LM.bpm: Lagrange Multiplier Test (Score Test)

Description

LM.bpm can be used to test the hypothesis of absence of endogeneity or sample selection before fitting a bivariate probit model.

Usage

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

Arguments

formula.eq1

A GAM formula for equation 1.

formula.eq2

A GAM 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 case.

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 for testing the null hypothesis $\rho$ (i.e. no endogeneity or 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. (submitted). Note that, for the case of endogeneity, when FI=TRUE a convenient simplification based on the result that the Fisher information matrix becomes block diagonal is employed (Marra et al., submitted). This is also consistent with the results by Kiefer (1982) for multivariate probit models.

References

Kiefer N.M. (1982), Testing for dependence in multivariate probit models. Biometrika, 69(1), 161-166. Marra G., Radice R. and Missiroli S., Testing for the Absence of Unobserved Confounding in Semiparametric Bivariate Probit Models. Submitted.

Examples

Run this code

## see examples for SemiParBIVProbit

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