gamlss.nl.package: The GAMLSS add on package for fiting parametric non linear...
In gamlss.nl: Fitting non linear parametric GAMLSS models

Description Details Author(s) References See Also Examples

The main purpose of this package is to allow non-linear fitting within a GAMLSS model. The main function nlgamlss() can fit any parametric (up to four distribution parameters) GAMLSS family of distributions.

Package:	gamlss-nl
Type:	Package
Version:	1.5.0
Date:	2005-12-12
License:	GPL (version 2 or later)

Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>, Bob Rigby <r.rigby@londonmet.ac.uk> based on work of Jim Lindsey and Philippe Lambert.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape, (with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2003) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/).

gamlss

data(la)
# fitting the Johnson's Su distribtion to the data
modJSU   <- nlgamlss(y=PET60, mu.fo= ~bflow*(1-p1*exp(-p2/bflow)), sigma.formula=~1, 
                       nu.fo=~1, mu.start = c(.6, 110), sigma.start= 3, nu.start=1, 
                       tau.start=0.6, family=JSU, data=la) 
plot(modJSU)
summary(modJSU)
vcov(modJSU)

Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data

Attaching package: 'gamlss.data'

The following object is masked from 'package:datasets':

    sleep

Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: nlme
Loading required package: parallel
 **********   GAMLSS Version 5.1-3  ********** 
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

Loading required package: survival
Warning messages:
1: In sqrt(diag(cov)) : NaNs produced
2: In sqrt(1/diag(V)) : NaNs produced
3: In cov2cor(cov) :
  diag(.) had 0 or NA entries; non-finite result is doubtful
******************************************************************
	      Summary of the Quantile Residuals
                           mean   =  0.05744272 
                       variance   =  1.01691 
               coef. of skewness  =  -0.02002806 
               coef. of kurtosis  =  2.768721 
Filliben correlation coefficient  =  0.997461 
******************************************************************
*******************************************************************
Family:  c("JSU", "Johnson SU") 

Call:  nlgamlss(y = PET60, mu.fo = ~bflow * (1 - p1 * exp(-p2/bflow)),  
    sigma.formula = ~1, nu.fo = ~1, mu.start = c(0.6, 110), sigma.start = 3,  
    nu.start = 1, tau.start = 0.6, family = JSU, data = la) 

Fitting method: "JL()" 

-------------------------------------------------------------------
Mu link function:  identity
Mu Coefficients:
    Estimate  Std. Error  t-value    p-value
p1    0.6192     0.01296    47.76  0.000e+00
p2  104.1209     8.14579    12.78  2.062e-37

-------------------------------------------------------------------
Sigma link function:  log
Migma Coefficients:
             Estimate  Std. Error  t-value  p-value
(Intercept)     3.105     0.05344     58.1        0

-------------------------------------------------------------------
Nu link function:  identity
Nu Coefficients:
             Estimate  Std. Error  t-value  p-value
(Intercept)     305.7         NaN      NaN      NaN

-------------------------------------------------------------------
Tau link function:  log
Tau Coefficients:
             Estimate  Std. Error  t-value    p-value
(Intercept)     1.271      0.2054    6.186  6.169e-10

-------------------------------------------------------------------
No. of observations in the fit:  251 
Degrees of Freedom for the fit:  5
      Residual Deg. of Freedom:  246 
                      at cycle:  48 
 
Global Deviance:     2253.45 
            AIC:     2263.45 
            SBC:     2281.077 
*******************************************************************
              [,1]          [,2]          [,3]          [,4]         [,5]
[1,]  1.680787e-04    0.08226641  5.054987e-05 -2.953835e-01  0.000603431
[2,]  8.226641e-02   66.35381863  1.312628e-01 -2.264095e+02  0.360611453
[3,]  5.054987e-05    0.13126282  2.855724e-03 -5.413819e-01 -0.005067525
[4,] -2.953835e-01 -226.40946128 -5.413819e-01 -4.426809e+10 -0.993694188
[5,]  6.034310e-04    0.36061145 -5.067525e-03 -9.936946e-01  0.042204125