Estimation of truncated regression models using the Symmetrically Trimmed Least Squares (STLS) estimator

Function for estimation of linear regression models with truncated response variables (fixed truncation point), using the STLS estimator (Powell 1986)

stls(formula, data, point = 0, direction = "left", beta = "ml", 
    covar = FALSE, na.action, ...)
## S3 method for class 'stls':
print(x, digits = max(3, getOption("digits") - 3), ...)
## S3 method for class 'stls':
summary(object, level=0.95, ...)
## S3 method for class 'summary.stls':
print(x, digits= max(3, getOption("digits") - 3), ...)
## S3 method for class 'stls':
## S3 method for class 'stls':
## S3 method for class 'stls':
## S3 method for class 'stls':
x, object
an object of class "stls"
a symbolic description of the model to be estimated
an optional data frame
the value of truncation (the default is 0)
the direction of truncation, either "left" (the default) or "right"
the method of determining the starting values of the regression coefficients (See Details for more information):
  • The default method is"ml", meaning that the estimated regression coefficients from fitting a maximum likelihood model fo
logical. Indicates whether or not the covariance matrix should be estimated. If TRUE the covariance matrix is estimated using bootstrap. The default number of replicates is 2000 but this can be adjusted (see argument ...). Howeve
a function which indicates what should happen when the data contain NAs.
the number of digits to be printed
the desired level of confidence, for confidence intervals provided by summary.stls. A number between 0 and 1. The default value is 0.95.
additional arguments. For stls the number of bootstrap replicates can be adjusted by setting R=the desired number of replicates. Also the control argument of optim can b

Uses optim ("Nelder--Mead" method) to minimize the objective function described in Powell (1986) wrt the vector of regression coefficients in order to find the STLS estimates (see Karlsson and Lindmark 2014 for more detailed information and background). The maximum number of iterations is set at 2000, but this can be adjusted by setting control=list(maxit=...) (for more information see the documentation for optim). As the starting values of the regression coefficients can have a great impact on the result of the minimization it is recommended to use one of the methods for generating these rather than supplying the values manually (unless one is confident that one has a good idea of what the starting values should be).


  • stls returns an object of class "stls". The function summary prints a summary of the results, including two types of confidence intervals (normal approximation and percentile method). The generic accessor functions coef, fitted, residuals and vcov extract various useful features of the value returned by stls An object of class "stls", a list with elements:
  • coefficientsthe named vector of coefficients
  • startcoefthe starting values of the regression coefficients used by optim
  • valuethe value of the objective function corresponding to coefficients
  • countsnumber of iterations used by optim. See the documentation for optim for further details
  • convergencefrom optim. An integer code. 0 indicates successful completion. Possible error codes are 1 indicating that the iteration limit maxit had been reached. 10 indicating degeneracy of the Nelder--Mead simplex.
  • messagefrom optim. A character string giving any additional information returned by the optimizer, or NULL.
  • residualsthe residuals of the model
  • fitted.valuesthe fitted values
  • df.residualthe residual degrees of freedom
  • callthe matched call
  • covarianceif covar=TRUE, the estimated covariance matrix
  • Rif covar=TRUE, the number of bootstrap replicates
  • bootreplif covar=TRUE, the bootstrap replicates


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

See Also, the function that does the actual fitting qme, for estimation of models with truncated response variables using the QME estimator lt, for estimation of models with truncated response variables using the LT estimator truncreg for estimating models with truncated response variables by maximum likelihood, assuming Gaussian errors

  • stls
  • print,stls-method
  • summary,stls-method
  • print,summary.stls-method
  • coef,stls-method
  • vcov,stls-method
  • residuals,stls-method
  • fitted,stls-method
##Simulate a data.frame
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="ml", covar=FALSE)

##Example using data "PM10trunc"

stlspm10 <- 
stls(PM10~cars+temp+wind.speed+temp.diff+wind.dir+hour+day, data=PM10trunc, point=2)

Documentation reproduced from package truncSP, version 1.2.2, License: GPL (>= 2)

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