hetprob function

Estimate heteroskedastic binary (Probit or Logit) model.

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

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.

Returns

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.

Details

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

with

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:

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)

References

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

Author(s)

Mauricio Sarrias.