SemiParBIVProbit (version 3.2-9)

LM.bpm: Lagrange Multiplier Test (Score Test)

Description

Before fitting a bivariate probit model, LM.bpm can be used to test the hypothesis of absence of endogeneity or correlated model equations/errors or non-random sample selection.

Usage

LM.bpm(formula.eq1, formula.eq2, data, selection=FALSE, FI=FALSE)

Arguments

formula.eq1

A formula for equation 1.

formula.eq2

A formula for equation 2.

data

An optional data frame, list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which LM.bpm is

selection

If TRUE, then the test is performed for the sample selection model case.

FI

If TRUE, then the Fisher (rather than the observed) information matrix is used.

Value

• It returns a numeric p-value corresponding to the null hypothesis $\rho$.

Details

This Lagrange multiplier test (also known as score test) is used here for testing the null hypothesis $\rho$ (i.e. no endogeneity or non-random sample selection, depending on the model being fitted). Its main advantage is that it does not require an estimate of the model parameter vector under the alternative hypothesis. Asymptotically, it takes a Chi-squared distribution with one degree of freedom. Full details can be found in Marra et al. (in press). Note that, when selection=FALSE and FI=TRUE, a convenient simplification based on the result that the Fisher information matrix becomes block diagonal is employed (Marra et al., in press). Also, the current version of the Fisher information is not adequate for the sample selection and endogeneity cases.

References

Marra G., Radice R. and Missiroli S. (in press), Testing the Hypothesis of Absence of Unobserved Confounding in Semiparametric Bivariate Probit Models. Computational Statistics.

See Also

SemiParBIVProbit

Examples

## see examples for SemiParBIVProbit