SemiParBIVProbit (version 3.3)

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, correlated model equations/errors or non-random sample selection.

Usage

LM.bpm(formula, data = list(), weights = NULL, subset = NULL, Model, 
       hess = TRUE, infl.fac = 1)

Arguments

formula

A list of two formulas, one for equation 1 and the other for equation 2. s terms are used to specify smooth smooth functions of predictors. Note that if Model = "BSS" then the first formula MUST refer

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).

weights

Optional vector of prior weights to be used in fitting.

subset

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

Model

It indicates the type of model to be used in the analysis. Possible values are "B" (bivariate model) and "BSS" (bivariate model with sample selection).

hess

If FALSE then the expected (rather than observed) information matrix is employed.

infl.fac

Inflation factor for the model degrees of freedom in the UBRE score. Smoother models can be obtained setting this parameter to a value greater than 1.

Value

• It returns a numeric p-value corresponding to the null hypothesis that $\rho$ is equal to 0.

WARNINGS

This test's implementation is only valid for models with normal errors and probit links.

Details

This Lagrange multiplier test (also known as score test) is used here for testing the null hypothesis that $\rho$ is equal to 0 (i.e. no endogeneity, non-random sample selection or correlated model equations/errors, 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. (2014) and Marra et al. (submitted).

References

Marra G., Radice R. and Filippou P. (submitted), Regression Spline Bivariate Probit Models: A Practical Approach to Testing for Exogeneity. Marra G., Radice R. and Missiroli S. (2014), Testing the Hypothesis of Absence of Unobserved Confounding in Semiparametric Bivariate Probit Models. Computational Statistics, 29(3-4), 715-741.

See Also

SemiParBIVProbit

Examples

## see examples for SemiParBIVProbit