sampleSelection (version 0.6-2)

probit: Probit binary choice model

Description

This function calculates probit binary choice model

Usage

probit(formula, subset, start = NULL, data = sys.frame(sys.parent()),
       x=FALSE, y = FALSE, model = FALSE, method="ML", ... )

Arguments

formula

a symbolic description of the model to be fit, in the form response ~ explanatory variables (see also details).

subset

an optional vector specifying a subset of observations to be used in the fitting process.

start

inital value of parameters.

data

an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which probit is called.

x, y, model

logicals. If TRUE the corresponding components of the fit (the model matrix, the response, the model frame) are returned.

method

the method to use; for fitting, currently only method = "ML" (Maximum Likelihood) is supported; method = "model.frame" returns the model frame (the same as with model = TRUE, see below).

...

further arguments for maxLik.

Value

• An object of class "probit". It is a list with following components:
• LRT
  Likelihood ration test. The full model is tested against H0: the parameters have no effect on the result. This is a list with components LRT{The LRT value} df{Degrees of freedom for LRT (= df of the model - 1)} LRT is distributed by chi2(df) under H0.
• nParam
  Number of parameters of the model including constant
• nObs
  Number of the observations
• N1
  Number of observations with non-zero (true) response
• N0
  Number of observations with zero (false) response
• df
  Number of free parameters
• x
  if requested, the model matrix used.
• y
  if requested, the model response used. The response is represented internally as 0/1 integer vector.
• model
  the model frame, only if model = TRUE or method = "model.frame".
• Other components are inherited from maxLik.

Details

The model is estimated using Maximum Likelihood method.

The dependent variable must have exactly two levels (e.g. '0' and '1', 'FALSE' and 'TRUE', or 'no' and 'yes'). probit always takes the first level as '0' and the second level as '1' -- no matter the actual value. However, by default levels are sorted in increasing order and thus, the second level is generally, e.g., '1' (after '0'), 'TRUE' (after 'FALSE'), or 'yes' (after 'no').

See Also

maxLik for ready-packaged likelihood maximisation routines and methods, glm for generalised linear models, including probit, binomial.

Examples

## A simple MC trial: note probit assumes normal errors
x <- runif(100)
e <- 0.5*rnorm(100)
y <- x + e
summary(probit((y > 0) ~ x))
## female labour force participation probability
data(Mroz87)
Mroz87$kids <- Mroz87$kids5 > 0 | Mroz87$kids618 > 0
Mroz87$age30.39 <- Mroz87$age < 40
Mroz87$age50.60 <- Mroz87$age >= 50
summary(probit(lfp ~ kids + age30.39 + age50.60 + educ + hushrs +
               huseduc + huswage + mtr + motheduc, data=Mroz87))