.2844316
[165,] 1.8521367
[166,] 0.8775092

$residuals
                [,1]
  [1,] -0.2382830843
  [2,] -0.0009979222
  [3,] -0.0021508753
  [4,]  0.0411446585
  [5,] -0.2095652541
  [6,] -0.0639254299
  [7,] -0.1494639214
  [8,]  0.1212891644
  [9,] -0.0190883342
 [10,]  0.0662862541
 [11,]  0.0049497280
 [12,] -0.0393964675
 [13,] -0.3752275068
 [14,]  0.0483886305
 [15,] -0.3121110803
 [16,] -0.2435541993
 [17,]  0.0595506969
 [18,]  0.4851418744
 [19,]  0.0367917710
 [20,]  0.1924871283
 [21,] -0.0354320325
 [22,]  0.0108232271
 [23,] -0.1585778670
 [24,] -0.2432722440
 [25,] -0.3908853989
 [26,] -0.2194781518
 [27,] -0.0782340063
 [28,]  0.1760876277
 [29,] -0.0410927177
 [30,] -0.3060329152
 [31,]  0.0350152046
 [32,]  0.0087563916
 [33,] -0.3093136125
 [34,]  0.3069273881
 [35,]  0.2773653471
 [36,]  0.1217241320
 [37,] -0.1353664647
 [38,] -0.0806267284
 [39,] -0.1573332010
 [40,] -0.1255636378
 [41,] -0.0881409118
 [42,]  0.3350647896
 [43,]  0.2944919628
 [44,]  0.4849458350
 [45,]  0.0178634829
 [46,]  0.0821211679
 [47,]  0.1895006217
 [48,]  0.3722325263
 [49,]  0.1888746258
 [50,] -0.1285434797
 [51,] -0.1430798488
 [52,] -0.2665017639
 [53,]  0.4172166189
 [54,]  0.2655227132
 [55,]  0.1345266119
 [56,]  0.3984526826
 [57,]  0.4049592650
 [58,]  0.6490464151
 [59,]  0.4260763600
 [60,]  0.6796602241
 [61,]  0.4410585650
 [62,] -0.2684480327
 [63,] -0.5417781608
 [64,] -0.3651242144
 [65,]  0.2610769732
 [66,] -0.4356483379
 [67,] -0.2443912824
 [68,]  0.5176845929
 [69,] -0.3494233308
 [70,]  0.5392864905
 [71,] -0.3982202554
 [72,] -0.3253886975
 [73,]  0.3674666417
 [74,] -0.0055438510
 [75,]  0.1476282464
 [76,]  0.3139600752
 [77,]  0.3775647065
 [78,] -0.0987889033
 [79,]  0.3580528701
 [80,] -0.1857141861
 [81,]  0.1479412228
 [82,] -0.1947627969
 [83,]  0.0580143786
 [84,]  0.1520976040
 [85,] -0.3322186433
 [86,] -0.4430717702
 [87,] -0.0744094555
 [88,]  0.0181533840
 [89,] -0.0920719102
 [90,] -0.3315877256
 [91,]  0.0035262416
 [92,] -0.2137659338
 [93,]  0.0806333573
 [94,] -0.3021890337
 [95,] -0.1898249859
 [96,]  0.0398300761
 [97,] -0.1425678776
 [98,] -0.0102312922
 [99,]  0.0609590648
[100,] -0.1767395922
[101,] -0.0216593339
[102,] -0.1460932115
[103,] -0.4398007956
[104,] -0.3795233747
[105,]  0.1342283548
[106,] -0.1955927763
[107,] -0.2557589727
[108,]  0.1865525989
[109,] -0.1598755055
[110,]  0.3712077734
[111,] -0.3797062453
[112,]  0.2310619227
[113,] -0.0716329311
[114,] -0.2099159228
[115,] -0.1578693836
[116,] -0.3061301168
[117,]  0.1757169582
[118,]  0.3376341852
[119,]  0.1054500063
[120,] -0.0149604898
[121,] -0.1876322531
[122,]  0.1861512699
[123,] -0.0951857224
[124,]  0.0054224906
[125,]  0.0115262711
[126,]  0.5338478149
[127,]  0.2202881501
[128,] -0.1311308741
[129,]  0.1842954080
[130,] -0.1723899129
[131,]  0.1722168166
[132,] -0.2740212798
[133,] -0.2232633996
[134,]  0.4059829583
[135,] -0.4262573771
[136,]  0.1355534073
[137,] -0.0183304208
[138,] -0.1856229601
[139,]  0.2868586908
[140,] -0.3240640175
[141,]  0.5326560464
[142,]  0.0267619974
[143,]  0.2072330953
[144,]  0.2904686606
[145,] -0.0823038647
[146,] -0.2195237212
[147,] -0.3056640648
[148,]  0.2088734468
[149,]  0.0776360103
[150,] -0.2891869764
[151,]  0.3003281285
[152,] -0.2458756359
[153,]  0.0450385838
[154,] -0.1884828677
[155,]  0.3760900823
[156,]  0.0492633557
[157,]  0.2547324884
[158,]  0.2009591041
[159,] -0.0063920272
[160,]  0.4659802063
[161,] -0.4805577208
[162,] -0.2061100281
[163,]  0.4361310867
[164,] -0.4844315950
[165,] -0.4521367404
[166,] -0.0775092082

$ssr
[1] 11.88504

$mse
[1] 0.07382011

$s2
[1] 0.07382011

$rmse
[1] 0.2716986

$s
[1] 0.2716986

$covb
              d0            d1            d2            d3            d4
d0  1.248679e-02 -1.880909e-03 -4.340259e-04 -1.028607e-03 -3.922872e-05
d1 -1.880909e-03  3.104092e-03 -3.028016e-04 -2.746389e-05 -9.581141e-07
d2 -4.340259e-04 -3.028016e-04  1.602081e-04 -2.333799e-05  4.391506e-07
d3 -1.028607e-03 -2.746389e-05 -2.333799e-05  2.002622e-04  8.819879e-07
d4 -3.922872e-05 -9.581141e-07  4.391506e-07  8.819879e-07  9.991958e-07

$r2
          [,1]
[1,] 0.7497204

$adjr2
          [,1]
[1,] 0.7435023

attr(,"class")
[1] "nlsystemfit.equation"


$resids
               [,1]          [,2]
  [1,] -0.573964520 -0.2382830843
  [2,] -0.550075608 -0.0009979222
  [3,]  2.748650175 -0.0021508753
  [4,]  1.211646123  0.0411446585
  [5,]  0.714682136 -0.2095652541
  [6,]  0.812070203 -0.0639254299
  [7,] -1.308229266 -0.1494639214
  [8,]  0.199982229  0.1212891644
  [9,] -0.466011426 -0.0190883342
 [10,] -0.742177382  0.0662862541
 [11,]  0.275354355  0.0049497280
 [12,] -0.385203859 -0.0393964675
 [13,] -0.250418794 -0.3752275068
 [14,]  0.499288710  0.0483886305
 [15,] -0.517431118 -0.3121110803
 [16,] -0.686810689 -0.2435541993
 [17,]  0.310689763  0.0595506969
 [18,] -0.132697694  0.4851418744
 [19,] -0.139005831  0.0367917710
 [20,] -0.638448813  0.1924871283
 [21,]  1.042326850 -0.0354320325
 [22,]  0.596908070  0.0108232271
 [23,]  0.996519991 -0.1585778670
 [24,] -0.409984447 -0.2432722440
 [25,]  0.391770734 -0.3908853989
 [26,]  0.081639596 -0.2194781518
 [27,]  0.365307634 -0.0782340063
 [28,] -0.735729938  0.1760876277
 [29,] -0.901845288 -0.0410927177
 [30,] -0.385053316 -0.3060329152
 [31,]  0.803865012  0.0350152046
 [32,] -0.943062425  0.0087563916
 [33,]  2.639264437 -0.3093136125
 [34,] -0.993226784  0.3069273881
 [35,] -0.436816594  0.2773653471
 [36,] -0.175632634  0.1217241320
 [37,]  0.058528850 -0.1353664647
 [38,]  0.515689471 -0.0806267284
 [39,] -0.219753700 -0.1573332010
 [40,]  0.202503093 -0.1255636378
 [41,]  0.323279304 -0.0881409118
 [42,]  0.910255652  0.3350647896
 [43,]  0.228855240  0.2944919628
 [44,] -2.178661776  0.4849458350
 [45,]  2.990582239  0.0178634829
 [46,] -2.740154630  0.0821211679
 [47,] -0.766571910  0.1895006217
 [48,]  1.315219383  0.3722325263
 [49,] -0.367802974  0.1888746258
 [50,]  1.181655118 -0.1285434797
 [51,]  1.347461370 -0.1430798488
 [52,]  1.545071219 -0.2665017639
 [53,] -1.588164969  0.4172166189
 [54,] -0.915911159  0.2655227132
 [55,] -1.166571910  0.1345266119
 [56,]  1.355559879  0.3984526826
 [57,]  0.101869371  0.4049592650
 [58,] -0.658752323  0.6490464151
 [59,] -1.412337002  0.4260763600
 [60,] -1.215137529  0.6796602241
 [61,] -1.717207735  0.4410585650
 [62,]  0.895463554 -0.2684480327
 [63,]  2.942534224 -0.5417781608
 [64,]  1.420161599 -0.3651242144
 [65,]  1.020773629  0.2610769732
 [66,]  0.472101710 -0.4356483379
 [67,] -1.878921151 -0.2443912824
 [68,]  1.577370165  0.5176845929
 [69,] -0.353045380 -0.3494233308
 [70,]  1.882345768  0.5392864905
 [71,]  1.936385811 -0.3982202554
 [72,]  1.263917761 -0.3253886975
 [73,] -1.576619467  0.3674666417
 [74,] -1.092504532 -0.0055438510
 [75,] -0.289391729  0.1476282464
 [76,] -0.660620425  0.3139600752
 [77,] -0.218292447  0.3775647065
 [78,]  0.046987087 -0.0987889033
 [79,] -1.091354779  0.3580528701
 [80,] -1.980754068 -0.1857141861
 [81,] -0.613692717  0.1479412228
 [82,] -0.734689642 -0.1947627969
 [83,] -0.760138596  0.0580143786
 [84,]  0.083912237  0.1520976040
 [85,]  1.267687943 -0.3322186433
 [86,]  0.313012577 -0.4430717702
 [87,] -0.382389465 -0.0744094555
 [88,] -0.373668647  0.0181533840
 [89,]  0.226431048 -0.0920719102
 [90,]  0.195826511 -0.3315877256
 [91,] -0.366827939  0.0035262416
 [92,]  0.169717330 -0.2137659338
 [93,] -0.838900993  0.0806333573
 [94,]  2.248580623 -0.3021890337
 [95,]  0.465584915 -0.1898249859
 [96,]  1.364007061  0.0398300761
 [97,]  0.483918831 -0.1425678776
 [98,]  0.562956014 -0.0102312922
 [99,]  0.438022822  0.0609590648
[100,]  0.273112775 -0.1767395922
[101,] -0.229449619 -0.0216593339
[102,]  0.003725964 -0.1460932115
[103,] -0.156077810 -0.4398007956
[104,] -0.185465699 -0.3795233747
[105,] -0.793397665  0.1342283548
[106,] -0.459481074 -0.1955927763
[107,] -0.516087763 -0.2557589727
[108,] -1.791604452  0.1865525989
[109,]  2.226431048 -0.1598755055
[110,]  2.589446534  0.3712077734
[111,]  0.652136703 -0.3797062453
[112,]  0.525006546  0.2310619227
[113,] -0.498915475 -0.0716329311
[114,]  1.636365558 -0.2099159228
[115,]  0.162956014 -0.1578693836
[116,]  1.415844139 -0.3061301168
[117,] -0.089958613  0.1757169582
[118,]  0.685090016  0.3376341852
[119,]  1.820658024  0.1054500063
[120,]  0.749595772 -0.0149604898
[121,]  1.852236368 -0.1876322531
[122,]  2.430364345  0.1861512699
[123,]  0.054326520 -0.0951857224
[124,] -0.076645595  0.0054224906
[125,] -1.022533241  0.0115262711
[126,] -2.202652877  0.5338478149
[127,] -1.621227899  0.2202881501
[128,] -0.584117925 -0.1311308741
[129,] -0.352412387  0.1842954080
[130,] -0.535674067 -0.1723899129
[131,] -1.091815139  0.1722168166
[132,]  3.797496299 -0.2740212798
[133,] -0.300158936 -0.2232633996
[134,] -1.581387205  0.4059829583
[135,]  1.483740595 -0.4262573771
[136,]  1.797226866  0.1355534073
[137,]  0.048591866 -0.0183304208
[138,] -0.906440601 -0.1856229601
[139,] -1.313841465  0.2868586908
[140,]  1.692624500 -0.3240640175
[141,] -0.681725356  0.5326560464
[142,] -0.177494014  0.0267619974
[143,] -0.213841465  0.2072330953
[144,] -0.024595676  0.2904686606
[145,]  0.858558615 -0.0823038647
[146,] -3.417260330 -0.2195237212
[147,] -0.840282784 -0.3056640648
[148,]  0.728514141  0.2088734468
[149,] -0.152543454  0.0776360103
[150,] -2.623752093 -0.2891869764
[151,]  0.068743551  0.3003281285
[152,] -1.059387907 -0.2458756359
[153,] -0.729926416  0.0450385838
[154,] -0.985544338 -0.1884828677
[155,] -1.475590485  0.3760900823
[156,] -3.001257378  0.0492633557
[157,] -1.701773635  0.2547324884
[158,] -1.783475122  0.2009591041
[159,]  3.249105309 -0.0063920272
[160,] -0.172761174  0.4659802063
[161,]  0.638698669 -0.4805577208
[162,] -1.315015259 -0.2061100281
[163,] -1.069797461  0.4361310867
[164,]  0.081199458 -0.4844315950
[165,]  1.084886269 -0.4521367404
[166,] -2.667245917 -0.0775092082

$method
[1] "SUR"

$n
[1] 332

$k
[1] 10

$b
           h0            h1            h2            h3            h4 
-4.715774e-01  3.858819e-01 -5.628742e-05  1.637233e-04  8.579685e-02 
           d0            d1            d2            d3            d4 
-3.029064e-01  1.319401e-01  1.434493e-01  1.736550e-02 -1.498560e-02 

$se
          h0           h1           h2           h3           h4           d0 
0.4625613594 0.2041058227 0.0002941711 0.0000220272 0.0147202403 0.1117442951 
          d1           d2           d3           d4 
0.0557143801 0.0126573338 0.0141514040 0.0009995978 

$t
         h0          h1          h2          h3          h4          d0 
 -1.0194916   1.8905972  -0.1913424   7.4327811   5.8284954  -2.7107106 
         d1          d2          d3          d4 
  2.3681512  11.3332913   1.2271224 -14.9916258 

$p
          h0           h1           h2           h3           h4           d0 
3.087350e-01 5.957581e-02 8.483779e-01 9.672263e-13 1.358015e-08 7.073872e-03 
          d1           d2           d3           d4 
1.846751e-02 0.000000e+00 2.206730e-01 0.000000e+00 

$solvtol
[1] 2.220446e-16

$covb
              h0            h1            h2            h3            h4
h0  2.139630e-01 -9.097014e-02  1.198172e-04  1.465294e-06 -3.664185e-04
h1 -9.097014e-02  4.165919e-02 -5.713139e-05 -1.417350e-06 -4.482972e-04
h2  1.198172e-04 -5.713139e-05  8.653665e-08  2.183748e-09  8.009434e-07
h3  1.465294e-06 -1.417350e-06  2.183748e-09  4.851974e-10  3.384438e-08
h4 -3.664185e-04 -4.482972e-04  8.009434e-07  3.384438e-08  2.166855e-04
d0 -3.659149e-03  4.650864e-04  4.267866e-07  1.107221e-07  3.041462e-04
d1  2.841350e-03 -1.034923e-03  5.857918e-07 -9.634007e-10 -1.728612e-05
d2  5.058013e-05  3.098361e-05 -4.663221e-08 -2.905959e-08 -3.213424e-06
d3  9.292410e-05  4.764382e-05 -3.813526e-08  1.206417e-08 -4.464736e-05
d4 -1.831689e-05  8.305753e-06 -1.554887e-08 -1.825388e-10 -1.428953e-07
              d0            d1            d2            d3            d4
h0 -3.659149e-03  2.841350e-03  5.058013e-05  9.292410e-05 -1.831689e-05
h1  4.650864e-04 -1.034923e-03  3.098361e-05  4.764382e-05  8.305753e-06
h2  4.267866e-07  5.857918e-07 -4.663221e-08 -3.813526e-08 -1.554887e-08
h3  1.107221e-07 -9.634007e-10 -2.905959e-08  1.206417e-08 -1.825388e-10
h4  3.041462e-04 -1.728612e-05 -3.213424e-06 -4.464736e-05 -1.428953e-07
d0  1.248679e-02 -1.880909e-03 -4.340259e-04 -1.028607e-03 -3.922872e-05
d1 -1.880909e-03  3.104092e-03 -3.028016e-04 -2.746389e-05 -9.581141e-07
d2 -4.340259e-04 -3.028016e-04  1.602081e-04 -2.333799e-05  4.391506e-07
d3 -1.028607e-03 -2.746389e-05 -2.333799e-05  2.002622e-04  8.819879e-07
d4 -3.922872e-05 -9.581141e-07  4.391506e-07  8.819879e-07  9.991958e-07

$rcov
            [,1]        [,2]
[1,]  1.61346253 -0.08634101
[2,] -0.08634101  0.07382011

$rcor
           [,1]       [,2]
[1,]  1.0000000 -0.2501753
[2,] -0.2501753  1.0000000

$drcov
[1] 0.1116512

$rcovest
            [,1]        [,2]
[1,]  1.61134330 -0.05189704
[2,] -0.05189704  0.07282824

$g
[1] 2

$nlmest
$nlmest$minimum
[1] 319.4409

$nlmest$estimate
 [1] -4.715774e-01  3.858819e-01 -5.628742e-05  1.637233e-04  8.579685e-02
 [6] -3.029064e-01  1.319401e-01  1.434493e-01  1.736550e-02 -1.498560e-02

$nlmest$gradient
 [1]  2.529550e-05 -9.743264e-05 -2.941808e-02 -2.409382e-01 -6.922808e-04
 [6]  1.006024e-04 -1.618747e-04  6.180282e-05 -1.947402e-04  3.881538e-04

$nlmest$code
[1] 1

$nlmest$iterations
[1] 68


attr(,"class")
[1] "nlsystemfit.system"
Warning messages:
1: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
2: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
$eq
$eq[[1]]
$method
[1] "2SLS"

$i
[1] 1

$eqnlabel
[1] "height.growth"

$formula
hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

$b
           h0            h1            h2            h3            h4 
-1.9342124903  1.0393024427 -0.0010056775  0.0001385357  0.0898858315 

$se
               h0
[1,] 1.3951881128
[2,] 0.6519172257
[3,] 0.0009691264
[4,] 0.0000294189
[5,] 0.0158145712

$t
            h0
[1,] -1.386345
[2,]  1.594225
[3,] -1.037716
[4,]  4.709071
[5,]  5.683735

$p
               h0
[1,] 1.675583e-01
[2,] 1.128470e-01
[3,] 3.009585e-01
[4,] 5.339062e-06
[5,] 6.037851e-08

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
           [,1]
  [1,] 3.577349
  [2,] 4.506488
  [3,] 6.142938
  [4,] 6.127386
  [5,] 5.650264
  [6,] 4.798460
  [7,] 5.682727
  [8,] 4.598654
  [9,] 4.154505
 [10,] 5.729331
 [11,] 3.241505
 [12,] 1.967867
 [13,] 3.489922
 [14,] 5.549112
 [15,] 5.220155
 [16,] 4.603237
 [17,] 4.928423
 [18,] 7.289750
 [19,] 3.269825
 [20,] 4.100601
 [21,] 3.040022
 [22,] 7.141282
 [23,] 6.648715
 [24,] 5.479213
 [25,] 5.682727
 [26,] 5.391938
 [27,] 6.667174
 [28,] 7.311549
 [29,] 6.983125
 [30,] 4.981260
 [31,] 2.796716
 [32,] 5.264729
 [33,] 6.100022
 [34,] 3.963371
 [35,] 3.463051
 [36,] 5.773423
 [37,] 7.078291
 [38,] 6.085110
 [39,] 5.257138
 [40,] 5.981762
 [41,] 5.994530
 [42,] 5.189236
 [43,] 4.533409
 [44,] 6.385381
 [45,] 6.248329
 [46,] 5.448418
 [47,] 5.491942
 [48,] 6.054848
 [49,] 6.778276
 [50,] 5.060537
 [51,] 4.372145
 [52,] 6.573806
 [53,] 7.917629
 [54,] 3.675787
 [55,] 5.491942
 [56,] 5.588051
 [57,] 3.041104
 [58,] 3.539580
 [59,] 6.088630
 [60,] 6.921216
 [61,] 5.593679
 [62,] 5.849046
 [63,] 5.236898
 [64,] 6.483235
 [65,] 6.231345
 [66,] 6.653126
 [67,] 5.402962
 [68,] 5.655685
 [69,] 3.412043
 [70,] 6.529929
 [71,] 6.688584
 [72,] 6.299916
 [73,] 7.542402
 [74,] 6.499113
 [75,] 6.854400
 [76,] 5.993326
 [77,] 5.725394
 [78,] 5.077583
 [79,] 4.724361
 [80,] 7.551007
 [81,] 4.246140
 [82,] 3.872317
 [83,] 4.457431
 [84,] 3.566899
 [85,] 2.846552
 [86,] 4.976726
 [87,] 3.615104
 [88,] 4.163164
 [89,] 4.097351
 [90,] 3.724010
 [91,] 4.557333
 [92,] 4.209945
 [93,] 4.285187
 [94,] 4.723024
 [95,] 3.309950
 [96,] 3.399294
 [97,] 3.157700
 [98,] 3.107075
 [99,] 2.634194
[100,] 2.763186
[101,] 3.907369
[102,] 4.337753
[103,] 2.619717
[104,] 2.887278
[105,] 4.208324
[106,] 3.964860
[107,] 3.566899
[108,] 4.405942
[109,] 4.097351
[110,] 3.260272
[111,] 4.299914
[112,] 4.768160
[113,] 3.848039
[114,] 5.380853
[115,] 3.107075
[116,] 4.192309
[117,] 5.094524
[118,] 3.680993
[119,] 3.905991
[120,] 4.692275
[121,] 5.049586
[122,] 3.383131
[123,] 4.375011
[124,] 4.334595
[125,] 4.492242
[126,] 4.864477
[127,] 5.205060
[128,] 4.114283
[129,] 5.285266
[130,] 4.806489
[131,] 4.312532
[132,] 4.066419
[133,] 5.329974
[134,] 5.063434
[135,] 4.245941
[136,] 4.285383
[137,] 4.638004
[138,] 4.836619
[139,] 4.410274
[140,] 4.403401
[141,] 4.327375
[142,] 4.495138
[143,] 4.410274
[144,] 4.477322
[145,] 4.799977
[146,] 3.872099
[147,] 4.218733
[148,] 4.496593
[149,] 4.020940
[150,] 4.196363
[151,] 4.247941
[152,] 4.498977
[153,] 4.924567
[154,] 4.383904
[155,] 4.444582
[156,] 4.487591
[157,] 3.959012
[158,] 4.493510
[159,] 4.368626
[160,] 4.114839
[161,] 4.114735
[162,] 4.035196
[163,] 4.710749
[164,] 4.480141
[165,] 5.213208
[166,] 4.883272

$residuals
               [,1]
  [1,] -0.077349479
  [2,] -0.506488483
  [3,]  2.557062399
  [4,]  0.972614439
  [5,]  0.449736039
  [6,]  0.901539656
  [7,] -1.582726993
  [8,]  0.201346063
  [9,] -0.254504526
 [10,] -1.029330574
 [11,]  0.758494796
 [12,]  0.532132509
 [13,]  0.110077914
 [14,]  0.250888405
 [15,] -0.620155410
 [16,] -0.503236575
 [17,]  0.171576824
 [18,] -0.089749586
 [19,]  0.330175461
 [20,] -0.400600628
 [21,]  1.459978054
 [22,]  0.158717503
 [23,]  0.651285383
 [24,] -0.679213047
 [25,]  0.117273007
 [26,] -0.091938274
 [27,]  0.032825814
 [28,] -1.111549097
 [29,] -0.283124627
 [30,] -0.381259514
 [31,]  1.503283599
 [32,] -1.064729027
 [33,]  2.699978256
 [34,] -0.863370683
 [35,] -0.063051402
 [36,] -0.473423397
 [37,] -0.378290757
 [38,]  0.614890339
 [39,]  0.442862224
 [40,]  0.518237955
 [41,]  0.005470414
 [42,]  1.010763985
 [43,]  0.266591146
 [44,] -2.185380734
 [45,]  2.851671201
 [46,] -2.748417626
 [47,] -0.791942196
 [48,]  1.245151847
 [49,] -0.578275848
 [50,]  1.339462939
 [51,]  1.627854569
 [52,]  1.326194011
 [53,] -1.917628603
 [54,]  0.124212655
 [55,] -1.191942196
 [56,]  1.211949450
 [57,]  0.658896324
 [58,] -0.339580485
 [59,] -1.288629792
 [60,] -1.421215936
 [61,] -1.593678643
 [62,]  0.750953742
 [63,]  2.863101864
 [64,]  1.216765175
 [65,]  0.868654910
 [66,]  0.246873940
 [67,] -2.002962383
 [68,]  1.444315018
 [69,]  0.387956531
 [70,]  1.670070874
 [71,]  1.711416280
 [72,]  1.200083802
 [73,] -1.542402239
 [74,] -1.299112811
 [75,] -0.454400016
 [76,] -0.493325949
 [77,]  0.074606226
 [78,]  0.022416590
 [79,] -1.124360888
 [80,] -2.051007468
 [81,] -0.646139928
 [82,] -0.572317189
 [83,] -1.057431285
 [84,]  0.233101126
 [85,]  1.353447650
 [86,] -0.176726192
 [87,] -0.415103885
 [88,] -0.363164039
 [89,]  0.102649332
 [90,] -0.024009803
 [91,] -0.557333150
 [92,] -0.009944886
 [93,] -1.185186941
 [94,]  1.976976083
 [95,]  0.590049602
 [96,]  1.600706178
 [97,]  0.542299909
 [98,]  0.792924659
 [99,]  1.065805560
[100,]  0.836814088
[101,] -0.407369331
[102,] -0.237752716
[103,]  0.180282929
[104,]  0.012722463
[105,] -1.108324451
[106,] -0.664860118
[107,] -0.366898874
[108,] -1.905942082
[109,]  2.102649332
[110,]  2.739727686
[111,]  0.300085831
[112,]  0.231839777
[113,] -0.648039219
[114,]  1.219147483
[115,]  0.392924659
[116,]  1.107690935
[117,] -0.594523809
[118,]  0.619007415
[119,]  1.794008846
[120,]  0.307725357
[121,]  1.350413906
[122,]  2.516868623
[123,]  0.224989240
[124,]  0.165405181
[125,] -0.392242245
[126,] -1.464476511
[127,] -1.405059753
[128,] -0.714283400
[129,] -0.285265822
[130,] -0.406488888
[131,] -0.812531610
[132,]  3.833581309
[133,] -0.329973760
[134,] -1.663433538
[135,]  2.454059295
[136,]  2.714616991
[137,]  0.461995949
[138,] -0.836618982
[139,] -1.210273961
[140,]  1.396598790
[141,] -0.427375138
[142,] -0.295138129
[143,] -0.110273961
[144,] -0.077321574
[145,]  1.000022824
[146,] -3.572098916
[147,] -1.018733397
[148,]  0.603407187
[149,] -0.020940169
[150,] -2.896362702
[151,]  0.452058561
[152,] -1.198977360
[153,] -0.924566934
[154,] -1.283903866
[155,] -1.444582321
[156,] -3.087590751
[157,] -1.959011593
[158,] -1.893509680
[159,]  3.431373994
[160,] -0.314839157
[161,]  0.485265184
[162,] -1.535195868
[163,] -1.410748768
[164,]  0.019859241
[165,]  1.286792187
[166,] -2.983272263

$ssr
[1] 273.3067

$mse
[1] 1.697557

$s2
[1] 1.697557

$rmse
[1] 1.302903

$s
[1] 1.302903

$covb
              h0            h1            h2            h3            h4
h0  1.946550e+00 -9.064511e-01  1.336713e-03  3.006946e-05  1.065860e-02
h1 -9.064511e-01  4.249961e-01 -6.290443e-04 -1.471836e-05 -5.545614e-03
h2  1.336713e-03 -6.290443e-04  9.392059e-07  2.195111e-08  8.441270e-06
h3  3.006946e-05 -1.471836e-05  2.195111e-08  8.654718e-10  2.091295e-07
h4  1.065860e-02 -5.545614e-03  8.441270e-06  2.091295e-07  2.501007e-04

$inst
~tht + dbh + elev + cr + ba

$r2
          [,1]
[1,] 0.3734832

$adjr2
          [,1]
[1,] 0.3579176

attr(,"class")
[1] "nlsystemfit.equation"

$eq[[2]]
$method
[1] "2SLS"

$i
[1] 2

$eqnlabel
[1] "diameter.growth"

$formula
dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

$b
          d0           d1           d2           d3           d4 
-0.628959731  0.009037039  0.230996741  0.004895757 -0.013304979 

$se
              d0
[1,] 0.142344774
[2,] 0.081198612
[3,] 0.028979566
[4,] 0.017024123
[5,] 0.001201182

$t
              d0
[1,]  -4.4185657
[2,]   0.1112955
[3,]   7.9710214
[4,]   0.2875776
[5,] -11.0765687

$p
               d0
[1,] 1.817929e-05
[2,] 9.115207e-01
[3,] 2.731149e-13
[4,] 7.740399e-01
[5,] 0.000000e+00

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
            [,1]
  [1,] 0.4377423
  [2,] 0.4934276
  [3,] 1.4782134
  [4,] 1.0200752
  [5,] 0.8070467
  [6,] 0.7353594
  [7,] 0.5095481
  [8,] 0.5947791
  [9,] 0.5112926
 [10,] 0.6209506
 [11,] 0.5191046
 [12,] 0.3616895
 [13,] 0.4738248
 [14,] 0.7983286
 [15,] 0.6059266
 [16,] 0.5380961
 [17,] 0.6763685
 [18,] 1.1230987
 [19,] 0.4729942
 [20,] 0.4884139
 [21,] 0.5807704
 [22,] 1.3483265
 [23,] 1.3409421
 [24,] 0.7427676
 [25,] 0.9416831
 [26,] 0.8382870
 [27,] 1.1685306
 [28,] 1.0463699
 [29,] 1.1774303
 [30,] 0.8875544
 [31,] 0.8149407
 [32,] 0.8114916
 [33,] 2.3647945
 [34,] 0.6928847
 [35,] 0.7422765
 [36,] 1.1732688
 [37,] 1.6313342
 [38,] 1.6225118
 [39,] 1.2823139
 [40,] 1.5485400
 [41,] 1.3774875
 [42,] 0.3536507
 [43,] 0.2531190
 [44,] 0.2256741
 [45,] 2.2612991
 [46,] 0.5129053
 [47,] 0.8132351
 [48,] 1.4925148
 [49,] 1.1622254
 [50,] 1.2039103
 [51,] 1.0913967
 [52,] 1.7168616
 [53,] 1.3637237
 [54,] 0.8038334
 [55,] 0.9034842
 [56,] 1.6052090
 [57,] 0.7721151
 [58,] 0.6885861
 [59,] 1.0240785
 [60,] 1.2060703
 [61,] 0.8482272
 [62,] 1.5389326
 [63,] 2.5569145
 [64,] 2.3596754
 [65,] 2.0424886
 [66,] 1.9611262
 [67,] 0.8636208
 [68,] 2.0305791
 [69,] 0.9373648
 [70,] 2.6437780
 [71,] 2.7666079
 [72,] 2.5218228
 [73,] 1.8119954
 [74,] 1.4882978
 [75,] 1.9668531
 [76,] 1.6016615
 [77,] 1.7140444
 [78,] 1.4381974
 [79,] 1.0093456
 [80,] 1.6079748
 [81,] 0.6549759
 [82,] 0.6096100
 [83,] 0.6237404
 [84,] 0.6818072
 [85,] 0.7355693
 [86,] 0.8641962
 [87,] 0.5906674
 [88,] 0.6864225
 [89,] 0.7478075
 [90,] 0.6609687
 [91,] 0.7183789
 [92,] 0.7491928
 [93,] 0.5803063
 [94,] 1.6308964
 [95,] 0.8407763
 [96,] 1.0893296
 [97,] 0.7984300
 [98,] 0.8420830
 [99,] 0.8231199
[100,] 0.8075420
[101,] 0.7896532
[102,] 0.9129465
[103,] 0.6638214
[104,] 0.6811023
[105,] 0.7197045
[106,] 0.7540017
[107,] 0.7379437
[108,] 0.6322474
[109,] 1.7501717
[110,] 1.6588734
[111,] 1.2086098
[112,] 1.3359524
[113,] 0.8715547
[114,] 2.1313363
[115,] 1.0190779
[116,] 1.5518083
[117,] 1.3003165
[118,] 1.2299520
[119,] 1.7079031
[120,] 1.4527307
[121,] 2.0157934
[122,] 1.7799227
[123,] 0.3130979
[124,] 0.3062058
[125,] 0.2809175
[126,] 0.2401902
[127,] 0.2633025
[128,] 0.2352500
[129,] 0.4330699
[130,] 0.3750103
[131,] 0.3035219
[132,] 0.8315401
[133,] 0.4336048
[134,] 0.2990814
[135,] 0.6386369
[136,] 0.6857313
[137,] 0.4413072
[138,] 0.5348862
[139,] 0.4424648
[140,] 0.8051195
[141,] 0.5201195
[142,] 0.5561944
[143,] 0.5699391
[144,] 0.5837991
[145,] 0.8124025
[146,] 0.3509650
[147,] 0.6894139
[148,] 1.0675645
[149,] 0.8243800
[150,] 0.4416318
[151,] 0.9776981
[152,] 0.7045706
[153,] 0.8324916
[154,] 0.6708475
[155,] 0.6581514
[156,] 0.4545916
[157,] 0.6384757
[158,] 0.7402152
[159,] 2.4605103
[160,] 0.9700236
[161,] 1.1674549
[162,] 0.7191978
[163,] 0.8711146
[164,] 1.1463949
[165,] 1.8430980
[166,] 0.6307712

$residuals
               [,1]
  [1,] -0.237742262
  [2,]  0.006572417
  [3,] -0.378213369
  [4,] -0.120075248
  [5,] -0.307046733
  [6,] -0.135359422
  [7,] -0.109548148
  [8,]  0.105220912
  [9,] -0.011292640
 [10,]  0.079049351
 [11,] -0.019104552
 [12,] -0.061689548
 [13,] -0.373824841
 [14,]  0.001671380
 [15,] -0.305926607
 [16,] -0.238096124
 [17,]  0.023631537
 [18,]  0.376901317
 [19,]  0.027005801
 [20,]  0.211586119
 [21,] -0.080770444
 [22,] -0.148326539
 [23,] -0.340942066
 [24,] -0.242767592
 [25,] -0.441683058
 [26,] -0.238287033
 [27,] -0.168530550
 [28,]  0.153630056
 [29,] -0.077430260
 [30,] -0.287554446
 [31,] -0.014940686
 [32,]  0.088508386
 [33,] -0.764794509
 [34,]  0.407115262
 [35,]  0.357723536
 [36,]  0.226731216
 [37,] -0.231334215
 [38,] -0.122511810
 [39,] -0.082313910
 [40,] -0.148540015
 [41,] -0.077487480
 [42,]  0.246349309
 [43,]  0.246881010
 [44,]  0.474325856
 [45,] -0.661299132
 [46,]  0.187094710
 [47,]  0.186764870
 [48,]  0.107485214
 [49,]  0.137774582
 [50,] -0.303910308
 [51,] -0.291396731
 [52,] -0.616861631
 [53,]  0.436276280
 [54,]  0.296166624
 [55,]  0.196515805
 [56,]  0.194791005
 [57,]  0.427884913
 [58,]  0.711413879
 [59,]  0.475921462
 [60,]  0.693929704
 [61,]  0.551772771
 [62,] -0.438932585
 [63,] -1.056914462
 [64,] -0.659675411
 [65,]  0.057511436
 [66,] -0.561126243
 [67,] -0.063620815
 [68,]  0.269420856
 [69,] -0.337364816
 [70,]  0.056221951
 [71,] -0.966607932
 [72,] -0.621822752
 [73,]  0.588004581
 [74,]  0.111702187
 [75,]  0.133146888
 [76,]  0.398338524
 [77,]  0.385955603
 [78,] -0.038197434
 [79,]  0.490654414
 [80,] -0.007974801
 [81,]  0.245024055
 [82,] -0.109609989
 [83,]  0.176259580
 [84,]  0.218192837
 [85,] -0.335569348
 [86,] -0.364196218
 [87,]  0.009332612
 [88,]  0.113577479
 [89,] -0.047807478
 [90,] -0.260968652
 [91,]  0.081621057
 [92,] -0.149192753
 [93,]  0.219693701
 [94,] -0.430896371
 [95,] -0.140776266
 [96,]  0.010670375
 [97,] -0.098429960
 [98,]  0.057916979
 [99,]  0.076880105
[100,] -0.107541992
[101,]  0.110346764
[102,] -0.012946462
[103,] -0.363821365
[104,] -0.281102326
[105,]  0.280295456
[106,] -0.054001652
[107,] -0.137943673
[108,]  0.367752635
[109,] -0.250171664
[110,]  0.241126636
[111,] -0.208609802
[112,]  0.364047623
[113,]  0.128445259
[114,] -0.231336295
[115,] -0.019077858
[116,] -0.251808314
[117,]  0.399683533
[118,]  0.470048004
[119,]  0.092096943
[120,]  0.147269301
[121,] -0.215793413
[122,]  0.120077317
[123,] -0.113097878
[124,] -0.006205804
[125,]  0.019082485
[126,]  0.559809764
[127,]  0.236697548
[128,] -0.135250032
[129,]  0.166930076
[130,] -0.175010286
[131,]  0.196478078
[132,] -0.531540112
[133,] -0.233604765
[134,]  0.400918599
[135,] -0.538636911
[136,]  0.014268717
[137,] -0.041307227
[138,] -0.134886184
[139,]  0.357535235
[140,] -0.405119522
[141,]  0.579880521
[142,]  0.043805602
[143,]  0.230060873
[144,]  0.316200896
[145,] -0.112402548
[146,] -0.050965024
[147,] -0.189413880
[148,]  0.232435534
[149,]  0.175620016
[150,] -0.141631836
[151,]  0.422301929
[152,] -0.104570646
[153,]  0.167508441
[154,] -0.070847512
[155,]  0.541848569
[156,]  0.245408443
[157,]  0.461524294
[158,]  0.459784783
[159,] -0.360510263
[160,]  0.629976417
[161,] -0.367454850
[162,] -0.019197837
[163,]  0.628885353
[164,] -0.346394867
[165,] -0.443097958
[166,]  0.169228826

$ssr
[1] 17.28106

$mse
[1] 0.1073358

$s2
[1] 0.1073358

$rmse
[1] 0.3276214

$s
[1] 0.3276214

$covb
              d0            d1            d2            d3            d4
d0  2.026203e-02  1.166431e-03 -2.136763e-03 -1.162945e-03 -6.075379e-05
d1  1.166431e-03  6.593215e-03 -1.693438e-03  1.240674e-04 -7.930353e-06
d2 -2.136763e-03 -1.693438e-03  8.398152e-04 -1.229485e-04  2.681610e-06
d3 -1.162945e-03  1.240674e-04 -1.229485e-04  2.898208e-04  7.802461e-07
d4 -6.075379e-05 -7.930353e-06  2.681610e-06  7.802461e-07  1.442839e-06

$inst
~tht + dbh + elev + cr + ba

$r2
         [,1]
[1,] 0.636089

$adjr2
          [,1]
[1,] 0.6270478

attr(,"class")
[1] "nlsystemfit.equation"


$resids
               [,1]         [,2]
  [1,] -0.077349479 -0.237742262
  [2,] -0.506488483  0.006572417
  [3,]  2.557062399 -0.378213369
  [4,]  0.972614439 -0.120075248
  [5,]  0.449736039 -0.307046733
  [6,]  0.901539656 -0.135359422
  [7,] -1.582726993 -0.109548148
  [8,]  0.201346063  0.105220912
  [9,] -0.254504526 -0.011292640
 [10,] -1.029330574  0.079049351
 [11,]  0.758494796 -0.019104552
 [12,]  0.532132509 -0.061689548
 [13,]  0.110077914 -0.373824841
 [14,]  0.250888405  0.001671380
 [15,] -0.620155410 -0.305926607
 [16,] -0.503236575 -0.238096124
 [17,]  0.171576824  0.023631537
 [18,] -0.089749586  0.376901317
 [19,]  0.330175461  0.027005801
 [20,] -0.400600628  0.211586119
 [21,]  1.459978054 -0.080770444
 [22,]  0.158717503 -0.148326539
 [23,]  0.651285383 -0.340942066
 [24,] -0.679213047 -0.242767592
 [25,]  0.117273007 -0.441683058
 [26,] -0.091938274 -0.238287033
 [27,]  0.032825814 -0.168530550
 [28,] -1.111549097  0.153630056
 [29,] -0.283124627 -0.077430260
 [30,] -0.381259514 -0.287554446
 [31,]  1.503283599 -0.014940686
 [32,] -1.064729027  0.088508386
 [33,]  2.699978256 -0.764794509
 [34,] -0.863370683  0.407115262
 [35,] -0.063051402  0.357723536
 [36,] -0.473423397  0.226731216
 [37,] -0.378290757 -0.231334215
 [38,]  0.614890339 -0.122511810
 [39,]  0.442862224 -0.082313910
 [40,]  0.518237955 -0.148540015
 [41,]  0.005470414 -0.077487480
 [42,]  1.010763985  0.246349309
 [43,]  0.266591146  0.246881010
 [44,] -2.185380734  0.474325856
 [45,]  2.851671201 -0.661299132
 [46,] -2.748417626  0.187094710
 [47,] -0.791942196  0.186764870
 [48,]  1.245151847  0.107485214
 [49,] -0.578275848  0.137774582
 [50,]  1.339462939 -0.303910308
 [51,]  1.627854569 -0.291396731
 [52,]  1.326194011 -0.616861631
 [53,] -1.917628603  0.436276280
 [54,]  0.124212655  0.296166624
 [55,] -1.191942196  0.196515805
 [56,]  1.211949450  0.194791005
 [57,]  0.658896324  0.427884913
 [58,] -0.339580485  0.711413879
 [59,] -1.288629792  0.475921462
 [60,] -1.421215936  0.693929704
 [61,] -1.593678643  0.551772771
 [62,]  0.750953742 -0.438932585
 [63,]  2.863101864 -1.056914462
 [64,]  1.216765175 -0.659675411
 [65,]  0.868654910  0.057511436
 [66,]  0.246873940 -0.561126243
 [67,] -2.002962383 -0.063620815
 [68,]  1.444315018  0.269420856
 [69,]  0.387956531 -0.337364816
 [70,]  1.670070874  0.056221951
 [71,]  1.711416280 -0.966607932
 [72,]  1.200083802 -0.621822752
 [73,] -1.542402239  0.588004581
 [74,] -1.299112811  0.111702187
 [75,] -0.454400016  0.133146888
 [76,] -0.493325949  0.398338524
 [77,]  0.074606226  0.385955603
 [78,]  0.022416590 -0.038197434
 [79,] -1.124360888  0.490654414
 [80,] -2.051007468 -0.007974801
 [81,] -0.646139928  0.245024055
 [82,] -0.572317189 -0.109609989
 [83,] -1.057431285  0.176259580
 [84,]  0.233101126  0.218192837
 [85,]  1.353447650 -0.335569348
 [86,] -0.176726192 -0.364196218
 [87,] -0.415103885  0.009332612
 [88,] -0.363164039  0.113577479
 [89,]  0.102649332 -0.047807478
 [90,] -0.024009803 -0.260968652
 [91,] -0.557333150  0.081621057
 [92,] -0.009944886 -0.149192753
 [93,] -1.185186941  0.219693701
 [94,]  1.976976083 -0.430896371
 [95,]  0.590049602 -0.140776266
 [96,]  1.600706178  0.010670375
 [97,]  0.542299909 -0.098429960
 [98,]  0.792924659  0.057916979
 [99,]  1.065805560  0.076880105
[100,]  0.836814088 -0.107541992
[101,] -0.407369331  0.110346764
[102,] -0.237752716 -0.012946462
[103,]  0.180282929 -0.363821365
[104,]  0.012722463 -0.281102326
[105,] -1.108324451  0.280295456
[106,] -0.664860118 -0.054001652
[107,] -0.366898874 -0.137943673
[108,] -1.905942082  0.367752635
[109,]  2.102649332 -0.250171664
[110,]  2.739727686  0.241126636
[111,]  0.300085831 -0.208609802
[112,]  0.231839777  0.364047623
[113,] -0.648039219  0.128445259
[114,]  1.219147483 -0.231336295
[115,]  0.392924659 -0.019077858
[116,]  1.107690935 -0.251808314
[117,] -0.594523809  0.399683533
[118,]  0.619007415  0.470048004
[119,]  1.794008846  0.092096943
[120,]  0.307725357  0.147269301
[121,]  1.350413906 -0.215793413
[122,]  2.516868623  0.120077317
[123,]  0.224989240 -0.113097878
[124,]  0.165405181 -0.006205804
[125,] -0.392242245  0.019082485
[126,] -1.464476511  0.559809764
[127,] -1.405059753  0.236697548
[128,] -0.714283400 -0.135250032
[129,] -0.285265822  0.166930076
[130,] -0.406488888 -0.175010286
[131,] -0.812531610  0.196478078
[132,]  3.833581309 -0.531540112
[133,] -0.329973760 -0.233604765
[134,] -1.663433538  0.400918599
[135,]  2.454059295 -0.538636911
[136,]  2.714616991  0.014268717
[137,]  0.461995949 -0.041307227
[138,] -0.836618982 -0.134886184
[139,] -1.210273961  0.357535235
[140,]  1.396598790 -0.405119522
[141,] -0.427375138  0.579880521
[142,] -0.295138129  0.043805602
[143,] -0.110273961  0.230060873
[144,] -0.077321574  0.316200896
[145,]  1.000022824 -0.112402548
[146,] -3.572098916 -0.050965024
[147,] -1.018733397 -0.189413880
[148,]  0.603407187  0.232435534
[149,] -0.020940169  0.175620016
[150,] -2.896362702 -0.141631836
[151,]  0.452058561  0.422301929
[152,] -1.198977360 -0.104570646
[153,] -0.924566934  0.167508441
[154,] -1.283903866 -0.070847512
[155,] -1.444582321  0.541848569
[156,] -3.087590751  0.245408443
[157,] -1.959011593  0.461524294
[158,] -1.893509680  0.459784783
[159,]  3.431373994 -0.360510263
[160,] -0.314839157  0.629976417
[161,]  0.485265184 -0.367454850
[162,] -1.535195868 -0.019197837
[163,] -1.410748768  0.628885353
[164,]  0.019859241 -0.346394867
[165,]  1.286792187 -0.443097958
[166,] -2.983272263  0.169228826

$method
[1] "2SLS"

$n
[1] 332

$k
[1] 10

$b
           h0            h1            h2            h3            h4 
-1.9342124903  1.0393024427 -0.0010056775  0.0001385357  0.0898858315 
           d0            d1            d2            d3            d4 
-0.6289597309  0.0090370390  0.2309967411  0.0048957567 -0.0133049786 

$se
          h0           h1           h2           h3           h4           d0 
1.3951881128 0.6519172257 0.0009691264 0.0000294189 0.0158145712 0.1423447737 
          d1           d2           d3           d4 
0.0811986117 0.0289795659 0.0170241233 0.0012011823 

$t
         h0          h1          h2          h3          h4          d0 
 -1.3863453   1.5942245  -1.0377155   4.7090706   5.6837350  -4.4185657 
         d1          d2          d3          d4 
  0.1112955   7.9710214   0.2875776 -11.0765687 

$p
          h0           h1           h2           h3           h4           d0 
1.666006e-01 1.118668e-01 3.001811e-01 3.704421e-06 2.953564e-08 1.359267e-05 
          d1           d2           d3           d4 
9.114514e-01 2.753353e-14 7.738551e-01 0.000000e+00 

$solvtol
[1] 2.220446e-16

$covb
              h0            h1            h2            h3            h4
h0  1.946550e+00 -9.064511e-01  1.336713e-03  3.006946e-05  1.065860e-02
h1 -9.064511e-01  4.249961e-01 -6.290443e-04 -1.471836e-05 -5.545614e-03
h2  1.336713e-03 -6.290443e-04  9.392059e-07  2.195111e-08  8.441270e-06
h3  3.006946e-05 -1.471836e-05  2.195111e-08  8.654718e-10  2.091295e-07
h4  1.065860e-02 -5.545614e-03  8.441270e-06  2.091295e-07  2.501007e-04
d0  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d1  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d2  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d3  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
              d0            d1            d2            d3            d4
h0  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h1  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h2  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h3  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
h4  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
d0  2.026203e-02  1.166431e-03 -2.136763e-03 -1.162945e-03 -6.075379e-05
d1  1.166431e-03  6.593215e-03 -1.693438e-03  1.240674e-04 -7.930353e-06
d2 -2.136763e-03 -1.693438e-03  8.398152e-04 -1.229485e-04  2.681610e-06
d3 -1.162945e-03  1.240674e-04 -1.229485e-04  2.898208e-04  7.802461e-07
d4 -6.075379e-05 -7.930353e-06  2.681610e-06  7.802461e-07  1.442839e-06

$rcov
           [,1]       [,2]
[1,]  1.6975574 -0.2210467
[2,] -0.2210467  0.1073358

$rcor
           [,1]       [,2]
[1,]  1.0000000 -0.5179185
[2,] -0.5179185  1.0000000

$drcov
[1] 0.133347

$g
[1] 2

$nlmest
$nlmest$minimum
[1] 9.99963e-06

$nlmest$estimate
 [1] -1.9342124903  1.0393024427 -0.0010056775  0.0001385357  0.0898858315
 [6] -0.6289597309  0.0090370390  0.2309967411  0.0048957567 -0.0133049786

$nlmest$gradient
 [1]  1.714752e-05  3.651932e-05 -1.877645e-03  5.998463e-02  1.071991e-04
 [6] -6.660437e-05 -4.818747e-03  1.453480e-05  8.529849e-02  4.968707e-05

$nlmest$code
[1] 2

$nlmest$iterations
[1] 74


attr(,"class")
[1] "nlsystemfit.system"
Warning messages:
1: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
2: In nlm(knls, startvals, typsize = abs(startvals), iterlim = maxiter,  :
  NA/Inf replaced by maximum positive value
$eq
$eq[[1]]
$method
[1] "3SLS"

$i
[1] 1

$eqnlabel
[1] "height.growth"

$formula
hg ~ exp(h0 + h1 * log(tht) + h2 * tht^2 + h3 * elev + h4 * cr)

$b
           h0            h1            h2            h3            h4 
-1.9342127533  1.0393025542 -0.0010056776  0.0001385357  0.0898858315 

$se
               h0
[1,] 1.630889e+00
[2,] 7.620515e-01
[3,] 1.132460e-03
[4,] 3.420511e-05
[5,] 1.848482e-02

$t
             h0
[1,] -1.1859870
[2,]  1.3638220
[3,] -0.8880471
[4,]  4.0501458
[5,]  4.8626839

$p
               h0
[1,] 2.373748e-01
[2,] 1.745273e-01
[3,] 3.758402e-01
[4,] 7.939130e-05
[5,] 2.733731e-06

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
           [,1]
  [1,] 3.577349
  [2,] 4.506488
  [3,] 6.142938
  [4,] 6.127386
  [5,] 5.650264
  [6,] 4.798460
  [7,] 5.682727
  [8,] 4.598654
  [9,] 4.154504
 [10,] 5.729331
 [11,] 3.241505
 [12,] 1.967867
 [13,] 3.489922
 [14,] 5.549112
 [15,] 5.220155
 [16,] 4.603237
 [17,] 4.928423
 [18,] 7.289750
 [19,] 3.269824
 [20,] 4.100601
 [21,] 3.040022
 [22,] 7.141283
 [23,] 6.648715
 [24,] 5.479213
 [25,] 5.682727
 [26,] 5.391938
 [27,] 6.667174
 [28,] 7.311549
 [29,] 6.983125
 [30,] 4.981259
 [31,] 2.796716
 [32,] 5.264729
 [33,] 6.100022
 [34,] 3.963371
 [35,] 3.463051
 [36,] 5.773423
 [37,] 7.078291
 [38,] 6.085110
 [39,] 5.257138
 [40,] 5.981762
 [41,] 5.994530
 [42,] 5.189236
 [43,] 4.533409
 [44,] 6.385381
 [45,] 6.248329
 [46,] 5.448418
 [47,] 5.491942
 [48,] 6.054848
 [49,] 6.778276
 [50,] 5.060537
 [51,] 4.372145
 [52,] 6.573806
 [53,] 7.917629
 [54,] 3.675787
 [55,] 5.491942
 [56,] 5.588051
 [57,] 3.041104
 [58,] 3.539580
 [59,] 6.088630
 [60,] 6.921216
 [61,] 5.593679
 [62,] 5.849046
 [63,] 5.236898
 [64,] 6.483235
 [65,] 6.231345
 [66,] 6.653126
 [67,] 5.402962
 [68,] 5.655685
 [69,] 3.412043
 [70,] 6.529929
 [71,] 6.688584
 [72,] 6.299916
 [73,] 7.542402
 [74,] 6.499113
 [75,] 6.854400
 [76,] 5.993326
 [77,] 5.725394
 [78,] 5.077583
 [79,] 4.724361
 [80,] 7.551007
 [81,] 4.246140
 [82,] 3.872317
 [83,] 4.457431
 [84,] 3.566899
 [85,] 2.846552
 [86,] 4.976726
 [87,] 3.615104
 [88,] 4.163164
 [89,] 4.097351
 [90,] 3.724010
 [91,] 4.557333
 [92,] 4.209945
 [93,] 4.285187
 [94,] 4.723024
 [95,] 3.309950
 [96,] 3.399294
 [97,] 3.157700
 [98,] 3.107075
 [99,] 2.634194
[100,] 2.763186
[101,] 3.907369
[102,] 4.337753
[103,] 2.619717
[104,] 2.887277
[105,] 4.208324
[106,] 3.964860
[107,] 3.566899
[108,] 4.405942
[109,] 4.097351
[110,] 3.260272
[111,] 4.299914
[112,] 4.768160
[113,] 3.848039
[114,] 5.380853
[115,] 3.107075
[116,] 4.192309
[117,] 5.094524
[118,] 3.680993
[119,] 3.905991
[120,] 4.692275
[121,] 5.049586
[122,] 3.383131
[123,] 4.375011
[124,] 4.334595
[125,] 4.492242
[126,] 4.864476
[127,] 5.205060
[128,] 4.114283
[129,] 5.285266
[130,] 4.806489
[131,] 4.312532
[132,] 4.066419
[133,] 5.329974
[134,] 5.063433
[135,] 4.245941
[136,] 4.285383
[137,] 4.638004
[138,] 4.836619
[139,] 4.410274
[140,] 4.403401
[141,] 4.327375
[142,] 4.495138
[143,] 4.410274
[144,] 4.477322
[145,] 4.799977
[146,] 3.872099
[147,] 4.218733
[148,] 4.496593
[149,] 4.020940
[150,] 4.196363
[151,] 4.247941
[152,] 4.498977
[153,] 4.924567
[154,] 4.383904
[155,] 4.444582
[156,] 4.487591
[157,] 3.959012
[158,] 4.493510
[159,] 4.368626
[160,] 4.114839
[161,] 4.114735
[162,] 4.035196
[163,] 4.710749
[164,] 4.480141
[165,] 5.213208
[166,] 4.883272

$residuals
               [,1]
  [1,] -0.077349367
  [2,] -0.506488444
  [3,]  2.557062358
  [4,]  0.972614396
  [5,]  0.449736021
  [6,]  0.901539710
  [7,] -1.582727013
  [8,]  0.201346094
  [9,] -0.254504457
 [10,] -1.029330598
 [11,]  0.758494900
 [12,]  0.532132656
 [13,]  0.110078001
 [14,]  0.250888364
 [15,] -0.620155392
 [16,] -0.503236504
 [17,]  0.171576827
 [18,] -0.089749602
 [19,]  0.330175563
 [20,] -0.400600555
 [21,]  1.459978144
 [22,]  0.158717456
 [23,]  0.651285335
 [24,] -0.679213086
 [25,]  0.117272987
 [26,] -0.091938271
 [27,]  0.032825766
 [28,] -1.111549149
 [29,] -0.283124581
 [30,] -0.381259475
 [31,]  1.503283732
 [32,] -1.064729013
 [33,]  2.699978239
 [34,] -0.863370634
 [35,] -0.063051314
 [36,] -0.473423425
 [37,] -0.378290801
 [38,]  0.614890327
 [39,]  0.442862271
 [40,]  0.518237965
 [41,]  0.005470372
 [42,]  1.010764031
 [43,]  0.266591167
 [44,] -2.185380694
 [45,]  2.851671203
 [46,] -2.748417602
 [47,] -0.791942176
 [48,]  1.245151865
 [49,] -0.578275881
 [50,]  1.339462995
 [51,]  1.627854641
 [52,]  1.326193989
 [53,] -1.917628632
 [54,]  0.124212847
 [55,] -1.191942176
 [56,]  1.211949425
 [57,]  0.658896429
 [58,] -0.339580417
 [59,] -1.288629727
 [60,] -1.421215940
 [61,] -1.593678585
 [62,]  0.750953733
 [63,]  2.863101864
 [64,]  1.216765159
 [65,]  0.868654879
 [66,]  0.246873913
 [67,] -2.002962396
 [68,]  1.444314990
 [69,]  0.387956671
 [70,]  1.670070855
 [71,]  1.711416251
 [72,]  1.200083774
 [73,] -1.542402258
 [74,] -1.299112828
 [75,] -0.454400050
 [76,] -0.493325876
 [77,]  0.074606321
 [78,]  0.022416603
 [79,] -1.124360883
 [80,] -2.051007496
 [81,] -0.646139878
 [82,] -0.572317108
 [83,] -1.057431291
 [84,]  0.233101198
 [85,]  1.353447694
 [86,] -0.176726244
 [87,] -0.415103850
 [88,] -0.363163982
 [89,]  0.102649358
 [90,] -0.024009809
 [91,] -0.557333128
 [92,] -0.009944870
 [93,] -1.185186966
 [94,]  1.976976091
 [95,]  0.590049663
 [96,]  1.600706263
 [97,]  0.542299954
 [98,]  0.792924736
 [99,]  1.065805695
[100,]  0.836814215
[101,] -0.407369322
[102,] -0.237752712
[103,]  0.180283015
[104,]  0.012722530
[105,] -1.108324469
[106,] -0.664860114
[107,] -0.366898802
[108,] -1.905942046
[109,]  2.102649358
[110,]  2.739727751
[111,]  0.300085805
[112,]  0.231839780
[113,] -0.648039205
[114,]  1.219147472
[115,]  0.392924736
[116,]  1.107690919
[117,] -0.594523869
[118,]  0.619007445
[119,]  1.794008889
[120,]  0.307725300
[121,]  1.350413849
[122,]  2.516868678
[123,]  0.224989236
[124,]  0.165405186
[125,] -0.392242197
[126,] -1.464476450
[127,] -1.405059750
[128,] -0.714283435
[129,] -0.285265836
[130,] -0.406488896
[131,] -0.812531601
[132,]  3.833581291
[133,] -0.329973785
[134,] -1.663433496
[135,]  2.454059380
[136,]  2.714617070
[137,]  0.461995973
[138,] -0.836618996
[139,] -1.210273972
[140,]  1.396598747
[141,] -0.427375132
[142,] -0.295138162
[143,] -0.110273972
[144,] -0.077321601
[145,]  1.000022818
[146,] -3.572098918
[147,] -1.018733397
[148,]  0.603407153
[149,] -0.020940177
[150,] -2.896362731
[151,]  0.452058581
[152,] -1.198977396
[153,] -0.924566975
[154,] -1.283903909
[155,] -1.444582339
[156,] -3.087590782
[157,] -1.959011629
[158,] -1.893509713
[159,]  3.431373992
[160,] -0.314839193
[161,]  0.485265147
[162,] -1.535195884
[163,] -1.410748809
[164,]  0.019859212
[165,]  1.286792188
[166,] -2.983272312

$ssr
[1] 273.3067

$mse
[1] 1.697557

$s2
[1] 1.697557

$rmse
[1] 1.302903

$s
[1] 1.302903

$covb
              h0            h1            h2            h3            h4
h0  2.659798e+00 -1.238591e+00  1.826398e-03  4.110194e-05  1.456323e-02
h1 -1.238591e+00  5.807225e-01 -8.594927e-04 -2.011737e-05 -7.577279e-03
h2  1.826398e-03 -8.594927e-04  1.282465e-06  3.010044e-08  1.152736e-05
h3  4.110194e-05 -2.011737e-05  3.010044e-08  1.169990e-09  2.865941e-07
h4  1.456323e-02 -7.577279e-03  1.152736e-05  2.865941e-07  3.416885e-04

$inst
~tht + dbh + elev + cr + ba

$r2
          [,1]
[1,] 0.3734832

$adjr2
          [,1]
[1,] 0.3579176

attr(,"class")
[1] "nlsystemfit.equation"

$eq[[2]]
$method
[1] "3SLS"

$i
[1] 2

$eqnlabel
[1] "diameter.growth"

$formula
dg ~ exp(d0 + d1 * log(dbh) + d2 * hg + d3 * cr + d4 * ba)

$b
          d0           d1           d2           d3           d4 
-0.626882658  0.009485091  0.230774506  0.004688322 -0.013308860 

$se
              d0
[1,] 0.166211975
[2,] 0.090191755
[3,] 0.032920833
[4,] 0.019877662
[5,] 0.001400395

$t
             d0
[1,] -3.7715854
[2,]  0.1051658
[3,]  7.0099837
[4,]  0.2358588
[5,] -9.5036443

$p
               d0
[1,] 2.274899e-04
[2,] 9.163751e-01
[3,] 6.203082e-11
[4,] 8.138420e-01
[5,] 0.000000e+00

$n
[1] 166

$k
[1] 5

$df
[1] 161

$predicted
            [,1]
  [1,] 0.4378045
  [2,] 0.4935468
  [3,] 1.4772064
  [4,] 1.0196740
  [5,] 0.8067784
  [6,] 0.7351576
  [7,] 0.5096592
  [8,] 0.5948765
  [9,] 0.5114059
 [10,] 0.6209911
 [11,] 0.5192374
 [12,] 0.3617997
 [13,] 0.4740148
 [14,] 0.7984329
 [15,] 0.6059377
 [16,] 0.5380798
 [17,] 0.6764251
 [18,] 1.1223779
 [19,] 0.4731427
 [20,] 0.4885540
 [21,] 0.5810225
 [22,] 1.3473182
 [23,] 1.3401777
 [24,] 0.7429374
 [25,] 0.9415588
 [26,] 0.8382359
 [27,] 1.1680765
 [28,] 1.0458721
 [29,] 1.1768857
 [30,] 0.8875469
 [31,] 0.8150731
 [32,] 0.8116696
 [33,] 2.3637153
 [34,] 0.6934051
 [35,] 0.7427681
 [36,] 1.1735954
 [37,] 1.6303145
 [38,] 1.6225218
 [39,] 1.2829100
 [40,] 1.5485828
 [41,] 1.3775726
 [42,] 0.3534698
 [43,] 0.2531574
 [44,] 0.2255988
 [45,] 2.2591936
 [46,] 0.5132552
 [47,] 0.8133853
 [48,] 1.4917451
 [49,] 1.1621389
 [50,] 1.2036548
 [51,] 1.0914440
 [52,] 1.7158698
 [53,] 1.3631533
 [54,] 0.8038012
 [55,] 0.9038157
 [56,] 1.6054105
 [57,] 0.7728351
 [58,] 0.6893392
 [59,] 1.0239156
 [60,] 1.2058030
 [61,] 0.8484734
 [62,] 1.5388092
 [63,] 2.5566540
 [64,] 2.3589385
 [65,] 2.0424594
 [66,] 1.9608422
 [67,] 0.8644465
 [68,] 2.0308756
 [69,] 0.9376912
 [70,] 2.6424212
 [71,] 2.7649573
 [72,] 2.5216497
 [73,] 1.8122759
 [74,] 1.4885775
 [75,] 1.9668547
 [76,] 1.6014610
 [77,] 1.7135894
 [78,] 1.4390001
 [79,] 1.0103201
 [80,] 1.6080871
 [81,] 0.6548657
 [82,] 0.6094731
 [83,] 0.6238616
 [84,] 0.6817645
 [85,] 0.7358496
 [86,] 0.8642096
 [87,] 0.5908317
 [88,] 0.6863002
 [89,] 0.7476942
 [90,] 0.6612769
 [91,] 0.7181942
 [92,] 0.7491480
 [93,] 0.5806362
 [94,] 1.6297483
 [95,] 0.8408070
 [96,] 1.0888773
 [97,] 0.7986372
 [98,] 0.8421787
 [99,] 0.8228098
[100,] 0.8074155
[101,] 0.7899300
[102,] 0.9130272
[103,] 0.6640650
[104,] 0.6814250
[105,] 0.7200081
[106,] 0.7542994
[107,] 0.7379768
[108,] 0.6323124
[109,] 1.7494267
[110,] 1.6583811
[111,] 1.2090303
[112,] 1.3356106
[113,] 0.8719757
[114,] 2.1297342
[115,] 1.0192904
[116,] 1.5518750
[117,] 1.3005329
[118,] 1.2301899
[119,] 1.7073477
[120,] 1.4531294
[121,] 2.0152290
[122,] 1.7796340
[123,] 0.3132177
[124,] 0.3063426
[125,] 0.2810279
[126,] 0.2402742
[127,] 0.2633642
[128,] 0.2354076
[129,] 0.4330455
[130,] 0.3751085
[131,] 0.3037446
[132,] 0.8313584
[133,] 0.4336068
[134,] 0.2988929
[135,] 0.6385123
[136,] 0.6856147
[137,] 0.4413780
[138,] 0.5351557
[139,] 0.4428583
[140,] 0.8052917
[141,] 0.5205010
[142,] 0.5565035
[143,] 0.5702803
[144,] 0.5841625
[145,] 0.8125733
[146,] 0.3514647
[147,] 0.6898201
[148,] 1.0681386
[149,] 0.8252161
[150,] 0.4421359
[151,] 0.9785274
[152,] 0.7052403
[153,] 0.8329903
[154,] 0.6714201
[155,] 0.6588583
[156,] 0.4552317
[157,] 0.6393690
[158,] 0.7411586
[159,] 2.4608007
[160,] 0.9711098
[161,] 1.1685812
[162,] 0.7199268
[163,] 0.8717457
[164,] 1.1472884
[165,] 1.8432280
[166,] 0.6314422

$residuals
               [,1]
  [1,] -0.237804496
  [2,]  0.006453176
  [3,] -0.377206377
  [4,] -0.119673974
  [5,] -0.306778419
  [6,] -0.135157565
  [7,] -0.109659173
  [8,]  0.105123466
  [9,] -0.011405899
 [10,]  0.079008899
 [11,] -0.019237431
 [12,] -0.061799698
 [13,] -0.374014844
 [14,]  0.001567070
 [15,] -0.305937695
 [16,] -0.238079770
 [17,]  0.023574920
 [18,]  0.377622065
 [19,]  0.026857292
 [20,]  0.211446032
 [21,] -0.081022524
 [22,] -0.147318234
 [23,] -0.340177656
 [24,] -0.242937438
 [25,] -0.441558800
 [26,] -0.238235902
 [27,] -0.168076487
 [28,]  0.154127923
 [29,] -0.076885658
 [30,] -0.287546907
 [31,] -0.015073109
 [32,]  0.088330353
 [33,] -0.763715258
 [34,]  0.406594909
 [35,]  0.357231852
 [36,]  0.226404632
 [37,] -0.230314462
 [38,] -0.122521823
 [39,] -0.082910014
 [40,] -0.148582811
 [41,] -0.077572550
 [42,]  0.246530211
 [43,]  0.246842605
 [44,]  0.474401240
 [45,] -0.659193598
 [46,]  0.186744843
 [47,]  0.186614690
 [48,]  0.108254861
 [49,]  0.137861148
 [50,] -0.303654845
 [51,] -0.291444046
 [52,] -0.615869785
 [53,]  0.436846711
 [54,]  0.296198800
 [55,]  0.196184298
 [56,]  0.194589504
 [57,]  0.427164866
 [58,]  0.710660786
 [59,]  0.476084414
 [60,]  0.694197018
 [61,]  0.551526574
 [62,] -0.438809213
 [63,] -1.056653977
 [64,] -0.658938518
 [65,]  0.057540567
 [66,] -0.560842200
 [67,] -0.064446497
 [68,]  0.269124440
 [69,] -0.337691189
 [70,]  0.057578820
 [71,] -0.964957325
 [72,] -0.621649730
 [73,]  0.587724060
 [74,]  0.111422529
 [75,]  0.133145284
 [76,]  0.398539045
 [77,]  0.386410606
 [78,] -0.039000147
 [79,]  0.489679895
 [80,] -0.008087108
 [81,]  0.245134282
 [82,] -0.109473088
 [83,]  0.176138448
 [84,]  0.218235512
 [85,] -0.335849585
 [86,] -0.364209559
 [87,]  0.009168275
 [88,]  0.113699837
 [89,] -0.047694203
 [90,] -0.261276906
 [91,]  0.081805800
 [92,] -0.149148006
 [93,]  0.219363837
 [94,] -0.429748323
 [95,] -0.140807041
 [96,]  0.011122670
 [97,] -0.098637233
 [98,]  0.057821313
 [99,]  0.077190201
[100,] -0.107415528
[101,]  0.110070018
[102,] -0.013027203
[103,] -0.364065015
[104,] -0.281425004
[105,]  0.279991875
[106,] -0.054299429
[107,] -0.137976793
[108,]  0.367687613
[109,] -0.249426716
[110,]  0.241618939
[111,] -0.209030307
[112,]  0.364389423
[113,]  0.128024292
[114,] -0.229734220
[115,] -0.019290417
[116,] -0.251875008
[117,]  0.399467075
[118,]  0.469810144
[119,]  0.092652252
[120,]  0.146870606
[121,] -0.215229030
[122,]  0.120366007
[123,] -0.113217677
[124,] -0.006342551
[125,]  0.018972140
[126,]  0.559725829
[127,]  0.236635826
[128,] -0.135407585
[129,]  0.166954497
[130,] -0.175108543
[131,]  0.196255351
[132,] -0.531358416
[133,] -0.233606847
[134,]  0.401107059
[135,] -0.538512315
[136,]  0.014385300
[137,] -0.041378045
[138,] -0.135155670
[139,]  0.357141746
[140,] -0.405291714
[141,]  0.579498950
[142,]  0.043496473
[143,]  0.229719684
[144,]  0.315837523
[145,] -0.112573299
[146,] -0.051464700
[147,] -0.189820121
[148,]  0.231861404
[149,]  0.174783863
[150,] -0.142135868
[151,]  0.421472598
[152,] -0.105240270
[153,]  0.167009714
[154,] -0.071420139
[155,]  0.541141723
[156,]  0.244768325
[157,]  0.460631035
[158,]  0.458841416
[159,] -0.360800658
[160,]  0.628890204
[161,] -0.368581224
[162,] -0.019926768
[163,]  0.628254283
[164,] -0.347288412
[165,] -0.443227996
[166,]  0.168557758

$ssr
[1] 17.25885

$mse
[1] 0.1071979

$s2
[1] 0.1071979

$rmse
[1] 0.3274108

$s
[1] 0.3274108

$covb
              d0            d1            d2            d3            d4
d0  2.762642e-02  1.523537e-03 -2.896570e-03 -1.586865e-03 -8.309846e-05
d1  1.523537e-03  8.134553e-03 -2.079113e-03  1.522893e-04 -1.341763e-05
d2 -2.896570e-03 -2.079113e-03  1.083781e-03 -1.633640e-04  4.359280e-06
d3 -1.586865e-03  1.522893e-04 -1.633640e-04  3.951214e-04  1.010902e-06
d4 -8.309846e-05 -1.341763e-05  4.359280e-06  1.010902e-06  1.961107e-06

$inst
~tht + dbh + elev + cr + ba

$r2
          [,1]
[1,] 0.6365566

$adjr2
          [,1]
[1,] 0.6275269

attr(,"class")
[1] "nlsystemfit.equation"


$resids
               [,1]         [,2]
  [1,] -0.077349367 -0.237804496
  [2,] -0.506488444  0.006453176
  [3,]  2.557062358 -0.377206377
  [4,]  0.972614396 -0.119673974
  [5,]  0.449736021 -0.306778419
  [6,]  0.901539710 -0.135157565
  [7,] -1.582727013 -0.109659173
  [8,]  0.201346094  0.105123466
  [9,] -0.254504457 -0.011405899
 [10,] -1.029330598  0.079008899
 [11,]  0.758494900 -0.019237431
 [12,]  0.532132656 -0.061799698
 [13,]  0.110078001 -0.374014844
 [14,]  0.250888364  0.001567070
 [15,] -0.620155392 -0.305937695
 [16,] -0.503236504 -0.238079770
 [17,]  0.171576827  0.023574920
 [18,] -0.089749602  0.377622065
 [19,]  0.330175563  0.026857292
 [20,] -0.400600555  0.211446032
 [21,]  1.459978144 -0.081022524
 [22,]  0.158717456 -0.147318234
 [23,]  0.651285335 -0.340177656
 [24,] -0.679213086 -0.242937438
 [25,]  0.117272987 -0.441558800
 [26,] -0.091938271 -0.238235902
 [27,]  0.032825766 -0.168076487
 [28,] -1.111549149  0.154127923
 [29,] -0.283124581 -0.076885658
 [30,] -0.381259475 -0.287546907
 [31,]  1.503283732 -0.015073109
 [32,] -1.064729013  0.088330353
 [33,]  2.699978239 -0.763715258
 [34,] -0.863370634  0.406594909
 [35,] -0.063051314  0.357231852
 [36,] -0.473423425  0.226404632
 [37,] -0.378290801 -0.230314462
 [38,]  0.614890327 -0.122521823
 [39,]  0.442862271 -0.082910014
 [40,]  0.518237965 -0.148582811
 [41,]  0.005470372 -0.077572550
 [42,]  1.010764031  0.246530211
 [43,]  0.266591167  0.246842605
 [44,] -2.185380694  0.474401240
 [45,]  2.851671203 -0.659193598
 [46,] -2.748417602  0.186744843
 [47,] -0.791942176  0.186614690
 [48,]  1.245151865  0.108254861
 [49,] -0.578275881  0.137861148
 [50,]  1.339462995 -0.303654845
 [51,]  1.627854641 -0.291444046
 [52,]  1.326193989 -0.615869785
 [53,] -1.917628632  0.436846711
 [54,]  0.124212847  0.296198800
 [55,] -1.191942176  0.196184298
 [56,]  1.211949425  0.194589504
 [57,]  0.658896429  0.427164866
 [58,] -0.339580417  0.710660786
 [59,] -1.288629727  0.476084414
 [60,] -1.421215940  0.694197018
 [61,] -1.593678585  0.551526574
 [62,]  0.750953733 -0.438809213
 [63,]  2.863101864 -1.056653977
 [64,]  1.216765159 -0.658938518
 [65,]  0.868654879  0.057540567
 [66,]  0.246873913 -0.560842200
 [67,] -2.002962396 -0.064446497
 [68,]  1.444314990  0.269124440
 [69,]  0.387956671 -0.337691189
 [70,]  1.670070855  0.057578820
 [71,]  1.711416251 -0.964957325
 [72,]  1.200083774 -0.621649730
 [73,] -1.542402258  0.587724060
 [74,] -1.299112828  0.111422529
 [75,] -0.454400050  0.133145284
 [76,] -0.493325876  0.398539045
 [77,]  0.074606321  0.386410606
 [78,]  0.022416603 -0.039000147
 [79,] -1.124360883  0.489679895
 [80,] -2.051007496 -0.008087108
 [81,] -0.646139878  0.245134282
 [82,] -0.572317108 -0.109473088
 [83,] -1.057431291  0.176138448
 [84,]  0.233101198  0.218235512
 [85,]  1.353447694 -0.335849585
 [86,] -0.176726244 -0.364209559
 [87,] -0.415103850  0.009168275
 [88,] -0.363163982  0.113699837
 [89,]  0.102649358 -0.047694203
 [90,] -0.024009809 -0.261276906
 [91,] -0.557333128  0.081805800
 [92,] -0.009944870 -0.149148006
 [93,] -1.185186966  0.219363837
 [94,]  1.976976091 -0.429748323
 [95,]  0.590049663 -0.140807041
 [96,]  1.600706263  0.011122670
 [97,]  0.542299954 -0.098637233
 [98,]  0.792924736  0.057821313
 [99,]  1.065805695  0.077190201
[100,]  0.836814215 -0.107415528
[101,] -0.407369322  0.110070018
[102,] -0.237752712 -0.013027203
[103,]  0.180283015 -0.364065015
[104,]  0.012722530 -0.281425004
[105,] -1.108324469  0.279991875
[106,] -0.664860114 -0.054299429
[107,] -0.366898802 -0.137976793
[108,] -1.905942046  0.367687613
[109,]  2.102649358 -0.249426716
[110,]  2.739727751  0.241618939
[111,]  0.300085805 -0.209030307
[112,]  0.231839780  0.364389423
[113,] -0.648039205  0.128024292
[114,]  1.219147472 -0.229734220
[115,]  0.392924736 -0.019290417
[116,]  1.107690919 -0.251875008
[117,] -0.594523869  0.399467075
[118,]  0.619007445  0.469810144
[119,]  1.794008889  0.092652252
[120,]  0.307725300  0.146870606
[121,]  1.350413849 -0.215229030
[122,]  2.516868678  0.120366007
[123,]  0.224989236 -0.113217677
[124,]  0.165405186 -0.006342551
[125,] -0.392242197  0.018972140
[126,] -1.464476450  0.559725829
[127,] -1.405059750  0.236635826
[128,] -0.714283435 -0.135407585
[129,] -0.285265836  0.166954497
[130,] -0.406488896 -0.175108543
[131,] -0.812531601  0.196255351
[132,]  3.833581291 -0.531358416
[133,] -0.329973785 -0.233606847
[134,] -1.663433496  0.401107059
[135,]  2.454059380 -0.538512315
[136,]  2.714617070  0.014385300
[137,]  0.461995973 -0.041378045
[138,] -0.836618996 -0.135155670
[139,] -1.210273972  0.357141746
[140,]  1.396598747 -0.405291714
[141,] -0.427375132  0.579498950
[142,] -0.295138162  0.043496473
[143,] -0.110273972  0.229719684
[144,] -0.077321601  0.315837523
[145,]  1.000022818 -0.112573299
[146,] -3.572098918 -0.051464700
[147,] -1.018733397 -0.189820121
[148,]  0.603407153  0.231861404
[149,] -0.020940177  0.174783863
[150,] -2.896362731 -0.142135868
[151,]  0.452058581  0.421472598
[152,] -1.198977396 -0.105240270
[153,] -0.924566975  0.167009714
[154,] -1.283903909 -0.071420139
[155,] -1.444582339  0.541141723
[156,] -3.087590782  0.244768325
[157,] -1.959011629  0.460631035
[158,] -1.893509713  0.458841416
[159,]  3.431373992 -0.360800658
[160,] -0.314839193  0.628890204
[161,]  0.485265147 -0.368581224
[162,] -1.535195884 -0.019926768
[163,] -1.410748809  0.628254283
[164,]  0.019859212 -0.347288412
[165,]  1.286792188 -0.443227996
[166,] -2.983272312  0.168557758

$method
[1] "3SLS"

$n
[1] 332

$k
[1] 10

$b
           h0            h1            h2            h3            h4 
-1.9342127533  1.0393025542 -0.0010056776  0.0001385357  0.0898858315 
           d0            d1            d2            d3            d4 
-0.6268826578  0.0094850913  0.2307745058  0.0046883218 -0.0133088600 

$se
          h0           h1           h2           h3           h4           d0 
1.630889e+00 7.620515e-01 1.132460e-03 3.420511e-05 1.848482e-02 1.662120e-01 
          d1           d2           d3           d4 
9.019176e-02 3.292083e-02 1.987766e-02 1.400395e-03 

$t
        h0         h1         h2         h3         h4         d0         d1 
-1.1859870  1.3638220 -0.8880471  4.0501458  4.8626839 -3.7715854  0.1051658 
        d2         d3         d4 
 7.0099837  0.2358588 -9.5036443 

$p
          h0           h1           h2           h3           h4           d0 
2.365018e-01 1.735762e-01 3.751783e-01 6.419123e-05 1.814012e-06 1.929943e-04 
          d1           d2           d3           d4 
9.163097e-01 1.404699e-11 8.136922e-01 0.000000e+00 

$solvtol
[1] 2.220446e-16

$covb
              h0            h1            h2            h3            h4
h0  2.659798e+00 -1.238591e+00  1.826398e-03  4.110194e-05  1.456323e-02
h1 -1.238591e+00  5.807225e-01 -8.594927e-04 -2.011737e-05 -7.577279e-03
h2  1.826398e-03 -8.594927e-04  1.282465e-06  3.010044e-08  1.152736e-05
h3  4.110194e-05 -2.011737e-05  3.010044e-08  1.169990e-09  2.865941e-07
h4  1.456323e-02 -7.577279e-03  1.152736e-05  2.865941e-07  3.416885e-04
d0  3.797268e-02 -2.282831e-02  3.732885e-05  1.771762e-06  1.350187e-03
d1  2.231773e-02 -1.037112e-02  1.234541e-05  7.414155e-07  8.090764e-05
d2 -2.380759e-03  1.699793e-03 -2.468352e-06 -3.887392e-07 -5.331850e-05
d3 -1.425432e-03  9.039102e-04 -1.251981e-06  5.125870e-08 -1.512371e-04
d4 -1.084528e-03  5.099640e-04 -7.690228e-07 -1.863960e-08 -6.514127e-06
              d0            d1            d2            d3            d4
h0  3.797269e-02  2.231773e-02 -2.380759e-03 -1.425432e-03 -1.084528e-03
h1 -2.282831e-02 -1.037112e-02  1.699793e-03  9.039102e-04  5.099640e-04
h2  3.732885e-05  1.234541e-05 -2.468352e-06 -1.251981e-06 -7.690228e-07
h3  1.771762e-06  7.414155e-07 -3.887392e-07  5.125870e-08 -1.863960e-08
h4  1.350187e-03  8.090764e-05 -5.331850e-05 -1.512371e-04 -6.514127e-06
d0  2.762642e-02  1.523537e-03 -2.896570e-03 -1.586865e-03 -8.309846e-05
d1  1.523537e-03  8.134553e-03 -2.079113e-03  1.522893e-04 -1.341763e-05
d2 -2.896570e-03 -2.079113e-03  1.083781e-03 -1.633640e-04  4.359280e-06
d3 -1.586865e-03  1.522893e-04 -1.633640e-04  3.951214e-04  1.010902e-06
d4 -8.309846e-05 -1.341763e-05  4.359280e-06  1.010902e-06  1.961107e-06

$rcov
          [,1]       [,2]
[1,]  1.697557 -0.2207250
[2,] -0.220725  0.1071979

$rcor
           [,1]       [,2]
[1,]  1.0000000 -0.5174961
[2,] -0.5174961  1.0000000

$drcov
[1] 0.133255

$rcovest
           [,1]       [,2]
[1,]  1.6975574 -0.2210467
[2,] -0.2210467  0.1073358

$g
[1] 2

$nlmest
$nlmest$minimum
[1] -5.602409e-16

$nlmest$estimate
 [1] -1.9342127533  1.0393025542 -0.0010056776  0.0001385357  0.0898858315
 [6] -0.6268826578  0.0094850913  0.2307745058  0.0046883218 -0.0133088600

$nlmest$gradient
 [1] -1.891706e-08 -4.074033e-08 -2.818851e-06  2.248229e-05 -6.576462e-08
 [6] -6.596022e-08 -2.055205e-07 -3.824104e-07 -2.942835e-06  4.838612e-07

$nlmest$code
[1] 1

$nlmest$iterations
[1] 98


attr(,"class")
[1] "nlsystemfit.system"

systemfit documentation built on May 29, 2017, 9:50 p.m.