Estimators of semi-parametric truncated regression models

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

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

 ##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)

Air pollution data

Description

The data are a subsample of 500 observations from a data set that originates in a study where air pollution at a road is related to traffic volume and meteorological variables, collected by the Norwegian Public Roads Administration. The response variable consists of hourly values of the logarithm of the concentration of PM10 (particles), measured at Alnabru in Oslo, Norway, between October 2001 and August 2003. (Source: Statlib)

Usage

data(PM10)

Format

A data frame with 500 observations on the following 8 variables.

PM10

Hourly values of the logarithm of the concentration of PM10 (particles)

cars

The logarithm of the number of cars per hour

temp

Temperature 2 meters above ground (degree C)

wind.speed

Wind speed (meters/second)

temp.diff

The temperature difference between 25 and 2 meters above ground (degree C)

wind.dir

Wind direction (degrees between 0 and 360)

hour

Hour of day

day

Day number from October 1. 2001

Source

http://lib.stat.cmu.edu/, dataset PM10, submitted by Magne Aldrin on July 28, 2004

References

Aldrin, M. (2006) Improved predictions penalizing both slope and curvature in additive models, Computational Statistics & Data Analysis, 50, pp 267–284

Examples

data(PM10)

Air pollution data (Truncated)

Description

Dataset PM10, truncated from the left at variable value PM10 = 2 (8 percent truncation).

Usage

data(PM10trunc)

Format

A data frame with 460 observations on the following 8 variables.

PM10

Hourly values of the logarithm of the concentration of PM10 (particles). Left-truncated at point 2.

cars

The logarithm of the number of cars per hour

temp

Temperature 2 meters above ground (degree C)

wind.speed

Wind speed (meters/second)

temp.diff

The temperature difference between 25 and 2 meters above ground (degree C)

wind.dir

Wind direction (degrees between 0 and 360)

hour

Hour of day

day

Day number from October 1. 2001

Examples

data(PM10trunc)

Estimation of truncated regression models using the Left Truncated (LT) estimator

Description

Estimates linear regression models with truncated response variables (fixed truncation point), using the LT estimator (Karlsson 2006).

Usage

lt(formula, data, point = 0, direction = "left", clower = "ml", const = 1, cupper = 2,
   beta = "ml", covar = FALSE, na.action, ...)
## S4 method for signature 'lt'
print(x, digits = max(3, getOption("digits") - 3), ...)
## S4 method for signature 'lt'
summary(object, level=0.95, ...)
## S4 method for signature 'summary.lt'
print(x, digits= max(3, getOption("digits") - 3), ...)
## S4 method for signature 'lt'
coef(object,...)
## S4 method for signature 'lt'
vcov(object,...)
## S4 method for signature 'lt'
residuals(object,...)
## S4 method for signature 'lt'
fitted(object,...)

Arguments

Details

Minimizes the objective function described in Karlsson (2006) wrt the vector of regression coefficients, in order to find the LT estimates. The minimization is performed by optim using the "Nelder–Mead" method, and a maximum number of iterations of 2000. The maximum number of iterations can be adjusted by setting control=list(maxit=...) (for more information see the documentation for optim).

It is recommended to use one of the methods for generating the starting values of the regression coefficients (see argument beta) rather than supplying these manually, unless one is confident that one has a good idea of what these should be. This because the starting values can have a great impact on the result of the minimization.

Note that setting cupper=1 means that the LT estimates will coincide with the estimates from the Quadratic Mode Estimator (see function qme). For more detailed information see Karlsson and Lindmark (2014).

Value

lt returns an object of class "lt".

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 lt

An object of class "lt", a list with elements:

Author(s)

Anita Lindmark and Maria Karlsson

References

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/

See Also

lt.fit, the function that does the actual fitting

qme, for estimation of models with truncated response variables using the QME estimator

stls, for estimation of models with truncated response variables using the STLS estimator

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

Examples

##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 lt to consistently estimate the slope parameters
lt(y~x1+x2+x3, dtrunc, point=0, direction="left", clower="ml", const=1, 
   cupper=2, beta="ml", covar=FALSE)
   
##Example using data "PM10trunc"
data(PM10trunc)

ltpm10 <- lt(PM10~cars+temp+wind.speed+temp.diff+wind.dir+hour+day, 
   data=PM10trunc, point=2, control=list(maxit=2500))

summary(ltpm10)

Class "lt"

Description

Documentation on S4 class "lt".

Objects from the Class

Objects from the class are usually obtained by a call to the function lt.

Slots

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

cvalues:

Object of class "data.frame" containing information about the thresholds used

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Methods

coef

signature(object = "lt"): extracts the coefficients of the model fitted using lt

fitted

signature(object = "lt"): extracts the fitted values of the model fitted using lt

print

signature(x = "lt"): print method

residuals

signature(object = "lt"): extracts the residuals of the model fitted using lt

summary

signature(object = "lt"): summary method

vcov

signature(object = "lt"): extracts the covariance matrix of the model fitted using lt

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function lt and class "summary.lt"

Examples

showClass("lt")

Function for fitting LT

Description

Function to find LT estimates of the regression coefficients for regression models with truncated response variables. Uses optim. Intended to be called through lt, not on its own, since lt also transforms data into the correct form etc.

Usage

lt.fit(formula, mf, point, direction, bet, cl, cu, ...)

Arguments

Value

a list with components:

Author(s)

Anita Lindmark and Maria Karlsson

See Also

lt

Examples

require(utils)
##Model frame
n <- 10000
x <- rnorm(n,0,2)
y <- 2+x+4*rnorm(n)
d <- data.frame(y=y, x=x)
dl0 <- subset(d, y>0)
mf <- model.frame(y~x, data=dl0)

##Starting values and threshold values
lmmod <- lm(data=mf)
bet <- lmmod$coef
bet <- matrix(bet)
cl <- sqrt(deviance(lmmod)/df.residual(lmmod))
cu <- 2*cl

str(lt. <- lt.fit(y~x,mf,point=0,direction="left",bet,cl,cu))

Estimation of truncated regression models using the Quadratic Mode Estimator (QME)

Description

Estimation of linear regression models with truncated response variables (fixed truncation point), using the Quadratic Mode Estimator (QME) (Lee 1993 and Laitila 2001)

Usage

qme(formula, data, point = 0, direction = "left", cval = "ml", 
  const = 1, beta = "ml", covar = FALSE, na.action, ...)
## S4 method for signature 'qme'
print(x, digits = max(3, getOption("digits") - 3), ...)
## S4 method for signature 'qme'
summary(object, level=0.95, ...)
## S4 method for signature 'summary.qme'
print(x, digits = max(3, getOption("digits") - 3), ...)
## S4 method for signature 'qme'
coef(object,...)
## S4 method for signature 'qme'
vcov(object,...)
## S4 method for signature 'qme'
residuals(object,...)
## S4 method for signature 'qme'
fitted(object,...)

Arguments

Details

Finds the QME estimates of the regression coefficients by maximizing the objective function described in Lee (1993) wrt the vector of regression coefficients. The maximization is performed by optim using the "Nelder–Mead" method. 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).

The starting values of the regression coefficients can have a great impact on the result of the maximization. For this reason 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. For more detailed information see Karlsson and Lindmark (2014).

Value

qme returns an object of class "qme".

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 qme

An object of class "qme", a list with elements:

Author(s)

Anita Lindmark and Maria Karlsson

References

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

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

See Also

qme.fit, the function that does the actual fitting

lt, for estimation of models with truncated response variables using the LT estimator

stls, for estimation of models with truncated response variables using the STLS estimator

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

Examples

##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 to consistently estimate the slope parameters
qme(y~x1+x2+x3, dtrunc, point=0, direction="left", cval="ml", const=1, 
   beta="ml", covar=FALSE)
   
##Example using data "PM10trunc"
data(PM10trunc)

qmepm10 <- qme(PM10~cars+temp+wind.speed+temp.diff+wind.dir+hour+day, 
   data=PM10trunc, point=2, control=list(maxit=4500))

summary(qmepm10)

Class "qme"

Description

Documentation on S4 class "qme".

Objects from the Class

Objects from the class are usually obtained by a call to the function qme.

Slots

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

cval:

Object of class "data.frame" containing information about the threshold value used

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Methods

coef

signature(object = "qme"): extracts the coefficients of the model fitted using qme

fitted

signature(object = "qme"): extracts the fitted values of the model fitted using qme

print

signature(x = "qme"): print method

residuals

signature(object = "qme"): extracts the residuals of the model fitted using qme

summary

signature(object = "qme"): summary method

vcov

signature(object = "qme"): extracts the covariance matrix of the model fitted using qme

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function qme and class "summary.qme"

Examples

showClass("qme")

Function for fitting QME

Description

Function to find QME estimates of the regression coefficients for regression models with truncated response variables. Uses optim. Intended to be called through qme, not on its own, since qme also transforms data into the correct form etc.

Usage

qme.fit(formula, mf, point, direction, bet, cv, ...)

Arguments

Value

a list with components:

Author(s)

Anita Lindmark and Maria Karlsson

See Also

qme

Examples

require(utils)
##Model frame
n <- 10000
x <- rnorm(n,0,2)
y <- 2+x+4*rnorm(n)
d <- data.frame(y=y, x=x)
dl0 <- subset(d, y>0)
mf <- model.frame(y~x, data=dl0)

##Starting values and threshold value
lmmod <- lm(data=mf)
bet <- lmmod$coef
bet <- matrix(bet)
cv <- sqrt(deviance(lmmod)/df.residual(lmmod))

str(qme. <- qme.fit(y~x,mf,point=0,direction="left",bet,cv))

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

Description

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

Usage

stls(formula, data, point = 0, direction = "left", beta = "ml", 
    covar = FALSE, na.action, ...)
## S4 method for signature 'stls'
print(x, digits = max(3, getOption("digits") - 3), ...)
## S4 method for signature 'stls'
summary(object, level=0.95, ...)
## S4 method for signature 'summary.stls'
print(x, digits= max(3, getOption("digits") - 3), ...)
## S4 method for signature 'stls'
coef(object,...)
## S4 method for signature 'stls'
vcov(object,...)
## S4 method for signature 'stls'
residuals(object,...)
## S4 method for signature 'stls'
fitted(object,...)

Arguments

Details

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).

Value

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:

Author(s)

Anita Lindmark and Maria Karlsson

References

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/

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

See Also

stls.fit, 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

Examples

##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"
data(PM10trunc)

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

summary(stlspm10)

Class "stls"

Description

Documentation on S4 class "stls".

Objects from the Class

Objects from the class are usually obtained by a call to the function stls.

Slots

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Methods

coef

signature(object = "stls"): extracts the coefficients of the model fitted using stls

fitted

signature(object = "stls"): extracts the fitted values of the model fitted using stls

print

signature(x = "stls"): print method

residuals

signature(object = "stls"): extracts the residuals of the model fitted using stls

summary

signature(object = "stls"): summary method

vcov

signature(object = "stls"): extracts the covariance matrix of the model fitted using stls

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function stls and class "summary.stls"

Examples

showClass("stls")

Function for fitting STLS

Description

Function that utilizes optim to find STLS estimates of the regression coefficients for regression models with truncated response variables. Intended to be called through stls, not on its own, since stls also transforms data into the correct form etc.

Usage

stls.fit(formula,mf, point, direction, bet, ...)

Arguments

Value

a list with components:

Author(s)

Anita Lindmark and Maria Karlsson

See Also

stls

Examples

require(utils)
##Model frame
n <- 10000
x <- rnorm(n,0,2)
y <- 2+x+4*rnorm(n)
d <- data.frame(y=y, x=x)
dl0 <- subset(d, y>0)
mf <- model.frame(y~x, data=dl0)


##Starting values
lmmod <- lm(data=mf)
bet <- lmmod$coef
bet <- matrix(bet)

str(stls. <- stls.fit(y~x,mf,point=0,direction="left",bet))

Class "summary.lt"

Description

Documentation on S4 class "summary.lt"

Objects from the Class

Objects from the class are usually obtained by a calling summary on an object of class "lt".

Slots

level:

Object of class "numeric" the level of confidence for confidence intervals

confint:

Object of class "matrix" confidence intervals for regression coefficients

bootconfint:

Object of class "matrix" bootstrap confidence intervals for regression coefficients

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

cvalues:

Object of class "data.frame" containing information about the threshold values used

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Extends

Class "lt", directly.

Methods

print

signature(x = "summary.lt"): print method

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function lt and class "lt"

Examples

showClass("summary.lt")

Class "summary.qme"

Description

Documentation on S4 class "summary.qme"

Objects from the Class

Objects from the class are usually obtained by a calling summary on an object of class "qme".

Slots

level:

Object of class "numeric" the level of confidence for confidence intervals

confint:

Object of class "matrix" confidence intervals for regression coefficients

bootconfint:

Object of class "matrix" bootstrap confidence intervals for regression coefficients

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

cval:

Object of class "data.frame" containing information on the threshold value used

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Extends

Class "qme", directly.

Methods

print

signature(x = "summary.qme"): print method

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function qme and class "qme"

Examples

showClass("summary.qme")

Class "summary.stls"

Description

Documentation on S4 class "summary.stls"

Objects from the Class

Objects from the class are usually obtained by a calling summary on an object of class "stls".

Slots

level:

Object of class "numeric" the level of confidence for confidence intervals

confint:

Object of class "matrix" confidence intervals for regression coefficients

bootconfint:

Object of class "matrix" bootstrap confidence intervals for regression coefficients

call:

Object of class "call" the function call

coefficients:

Object of class "matrix" the estimated coefficients from fitting a model for truncated regression using the Quadratic Mode Estimator (QME)

startcoef:

Object of class "matrix" the starting coefficients used when fitting the model

value:

Object of class "numeric" the value of the objective function corresponding to coefficients

counts:

Object of class "integer" number of iterations until convergence

convergence:

Object of class "integer" indicating whether convergence was achieved

message:

Object of class "character" a character string giving any additional information returned by the optimizer

residuals:

Object of class "matrix" the residuals of the model

fitted.values:

Object of class "matrix" the fitted values

df.residual:

Object of class "integer" the residual degrees of freedom

covariance:

Object of class "matrix" the estimated covariance matrix

bootrepl:

Object of class "matrix" bootstrap replicates used to estimate the covariance matrix

Extends

Class "stls", directly.

Methods

print

signature(x = "summary.stls"): print method

Author(s)

Anita Lindmark and Maria Karlsson

See Also

Function stls and class "stls"

Examples

showClass("summary.stls")