Help for package Rchoice

Type:

Package

Title:

Discrete Choice (Binary, Poisson and Ordered) Models with Random Parameters

Version:

0.3-6

Date:

2023-03-10

Description:

An implementation of simulated maximum likelihood method for the estimation of Binary (Probit and Logit), Ordered (Probit and Logit) and Poisson models with random parameters for cross-sectional and longitudinal data as presented in Sarrias (2016) <doi:10.18637/jss.v074.i10>.

Depends:

R (≥ 4.0), Formula, maxLik

Imports:

sandwich, miscTools, numDeriv, memisc, msm, plm, plotrix, stats, graphics

Suggests:

car, lmtest, pglm, AER

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

URL:

https://github.com/mauricio1986/Rchoice

BugReports:

https://github.com/mauricio1986/Rchoice/issues

LazyData:

RoxygenNote:

7.2.3

Encoding:

UTF-8

NeedsCompilation:

Packaged:

2023-03-10 11:44:56 UTC; mauriciosarrias

Author:

Mauricio Sarrias

[aut, cre], Yves Croissant [ctb], Achim Zeileis [ctb]

Maintainer:

Mauricio Sarrias <msarrias86@gmail.com>

Repository:

CRAN

Date/Publication:

2023-03-10 12:30:06 UTC

Doctoral Publications

Description

Data from research by Long(1990) that analizes the scientist's level of publications.

Usage

data(Articles)

Format

A data frame with 915 observations on the following 6 variables:

art: Articles during last 3 years of Ph.D.,
fem: 1 if female scientist; else 0,
mar: 1 if married; else 0,
kid5: Number of children 5 or younger,
phd: Prestige of Ph.D. department,
ment: Articles by mentor during last 3 years,

Source

Long, J. S. (1990). The origins of sex differences in science. Social Forces, 68(4), 1297-1316.
Long, J. S. (1997). Regression models for categorical and limited dependent variables (Vol. 7). Sage.
Long, J. S., & Freese, J. (2006). Regression models for categorical and limited dependent variables using Stata. Stata Press, College Station, TX.

Examples

data(Articles)

Attituded toward working mothers

Description

In 1997 and 1989, the General Social Survey asked respondents to evaluate the following statement: "A working mother can establish just as warm and secure a relationship with her children as a mother who does not work".

Usage

data(Attitudes)

Format

A data frame with 2293 observations on the following 10 variables:

warm: 1 = Strongly disagree, 2 = disagree, 3 = agree, 4 = strongly agree,
yr89: survey year: 1 = 1989; 0 = 1977,
male: 1 = male; 0 = female,
white: 1 = white; 0 = nonwhite,
age: age in years,
ed: years of education,
prst: occupational prestige,

Source

Clogg, C. C., & Shihadeh, E. S. (1994). Statistical models for ordinal variables. Thousand Oaks, CA: Sage Publications.
Long, J. S. (1997). Regression models for categorical and limited dependent variables (Vol. 7). Sage.
Long, J. S., & Freese, J. (2006). Regression models for categorical and limited dependent variables using Stata. Stata Press, College Station, TX.

Examples

data(Attitudes)

German Health Care Data

Description

German Health Care Data, unbalanced panel.

Usage

data(Health)

Format

A data frame with 27326 observations on the following 27 variables:

id: person identification number
female: female =1, male =0
year: calendar year of the observation
age: age in years
hsat: health satisfaction, 0 (low),...,10 (high)
handdum: handicapped = 1, 0 otherwise
handper: degree of handicap in percent; 0,100
hhinc: household nominal monthly net income in German marks
hhkids: children under age 16 in the household = 1; otherwise = 0
educ: years of schooling
married: married =1, otherwise = 0
haupts: highest schooling degree is Hauptschul degree = 1; otherwise = 0
reals: highest schooling degree is Realschul degree = 1, otherwise = 0
fachhs: highest schooling degree is Polytechical degree = 1; otherwise = 0
abitur: highest schooling degree is Abitur = 1; otherwise = 0
univ: highest schooling degree is university degree =1; otherwise = 0
working: employed =1; otherwise = 0
bluec: blue-collar employee = 1; otherwise = 0
whitec: white-collar employeee =1; otherwise = 0
self: self-employed = 1; otherwise = 0
beamt: civil servant = 1; otherwise = 0
docvis: number of doctor visits in last three months
hospvis: number of hospital visits in last calendar year
public: insured in public health =1; otherwise = 0
addon: insured by add-on insurance =1; otherwise = 0
hsat2: 40 observations on hsat recorded between 6 and 7 were changed to 7
newhsat: recording of hsat, (0-2) = 0, (3-5)=1, (6-8)=2, (9)=3 (10)=4

Source

Riphahn, R. T., Wambach, A., & Million, A. (2003). Incentive effects in the demand for health care: a bivariate panel count data estimation. Journal of applied econometrics, 18(4), 387-405.

References

Greene, W. H. (2003). Econometric analysis. Pearson Education India.

Examples

data(Health)

Estimate discrete choice model with random parameters

Description

Estimation of discrete choice models such as Binary (logit and probit), Poisson and Ordered (logit and probit) model with random coefficients for cross-sectional and panel data using simulated maximum likelihood.

Usage

Rchoice(
  formula,
  data,
  subset,
  weights,
  na.action,
  family,
  start = NULL,
  ranp = NULL,
  R = 40,
  haltons = NA,
  seed = NULL,
  correlation = FALSE,
  panel = FALSE,
  index = NULL,
  mvar = NULL,
  print.init = FALSE,
  init.ran = 0.1,
  gradient = TRUE,
  ...
)

## S3 method for class 'Rchoice'
terms(x, ...)

## S3 method for class 'Rchoice'
model.matrix(object, ...)

## S3 method for class 'Rchoice'
coef(object, ...)

## S3 method for class 'Rchoice'
fitted(object, ...)

## S3 method for class 'Rchoice'
residuals(object, ...)

## S3 method for class 'Rchoice'
df.residual(object, ...)

## S3 method for class 'Rchoice'
update(object, new, ...)

## S3 method for class 'Rchoice'
logLik(object, ...)

## S3 method for class 'Rchoice'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  width = getOption("width"),
  ...
)

## S3 method for class 'Rchoice'
summary(object, ...)

## S3 method for class 'summary.Rchoice'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  width = getOption("width"),
  ...
)

Arguments

formula

a symbolic description of the model to be estimated. The formula consists in two parts. The first one is reserved for standard variables with fixed and random parameters. The second one is reserved for variables that enter in the mean of the random parameters. See for example rFormula,

data

the data. It may be a pdata.frame object or an ordinary data.frame,

subset

an optional vector specifying a subset of observations,

weights

an optional vector of weigths,

na.action

a function wich indicated what should happen when the data contains NA's,

family

the distribution to be used. It might be family = binomial("probit") for a Probit Model, family = binomial("logit") for a Logit model, family = ordinal("probit") for an Ordered Probit Model, family = ordinal("logit") for a Ordered Logit Model for an Ordered Logit Model, and family = "poisson" for a Poisson Model,

start

a vector of starting values,

ranp

a named vector whose names are the random parameters and values the distribution: "n" for normal, "ln" for log-normal, "cn" for truncated normal, "u" for uniform, "t" for triangular, "sb" for Johnson Sb,

R

the number of draws if ranp is not NULL,

haltons

only relevant if ranp is not NULL. If not NULL, halton sequence is used instead of pseudo-random numbers. If haltons=NA, some default values are used for the prime of the sequence and for the number of element dropped. Otherwise, haltons should be a list with elements prime and drop,

seed

the seed for the pseudo-random draws. This is only relevant if haltons = NULL,

correlation

only relevant if ranp is not NULL. If TRUE, the correlation between random parameters is taken into account,

panel

if TRUE a panel data model is estimated,

index

a string indicating the ‘id’ for individuals in the data. This argument is not required if data is a pdata.frame object,

mvar

only valid if ranp is not NULL. This is a named list, where the names correspond to the variables with random parameters, and the values correspond to the variables that enter in the mean of each random parameters,

print.init

if TRUE, the initial values for the optimization procedure are printed,

init.ran

initial values for standard deviation of random parameters. Default is 0.1,

gradient

if FALSE, numerical gradients are used for the optimization procedure of models with random parameters,

...

further arguments passed to maxLik,

x, object

and object of class Rchoice,

new

an updated formula for the update method,

digits

number of digits,

width

width,

Details

The models are estimated using the maxLik function from maxLik package.

If ranp is not NULL, the random parameter model is estimated. A random parameter model or random coefficient models permits regression parameter to vary across individuals according to some distribution. A fully parametric random parameter model specifies the latent variable y^{*} conditional on regressors x and given parameters \beta_i to have conditional density f(y|x, \beta_i) where \beta_i are iid with density g(\beta_i|\theta_i). The density is assumed a priori by the user by the argument ranp. If the parameters are assumed to be normally distributed \beta_i ~ N(\beta, \Sigma), then the random parameter are constructed as:

\beta_{ir}=\beta+L\omega_{ir}

where LL'=\Sigma and \omega_{ir} is the r-th draw from standard normal distribution for individual i.

Once the model is specified by the argument family, the model is estimated using Simulated Maximum Likelihood (SML). The probabilities, given by f(y|x, \beta_i), are simulated using R pseudo-draws if halton=NULL or R halton draws if halton = NA. The user can also specified the primes and the number of dropped elements for the halton draws. For example, if the model consists of two random parameters, the user can specify haltons = list("prime" = c(2, 3), "drop" = c(11, 11)).

A random parameter hierarchical model can be estimated by including heterogeneity in the mean of the random parameters:

\beta_{ir}=\beta+\pi's_i+L\omega_{ir}

Rchoice manages the variables in the hierarchical model by the formula object: all the hierarchical variables (s_i) are included after the | symbol. The argument mvar indicate which variables enter in each random parameter. See examples below

Value

An object of class “Rchoice”, a list elements:

coefficients

the named vector of coefficients,

family

type of model,

link

distribution of the errors,

logLik

a set of values of the maximum likelihood procedure,

mf

the model framed used,

formula

the formula (a Formula object),

time

proc.time() minus the start time,

freq

frequency of dependent variable,

draws

type of draws used,

R.model

TRUE if a random parameter model is fitted,

R

number of draws used,

bi

an array of dimension N \times R \times K with the individual parameters,

Qir

matrix of dimension N \times R representing P_{ir}/\sum_r P_{ir},

ranp

vector indicating the variables with random parameters and their distribution,

probabilities

the fitted probabilities for each individuals,

residuals

the residuals,

call

the matched call.

Author(s)

Mauricio Sarrias msarrias86@gmail.com

References

Greene, W. H. (2012). Econometric Analysis. 7 edition. Prentice Hall.

Train, K. (2009). Discrete Choice Methods with Simulation. Cambridge university press.

Examples


## Probit model
data("Workmroz")
probit <- Rchoice(lfp ~ k5 + k618 + age + wc + hc + lwg + inc,  
                 data = Workmroz, family = binomial('probit'))
summary(probit)

## Poisson model
data("Articles")
poisson <- Rchoice(art ~ fem + mar + kid5 + phd + ment, data = Articles, family = poisson)
summary(poisson)

## Ordered probit model
data("Health")
oprobit <- Rchoice(newhsat ~ age + educ + hhinc + married + hhkids, 
data = Health, family = ordinal('probit'), subset = year == 1988)
summary(oprobit)

## Poisson Model with Random Parameters
poisson.ran <- Rchoice(art ~ fem + mar + kid5 + phd + ment, 
                       data = Articles,  family = poisson,
                       ranp = c(kid5 = "n", phd = "n", ment = "n"))
summary(poisson.ran)                      

## Poisson Model with Correlated Random Parameters
poissonc.ran <- Rchoice(art ~ fem + mar + kid5 + phd + ment, 
                       data = Articles, 
                       ranp = c(kid5 = "n", phd = "n", ment = "n"), 
                       family = poisson, 
                       correlation =  TRUE,
                       R = 20)
summary(poissonc.ran)

## Hierarchical Poisson Model
poissonH.ran <- Rchoice(art ~ fem + mar + kid5 + phd + ment | fem + phd,
                       data = Articles,
                       ranp = c(kid5 = "n", phd = "n", ment = "n"),
                       mvar = list(phd = c("fem"), ment = c("fem", "phd")),
                       family = poisson,
                       R = 10)
summary(poissonH.ran)

## Ordered Probit Model with Random Effects and Random Parameters
Health$linc <- log(Health$hhinc)
oprobit.ran <- Rchoice(newhsat ~ age + educ + married + hhkids + linc,
                     data = Health[1:2000, ],
                     family = ordinal('probit'),
                     ranp = c(constant = "n", hhkids = "n", linc = "n"),
                     panel = TRUE,
                     index = "id",
                     R = 10,
                     print.init = TRUE)
summary(oprobit.ran)

Labor Force Participation

Description

Data extracted by Mroz(1987) from the 1976 Panel Study of Income Dynacmis. The sample consists of 753 white, married women between the ages of 30 and 60.

Usage

data(Workmroz)

Format

A data frame with 753 observations on the following 9 variables:

lfp: 1 if wife is in the paid labor force; else 0,
k5: Number of children ages 5 and younger,
k618: Number of children ages 6 to 18,
age: Wife's age in years,
wc: 1 if wife attended college; else 0,
hc: 1 if husband attended college; else 0,
lwg: Log of wife's estimated wage rate,
inc: Family income excluding wife's wage,
linc: Log of Family income excluding wife's wage,

Source

Mroz, T. A. (1987). The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions. Econometrica, 55(4), 765-799

Examples

data(Workmroz)

Bread for sandwiches

Description

Computes the “bread” of the sandwich covariance matrix for a model of class Rchoice

Usage

## S3 method for class 'Rchoice'
bread(x, ...)

Arguments

x

a fitted model of class Rchoice,

...

Other arguments when bread is applied to another class object.

Details

For more information see bread from the package sandwich.

Value

the covariance matrix times observations

References

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16.

Examples

## Probit model
data("Workmroz")
probit <- Rchoice(lfp ~ k5 + k618 + age + wc + hc + lwg + inc,  
                  data = Workmroz , family = binomial('probit'))
summary(probit)

library("sandwich")
bread(probit)

Get average marginal effects for heterokedastic binary models and IV probit models

Description

Obtain the average marginal effects from hetprob or ivpml class models.

Usage

effect(object, ...)

Arguments

object

an object of class hetprob or ivpml.

...

Additional arguments to be passed.

Value

Estimates of the average marginal effects computed as the average for each individual.

Examples


# Data
library("AER")
data("PSID1976")
PSID1976$lfp  <- as.numeric(PSID1976$participation == "yes")
PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
                                      levels = c(FALSE, TRUE), 
                                      labels = c("no", "yes")))
PSID1976$finc <-  PSID1976$fincome / 10000
                                 
# Average marginal effects for heteroskedastic Probit model
labor_het <- hetprob(lfp ~  age + I(age^2) + finc + education + factor(kids) | 
                            factor(kids) + finc,              
                     data = PSID1976,                        
                     link = "probit")
eff_labor_het <- effect(labor_het)
summary(eff_labor_het)

# Average marginal effects for IV probit model 
# (nwincome is endogenous and heducation is the additional instrument)
PSID1976$nwincome <- with(PSID1976, (fincome - hours * wage)/1000)
fiml.probit <- ivpml(lfp ~  education + experience + I(experience^2) + age + 
                            youngkids + oldkids + nwincome |
                            education + experience + I(experience^2) + age + 
                            youngkids + oldkids + heducation, 
                     data = PSID1976)
summary(effect(fiml.probit))
summary(effect(fiml.probit, asf = FALSE))

Get the conditional individual coefficients

Description

This a helper function to obtain the individuals' conditional estimate of the random parameters or compensating variations.

Usage

## S3 method for class 'Rchoice'
effect(object, par = NULL, effect = c("cv", "ce"), wrt = NULL, ...)

Arguments

object

an object of class Rchoice,

par

a string giving the name of the variable with random parameter,

effect

a string indicating what should be computed: the conditional expectation of the individual coefficients "ce", or the conditional expectation of the individual compensating variations "cv",

wrt

a string indicating respect to which variable the compensating variation should be computed,

...

further arguments. Ignored.

Value

A named list where “mean” contains the individuals' conditional mean for the random parameter or compensating variation, and where ‘sd.est’ contains their standard errors.

References

Greene, W. H. (2012). Econometric Analysis, Seventh Edition. Pearson Hall.
Train, K. (2009). Discrete Choice Methods with Simulation. Cambridge university press.

Examples


# Poisson with random parameters
data("Articles")
poisson.ran <- Rchoice(art ~ fem + mar + kid5 + phd + ment, 
                       data = Articles,  family = poisson,
                       ranp = c(kid5 = "n", phd = "n", ment = "n"), 
                       R = 10)

## Get the individuals' conditional mean and their standard errors for ment                      
bi.ment <- effect(poisson.ran, par = "ment", effect = "ce")
summary(bi.ment$mean)
summary(bi.ment$sd.est)

Get average marginal effects for heterokedastic binary models

Description

Obtain the average marginal effects from hetprob class model.

Usage

## S3 method for class 'hetprob'
effect(object, vcov = NULL, digits = max(3, getOption("digits") - 2), ...)

## S3 method for class 'effect.hetprob'
summary(object, ...)

## S3 method for class 'effect.hetprob'
print(x, ...)

## S3 method for class 'summary.effect.hetprob'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object

an object of class hetprob and effect.hetprob for summary and print method.

vcov

an estimate of the asymptotic variance-covariance matrix of the parameters for a hetprob object.

digits

the number of digits.

...

further arguments.Ignored.

x

an object of class effect.hetprob.

Details

This function allows to obtain the average marginal effects (not the marginal effects at the mean). The standard errors are computed using Delta Method.

Value

An object of class effect.heprob.

Author(s)

Mauricio Sarrias.

Examples


# Data
library("AER")
data("PSID1976")
PSID1976$lfp  <- as.numeric(PSID1976$participation == "yes")
PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
                                      levels = c(FALSE, TRUE), 
                                      labels = c("no", "yes")))
                                      PSID1976$finc <-  PSID1976$fincome / 10000
                                 
# Average marginal effects for heteroskedastic Probit model
labor_het <- hetprob(lfp ~  age + I(age^2) + finc + education + factor(kids) | 
                            factor(kids) + finc,              
                     data = PSID1976,                        
                     link = "probit")
eff_labor_het <- effect(labor_het)
summary(eff_labor_het)

Get average marginal effects for IV Probit model.

Description

Obtain the average marginal effects from ivpml class model.

Usage

## S3 method for class 'ivpml'
effect(
  object,
  vcov = NULL,
  asf = TRUE,
  digits = max(3, getOption("digits") - 2),
  ...
)

## S3 method for class 'effect.ivpml'
summary(object, ...)

## S3 method for class 'effect.ivpml'
print(x, ...)

## S3 method for class 'summary.effect.ivpml'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object

an object of class ivpml and effect.ivpml for summary and print method.

vcov

an estimate of the asymptotic variance-covariance matrix of the parameters for a ivpml object.

asf

if TRUE, the average structural function is used.

digits

the number of digits.

...

further arguments.Ignored.

x

an object of class effect.ivpml.

Details

This function allows to obtain the average marginal effects (not the marginal effects at the mean). The standard errors are computed using Delta Method.

Value

An object of class effect.ivpml.

Author(s)

Mauricio Sarrias.

Examples

 
# Data
library("AER")
data("PSID1976")
PSID1976$lfp  <- as.numeric(PSID1976$participation == "yes")
PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
                                      levels = c(FALSE, TRUE), 
                                      labels = c("no", "yes")))
                                      
# Average marginal effects for IV probit model 
# (nwincome is endogenous and heducation is the additional instrument)
PSID1976$nwincome <- with(PSID1976, (fincome - hours * wage)/1000)
fiml.probit <- ivpml(lfp ~  education + experience + I(experience^2) + age + 
                            youngkids + oldkids + nwincome |
                            education + experience + I(experience^2) + age + 
                            youngkids + oldkids + heducation, 
                     data = PSID1976)
summary(effect(fiml.probit))
summary(effect(fiml.probit, asf = FALSE))

Gradient for observations

Description

It extracts the gradient for each observations evaluated at the estimated parameters for a model of class Rchoice

Usage

## S3 method for class 'Rchoice'
estfun(x, ...)

Arguments

x

a fitted model of class Rchoice,

...

Other arguments when estfun is applied to another class object

Details

For more information see estfun from package sandwich.

Value

the gradient matrix of dimension n times k

References

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16.

Get Model Summaries for use with "mtable" for object of class Rchoice

Description

A generic function to collect coefficients and summary statistics from a Rchoice object. It is used in mtable

Usage

## S3 method for class 'Rchoice'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

a Rchoice object,

alpha

level of the confidence intervals,

...

further arguments,

Details

For more details see package memisc.

Get Model Summaries for use with "mtable" for objects of class effect.hetprob

Description

A generic function to collect coefficients and summary statistics from a effect.hetprob object. It is used in mtable

Usage

## S3 method for class 'effect.hetprob'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

an effect.hetprob object,

alpha

level of the confidence intervals,

...

further arguments,

Details

For more details see package memisc.

Get Model Summaries for use with "mtable" for objects of class effect.ivpml

Description

A generic function to collect coefficients and summary statistics from a effect.ivpml object. It is used in mtable

Usage

## S3 method for class 'effect.ivpml'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

an effect.ivpml object,

alpha

level of the confidence intervals,

...

further arguments,

Details

For more details see package memisc.

Get Model Summaries for use with "mtable" for objects of class hetprob

Description

A generic function to collect coefficients and summary statistics from a hetprob object. It is used in mtable

Usage

## S3 method for class 'hetprob'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

a hetprob object,

alpha

level of the confidence intervals,

...

further arguments,

Details

For more details see package memisc.

Get Model Summaries for use with "mtable" for objects of class ivpml

Description

A generic function to collect coefficients and summary statistics from a ivpml object. It is used in mtable

Usage

## S3 method for class 'ivpml'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

a ivpml object,

alpha

level of the confidence intervals,

...

further arguments,

Details

For more details see package memisc.

Estimate heteroskedastic binary (Probit or Logit) model.

Description

Estimation of binary dependent variables, either probit or logit, with heteroskedastic error terms for cross-sectional dataset.

Usage

hetprob(formula, data, link = c("probit", "logit"), ...)

## S3 method for class 'hetprob'
terms(x, ...)

## S3 method for class 'hetprob'
model.matrix(object, ...)

## S3 method for class 'hetprob'
estfun(x, ...)

## S3 method for class 'hetprob'
bread(x, ...)

## S3 method for class 'hetprob'
vcov(object, eigentol = 1e-12, ...)

## S3 method for class 'hetprob'
df.residual(object, ...)

## S3 method for class 'hetprob'
coef(object, ...)

## S3 method for class 'hetprob'
logLik(object, ...)

## S3 method for class 'hetprob'
print(x, ...)

## S3 method for class 'hetprob'
summary(object, eigentol = 1e-12, ...)

## S3 method for class 'summary.hetprob'
print(x, digits = max(3, getOption("digits") - 2), ...)

## S3 method for class 'hetprob'
predict(object, newdata = NULL, type = c("xb", "pr", "sigma"), ...)

Arguments

formula

a symbolic description of the model of the form y ~ x | z where y is the binary dependent variable and x and z are regressors variables for the mean of the model and lnsigma.

data

the data of class data.frame.

link

the assumption of the distribution of the error term. It could be either link = "probit" or link = "logit".

...

arguments passed to maxLik.

x, object

an object of class hetprob.

eigentol

the standard errors are only calculated if the ratio of the smallest and largest eigenvalue of the Hessian matrix is less than eigentol. Otherwise the Hessian is treated as singular.

digits

the number of digits.

newdata

optionally, a data frame in which to look for variables with which to predict.

type

the type of prediction required. The default, type = xb, is on the linear prediction without the variance. If type = pr, the predicted probabilities of a positive outcome is returned. Finally, if type = sigma the predictions of \sigma for each individual is returned.

Details

The heterokedastic binary model for cross-sectional data has the following structure:

y_i^* = x_i^\top\beta + \epsilon_i,

with

var(\epsilon_i|x_i, z_i) = \sigma_i^2 = \left[\exp\left(z_i^\top\delta\right)\right]^2,

where y_i^* is the latent (unobserved) dependent variable for individual i = 1,...,N; x_i is a K\times 1 vector of independent variables determining the latent variable y_i^* (x variables in formula); and \epsilon_i is the error term distributed either normally or logistically with E(\epsilon_i|z_i, x_i) = 0 and heterokedastic variance var(\epsilon_i|x_i, z_i) = \sigma_i^2, \forall i = 1,...,N. The variance for each individual is modeled parametrically assuming that it depends on a P\times 1 vector observed variables z_i (z in formula), whereas \delta is the vector of parameters associated with each variable. It is important to emphasize that z_i does not include a constant, otherwise the parameters are not identified.

The models are estimated using the maxLik function from maxLik package using both analytic gradient and hessian (if Hess = TRUE). In particular, the log-likelihood function is:

\log L(\theta) = \sum_i^n\log \left\lbrace \left[1- F\left(\frac{x_i^\top\beta}{\exp(z_i^\top\delta)}\right)\right]^{1-y_i}\left[F\left(\frac{x_i^\top\beta}{\exp(z_i^\top\delta)}\right)\right]^{y_i}\right\rbrace.

Value

An object of class “hetprob”, a list elements:

logLik0

logLik for the homokedastic model,

f1

the formula,

mf

the model framed used,

call

the matched call.

Author(s)

Mauricio Sarrias.

References

Greene, W. H. (2012). Econometric Analysis. 7 edition. Prentice Hall.

Examples


# Estimate a heteroskedastic probit and logit model
data("Health")

het.probit <- hetprob(working ~ factor(female) + factor(year) + educ + age + I(age^2) | 
                                factor(female) + age + I(age^2), 
                     data = Health, 
                     link = "probit")
summary(het.probit)

het.logit <- hetprob(working ~ factor(female) + factor(year) + educ + age + I(age^2) | 
                               factor(female) + age + I(age^2), 
                    data = Health, 
                    link = "logit")
summary(het.logit)

Estimate Instrumental Variable Probit model by Maximum Likelihood.

Description

Estimation of Probit model with one endogenous and continuous variable by Maximum Likelihood.

Usage

ivpml(formula, data, messages = TRUE, ...)

## S3 method for class 'ivpml'
terms(x, ...)

## S3 method for class 'ivpml'
model.matrix(object, ...)

## S3 method for class 'ivpml'
estfun(x, ...)

## S3 method for class 'ivpml'
bread(x, ...)

## S3 method for class 'ivpml'
vcov(object, ...)

## S3 method for class 'ivpml'
df.residual(object, ...)

## S3 method for class 'ivpml'
coef(object, ...)

## S3 method for class 'ivpml'
logLik(object, ...)

## S3 method for class 'ivpml'
print(x, ...)

## S3 method for class 'ivpml'
summary(object, eigentol = 1e-12, ...)

## S3 method for class 'summary.ivpml'
print(x, digits = max(3, getOption("digits") - 2), ...)

## S3 method for class 'ivpml'
predict(object, newdata = NULL, type = c("xb", "pr", "stdp"), asf = TRUE, ...)

Arguments

formula

a symbolic description of the model of the form y ~ x | z where y is the binary dependent variable, x includes the exogenous and the endogenous continuous variable, and z is the complete set of instruments.

data

the data of class data.frame.

messages

if TRUE, then additional messages for the estimation procedure are displayed.

...

arguments passed to maxLik.

x, object

an object of class ivpml.

eigentol

the standard errors are only calculated if the ratio of the smallest and largest eigenvalue of the Hessian matrix is less than eigentol. Otherwise the Hessian is treated as singular.

digits

the number of digits.

newdata

optionally, a data frame in which to look for variables with which to predict.

type

the type of prediction required. The default, type = xb, is on the linear prediction. If type = pr, the predicted probabilities of a positive outcome is returned. Finally, if type = stdp the standard errors of the linear predictions for each individual is returned.

asf

if TRUE, the average structural function is used. This option is not allowed with xb or stdp.

Details

The IV probit for cross-sectional data has the following structure:

y_{1i}^* = x_i^\top\beta + \gamma y_{2i}+ \epsilon_i,

with

y_{2i} = z_i^\top\delta + \upsilon_i,

where y_{1i}^* is the latent (unobserved) dependent variable for individual i = 1,...,N; y_{2i} is the endogenous continuous variable; z_i is the vector of exogenous variables which also includes the instruments for y_{2i}; and (\epsilon, \upsilon) are normal jointly distributed.

The model is estimated using the maxLik function from maxLik package using analytic gradient.

Author(s)

Mauricio Sarrias.

References

Greene, W. H. (2012). Econometric Analysis. 7 edition. Prentice Hall.

Examples

 
# Data
library("AER")
data("PSID1976")
PSID1976$lfp  <- as.numeric(PSID1976$participation == "yes")
PSID1976$kids <- with(PSID1976, factor((youngkids + oldkids) > 0,
                                      levels = c(FALSE, TRUE), 
                                      labels = c("no", "yes")))
                                      
# IV probit model by MLE
# (nwincome is endogenous and heducation is the additional instrument)
PSID1976$nwincome <- with(PSID1976, (fincome - hours * wage)/1000)
fiml.probit <- ivpml(lfp ~  education + experience + I(experience^2) + age + 
                            youngkids + oldkids + nwincome |
                            education + experience + I(experience^2) + age + 
                            youngkids + oldkids + heducation, 
                     data = PSID1976)
summary(fiml.probit)

Plot the distribution of conditional expectation for random parameters.

Description

Plot the distribution of the conditional expectation of the random parameters or compensating variations for objects of class Rchoice.

Usage

## S3 method for class 'Rchoice'
plot(
  x,
  par = NULL,
  effect = c("ce", "cv"),
  wrt = NULL,
  type = c("density", "histogram"),
  adjust = 1,
  main = NULL,
  col = "indianred1",
  breaks = 10,
  ylab = NULL,
  xlab = NULL,
  ind = FALSE,
  id = NULL,
  ...
)

Arguments

x

a object of class Rchoice,

par

a string giving the name of the variable with random parameter,

effect

a string indicating what should be plotted: the conditional expectation of the individual coefficients "ce", or the conditional expectation of the individual compensating variations "cv",

wrt

a string indicating repect to which variable should be computed the compensating variation,

type

a string indicating the type of distribution: it can be a histogram or a density of the conditional expectation,

adjust

bandwidth for the kernel density,

main

an overall title for the plot,

col

color for the graph,

breaks

number of breaks for the histrogram if type = "histogram",

ylab

a title for the y axis,

xlab

a title for the x axis,

ind

a boolean. If TRUE, a 95 As default, the conditional expectation of par for the first 10 individual is plotted,

id

only relevant if ind is not NULL. This is a vector indicating the individuals for which the confidence intervals are plotted,

...

further arguments. Ignored.

Author(s)

Mauricio Sarrias

References

Greene, W. H. (2012). Econometric analysis, Seventh Edition. Pearson Hall.
Train, K. (2009). Discrete choice methods with simulation. Cambridge university press.

Examples


# Poisson with random parameters
data("Articles")
poisson.ran <- Rchoice(art ~ fem + mar + kid5 + phd + ment, 
                       data = Articles,  family = poisson,
                       ranp = c(kid5 = "n", phd = "n", ment = "n"), 
                       R = 10)

## Plot the distribution of the conditional mean for ment
plot(poisson.ran, par = "ment", type = "density")

## Plot the conditional mean for the first 20 individuals
plot(poisson.ran, par = "ment", ind =  TRUE, id = 1:20, col = "blue")

## Plot the compensating variation with respect to fem
plot(poisson.ran, par = "ment", effect = "cv", wrt = "fem", type = "histogram")

Model formula for Rchoice models

Description

Two kind of variables are used in models with individual heterogenetiy: the typical variables that enter in the latent process and those variables that enter in the random parameter (Hierarchical Model). rFormula deal with this type of models using suitable methods to extract the elements of the model.

Usage

rFormula(object)

is.rFormula(object)

## S3 method for class 'rFormula'
model.frame(formula, data, ..., lhs = NULL, rhs = NULL)

## S3 method for class 'rFormula'
model.matrix(object, data, rhs = NULL, ...)

Arguments

object

a formula form the rFormula function, for the model.matrix method, a rFormula object,

formula

a rFormula object,

data

a data.frame,

...

further arguments.

lhs

see Formula,

rhs

see Formula,

vcov method for Rchoice objects

Description

The vcov method for Rchoice objects extracts the covariance matrix of the coefficients or the random parameters. It also allows to get the standard errors for the variance-covariance matrix of the random parameters

Usage

## S3 method for class 'Rchoice'
vcov(
  object,
  what = c("coefficient", "ranp"),
  type = c("cov", "cor", "sd"),
  se = FALSE,
  digits = max(3, getOption("digits") - 2),
  ...
)

cov.Rchoice(x)

cor.Rchoice(x)

se.cov.Rchoice(x, sd = FALSE, digits = max(3, getOption("digits") - 2))

Arguments

object

a fitted model of class Rchoice,

what

indicates which covariance matrix has to be extracted. The default is coefficient. In this case the vcov behaves as usual. If what = "ranp" the covariance matrix of the random parameters is returned as default,

type

if the model is estimated with random parameters, then this argument indicates what matrix should be returned. If type = "cov", then the covariance matrix of the random parameters is returned; if type = "cor" then the correlation matrix of the random parameters is returned; if type = "sd" then the standard deviation of the random parameters is returned,

se

if TRUE and type = "cov" then the standard error of the covariance matrix of the random parameters is returned; if TRUE and type = "sd" the standard error of the standard deviation of the random parameter is returned. This argument if valid only if the model is estimated using correlated random parameters,

digits

number of digits,

...

further arguments

x

a fitted model of class Rchoice,

sd

if TRUE, then the standard deviation of the random parameters are returned,

Details

This new interface replaces the cor.Rchoice, cov.Rchoice and se.cov.Rchoice functions which are deprecated.

Doctoral Publications

Description

Usage

Format

Source

Examples

Attituded toward working mothers

Description

Usage

Format

Source

Examples

German Health Care Data

Description

Usage

Format

Source

References

Examples

Estimate discrete choice model with random parameters

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Labor Force Participation

Description

Usage

Format

Source

Examples

Bread for sandwiches

Description

Usage

Arguments

Details

Value

References

Examples

Get average marginal effects for heterokedastic binary models and IV probit models

Description

Usage

Arguments

Value

Examples

Get the conditional individual coefficients

Description

Usage

Arguments

Value

References

See Also

Examples

Get average marginal effects for heterokedastic binary models

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Get average marginal effects for IV Probit model.

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Gradient for observations

Description

Usage

Arguments

Details

Value

References