truncSP
Semi-parametric estimators of truncated regression models

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truncSP-package: Estimators of semi-parametric truncated regression models

truncSP-package: Estimators of semi-parametric truncated regression models
In truncSP: Semi-parametric estimators of truncated regression models

Description Details Author(s) References See Also Examples

Description

Functions for estimation of semi-parametric linear regression models with truncated response variables (fixed truncation point). Estimation using the Symmetrically Trimmed Least Squares (STLS) estimator (Powell 1986), Quadratic Mode (QME) estimator (Lee 1993) and Left Truncated (LT) estimator (Karlsson 2006).

Details

Package: truncSP
Type: Package
Version: 1.2.2
Date: 2014-05-05
License: GPL (>=2)
LazyLoad: yes
Depends: R(>= 2.10), methods, truncreg, boot

These semi-parametric estimators provide an alternative to maximum likelihood estimators, which are sensitive to distributional misspecification (Davidson and MacKinnon, 1993, p 536). All three estimators use trimming of the conditional density of the error terms. STLS assumes symmetrically distributed error terms, while QME and LT have been shown to be consistent for estimation of the slope parameters under asymmetrically distributed errors as well (Laitila 2001 and Karlsson 2006). The functions in the package (qme, lt and stls), all use optim to maximize or minimize objective functions wrt the vector of regression coefficients in order to find estimates (Karlsson and Lindmark, 2014). As the covariance matrices of the estimators depend on the density of the error distribution, the estimation of these is complicated and bootstrap (as described in Karlsson 2004 and Karlsson and Lindmark 2014) is used in all three functions.

Author(s)

Anita Lindmark and Maria Karlsson, Department of Statistics, Umea University

Maintainer: Anita Lindmark <anita.lindmark@stat.umu.se>

References

Davidson, R., MacKinnon, J. G. (1993) Estimation and Inference in Econometrics, Oxford University Press, USA

Karlsson, M. (2004) Finite sample properties of the QME, Communications in Statistics - Simulation and Computation, 5, pp 567–583

Karlsson, M. (2006) Estimators of regression parameters for truncated and censored data, Metrika, 63, pp 329–341

Karlsson, M., Lindmark, A. (2014) truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models, Journal of Statistical Software, 57(14), pp 1–19, http://www.jstatsoft.org/v57/i14/

Laitila, T. (2001) Properties of the QME under asymmetrically distributed disturbances, Statistics & Probability Letters, 52, pp 347–352

Lee, M. (1993) Quadratic mode regression, Journal of Econometrics, 57, pp 1-19

Lee, M., Kim, H. (1998) Semiparametric econometric estimators for a truncated regression model: a review with an extension, Statistica Neerlandica, 52(2), pp 200–225

Powell, J. (1986) Symmetrically Trimmed Least Squares Estimation for Tobit Models, Econometrika, 54(6), pp 1435–1460

See Also

truncreg, function for estimating models with truncated response variables by maximum likelihood assuming Gaussian errors

Examples

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 ##Simulate a data.frame (model with asymmetrically distributed errors)
n <- 10000
x1 <- runif(n,0,10)
x2 <- runif(n,0,10)
x3 <- runif(n,-5,5)
eps <- rexp(n,0.2)- 5
y <- 2-2*x1+x2+2*x3+eps
d <- data.frame(y=y,x1=x1,x2=x2,x3=x3)
   
##Use a truncated subsample
dtrunc <- subset(d, y>0)

##Use qme or lt to consistently estimate the slope parameters
qme(y~x1+x2+x3, dtrunc, point=0, direction="left", cval="ols", const=1, 
   beta="ols", covar=FALSE)
lt(y~x1+x2+x3, dtrunc, point=0, direction="left", clower="ols", const=1, 
   cupper=2, beta="ols", covar=FALSE)
   
##Simulate a data.frame (symmetrically distributed errors)
n <- 10000
x1 <- runif(n,0,10)
x2 <- runif(n,0,10)
x3 <- runif(n,-5,5)
y <- 1-2*x1+x2+2*x3+rnorm(n,0,2)
d <- data.frame(y=y,x1=x1,x2=x2,x3=x3)

##Use a truncated subsample
dtrunc <- subset(d, y>0)
  
##Use stls to estimate the model
stls(y~x1+x2+x3, dtrunc, point=0, direction="left", beta="ols", covar=FALSE)

Example output

Loading required package: truncreg
Loading required package: maxLik
Loading required package: miscTools

Please cite the 'maxLik' package as:
Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1.

If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site:
https://r-forge.r-project.org/projects/maxlik/
Loading required package: boot
$par
                      
(Intercept) -0.3149048
x1          -1.9914041
x2           0.9875271
x3           2.0952464

$value
[1] -62832.8

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function 
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$message
NULL

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$startcoef
                      
(Intercept)  5.7824136
x1          -0.9287844
x2           0.4839151
x3           0.8830568

$coefficients
 (Intercept)        x1        x2       x3
  -0.3149048 -1.991404 0.9875271 2.095246

$df.residual
[1] 3731

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1984    5.056859399
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9999   -1.337745887
10000   3.294244883

$call
qme(formula = y ~ x1 + x2 + x3, data = dtrunc, point = 0, direction = "left", 
    cval = "ols", const = 1, beta = "ols", covar = FALSE)

$cval
 Method Constant    Value
    ols        1 5.300257

attr(,"class")
[1] "qme"
$par
                      
(Intercept)  1.0674527
x1          -1.9516490
x2           0.9994027
x3           1.9882177

$value
[1] 34145.03

$counts
function 
     219 

$convergence
[1] 0

$message
NULL

$residuals
               [,1]
3     -1.692039e+00
6      2.089431e+01
9      3.919486e+00
11     1.408145e+00
15     6.118817e-01
16     7.612435e-01
21    -3.918198e+00
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9999   3.105767e+00
10000  5.642086e+00

$startcoef
                      
(Intercept)  5.7824136
x1          -0.9287844
x2           0.4839151
x3           0.8830568

$coefficients
 (Intercept)        x1        x2       x3
    1.067453 -1.951649 0.9994027 1.988218

$df.residual
[1] 3731

$fitted.values
                   
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1984    6.419204568
1985   -6.415165457
1988   -6.479587268
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2014    8.658914308
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9999    0.618929646
10000   4.657329939

$call
lt(formula = y ~ x1 + x2 + x3, data = dtrunc, point = 0, direction = "left", 
    clower = "ols", const = 1, cupper = 2, beta = "ols", covar = FALSE)

$cvalues
 Method Constant    Lower    Upper
    ols        1 5.300257 10.60051

attr(,"class")
[1] "lt"
$par
                      
(Intercept)  0.9457830
x1          -1.9335602
x2           0.9939685
x3           1.9705689

$value
[1] 10497.76

$counts
function 
     141 

$convergence
[1] 0

$message
NULL

$residuals
              [,1]
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9999  4.3809727199

$startcoef
                      
(Intercept)  1.9618909
x1          -1.6891491
x2           0.8670604
x3           1.7167377

$coefficients
 (Intercept)       x1        x2       x3
    0.945783 -1.93356 0.9939685 1.970569

$df.residual
[1] 3283

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1907  3.404451841
1914  2.717419148
1915  8.979871485
1919  5.719734290
1920  2.012490874
1921  2.196702908
1922  7.473370366
1931  2.859985484
1932 16.560157802
1934 14.042243109
1935  5.923311620
1938  5.788617150
1939 17.475877967
1943  3.376352373
1948  5.000726744
1950 14.572272110
1952  9.247438954
1958  6.321729669
1961 10.155007885
1965 -1.053523128
1968  3.376664508
1972  5.163409457
1973 -1.886044923
1974  4.208694122
1977  4.219392840
1982  0.443734424
1983  4.775926238
1984 19.112997413
1985  9.815804885
1986  6.105015256
1988  6.666608696
1989  2.259723544
1998  8.772869438
2007 11.125479531
2008  3.041898109
2011  5.220644096
2013  9.333625895
2017  7.937535085
2019  7.180171130
2020  5.268192642
2021 11.916335185
2022  6.729333612
2024  5.431042392
2026 17.342587601
2028  5.179047236
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2035 -2.653019782
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2091 14.782878163
2092 -0.753701138
2098  6.741737197
2100 11.633840576
2107  7.138930719
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2109 12.562844300
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2114 13.520547932
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2169 11.299653449
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2228 12.380729273
2232  4.495004218
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9141 15.295490134
9149  7.656954868
9151  4.855720240
9153 11.412603358
9155  3.007767863
9157  5.472928119
9162  5.906849600
9166  6.540407100
9169  1.409063990
9171  4.476555102
9172  5.133805407
9178 10.831140475
9181  4.201597489
9182 12.293476120
9192  2.564380278
9194  7.684878880
9197 -0.147377829
9201 -1.522274183
9203 11.219589608
9204  6.014397884
9209  4.200237449
9210  8.864709816
9211  3.795649540
9213  4.187139842
9215  8.347815636
9218 12.106585695
9221 10.148148388
9223 -0.005823275
9229  5.933463612
9231  5.557396098
9233  2.913422822
9234  8.766193308
9238  5.383120033
9239  7.385819316
9244  5.961325516
9256 11.238273518
9261  5.762235153
9262  7.706791992
9266  1.205451219
9268  5.290496667
9271  7.780249903
9280  1.078174092
9282  8.462923942
9283  3.795286410
9287  0.539418008
9291 11.976275350
9294  8.615388387
9297  4.762102279
9298  5.942908902
9300 -2.675632623
9304  0.639760627
9305 -0.868080501
9307  9.473806784
9308 17.168139029
9309 11.653292677
9310  3.542552049
9323  3.539408948
9325  5.345093825
9331  8.407013512
9334  8.820106704
9342  7.067293094
9343  0.871216861
9345  3.163642240
9347  2.985724621
9351  4.240578461
9357  6.720369878
9366 11.099032225
9367  0.928230658
9369  2.830747534
9373  4.540867923
9380  5.971196947
9386  7.088936253
9389 12.440657143
9390  5.729959260
9392  8.289500271
9403  0.795925633
9405  3.388426793
9406 -0.299867254
9408  5.228836168
9410  4.182904877
9413 12.649589615
9416  3.324412017
9417  3.461311801
9420 15.158680426
9423  2.329076460
9425 11.792457077
9427 -1.566901934
9428 14.692799522
9430  2.927417274
9436 -0.885559293
9441  0.014576248
9448 12.438782097
9450  2.116497513
9452 -0.920438267
9453  4.182771659
9455  7.591982533
9456 13.249728251
9461  2.679770381
9462  9.128697137
9463  4.406288722
9464  8.606917898
9467  1.404890268
9474  5.718279018
9475 10.204953890
9476  7.618477106
9477  3.649787109
9478  6.195659244
9479 10.306099215
9481  2.010381312
9483 15.487245331
9487  4.421225331
9491  4.406158583
9493 13.469709517
9494  4.637469950
9497  7.340445501
9501  8.958580694
9503  1.936063965
9505  5.464846923
9507  1.042720893
9517  6.557555281
9518  7.926972997
9519  6.130739887
9520 -3.026672457
9524  1.487549080
9534  0.939968142
9536  3.887721240
9539  8.756466406
9543  2.716507329
9549  3.776761555
9554  1.721651345
9561  4.367054212
9565  8.437671337
9569  1.473946571
9572  9.052570101
9574  6.189253353
9578  3.527748414
9580  6.606019503
9582 -0.196884936
9583 10.205072285
9586  3.018160015
9588  9.254812569
9589  4.491982645
9590  3.473097462
9592  4.092902451
9595 13.723928937
9597  7.506937862
9601  2.882094691
9604  1.497359221
9611  4.358062614
9612 16.652469688
9619 -0.161078661
9625  0.622565801
9627 13.080548272
9628  9.886497137
9629  5.949965616
9632  6.788160940
9637  1.685377124
9638  6.294448928
9640  2.174624976
9650  9.916895369
9651  0.573270563
9654  6.317606069
9655 12.097435016
9659 13.836083333
9662  2.654563371
9665  1.804521854
9668  9.534340752
9670  4.379041754
9671  3.320822517
9673  7.160747489
9674 -1.630779275
9676  5.859476111
9679  3.777325516
9683  1.700804117
9684 -0.479830780
9685 -2.476961243
9687  2.030295502
9688  4.048460969
9694  3.065092326
9697  6.404548004
9700  4.209023277
9704  3.759711017
9707  3.675332236
9710  1.769928802
9711  1.714550645
9712  1.994051702
9715  3.199563858
9717  2.926852526
9721 12.809130748
9726  1.186590155
9727  3.698406282
9728  2.472746309
9733  5.363743480
9734 -1.445853251
9735  2.034990513
9738  0.889780346
9740  1.348838340
9744  8.395802552
9752 11.018949622
9758  6.551535074
9759  3.567955728
9761  4.206173179
9766  5.434651442
9779  2.626955326
9783  5.808774902
9788 11.473372465
9792  8.855447336
9793  0.910871594
9795 -0.078845768
9796  8.249284912
9799 10.921141552
9803  6.646699412
9808  4.451538563
9810  6.636799135
9816  1.763059326
9818  5.246516692
9825  9.407840787
9827  1.508399482
9828  3.865982348
9830  7.888979204
9832  3.963306487
9833 14.004789193
9834 10.664181983
9835 10.548869426
9836 12.516563492
9839  0.490475527
9840  3.466240788
9843  0.439491597
9845  8.150979327
9846  5.737307521
9849  1.319557677
9851  3.295444312
9854  2.327862522
9860  4.344176115
9863  8.913673157
9867  5.190431112
9871  2.259184780
9873 13.270885268
9875  1.537972719
9876  2.595989686
9877  9.156779794
9878  6.446774511
9882  3.883513489
9886  5.718235237
9890  3.634975678
9892  5.204505609
9900  6.878163694
9901  4.431799182
9909 13.787288566
9910  3.474628607
9915 15.675690745
9920  7.547579886
9921 -2.792019450
9923 13.813062664
9927  1.879353720
9933  3.147155932
9934  8.570579928
9935  1.029147268
9936 17.290201386
9937 14.375466583
9940 11.423048965
9942  7.285339108
9944  0.240940735
9947  8.604380929
9949 -1.783754981
9957  4.802455527
9958  1.218474793
9963  2.884167837
9967 12.135020750
9971 10.869911246
9973  8.548493780
9982 -0.793788032
9985 -0.221183617
9988  7.359517139
9989 -0.988291411
9993  9.772299464
9995  5.018970023
9996 10.389187204
9999 -2.625535350

$call
stls(formula = y ~ x1 + x2 + x3, data = dtrunc, point = 0, direction = "left", 
    beta = "ols", covar = FALSE)

attr(,"class")
[1] "stls"

truncSP documentation built on May 1, 2019, 8:46 p.m.

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