Breusch-Pagan LM test for random effects

Source: man/performBPRandomEffectsTest.Rd · Help: ?performBPRandomEffectsTest

Lagrange Multiplier test for the presence of a random individual effect in panel data. This is not a test for heteroscedasticity and does not respond to one; use the auxiliary-regression diagnostics for that.

Usage

performBPRandomEffectsTest(model, data = NULL, id)

Arguments

model

an object of class lm, the pooled lm() of the panel; its observations may be in any order.

data

The data frame model was fitted to, holding the individual identifier named by id, or NULL, the default. The residuals and weights are read from the fit itself, and id from the rows of data that hold the observations of the fit. Without data it is read from the model frame of model, which holds it only when it is a variable of the model under its own name (id, not factor(id)); an identifier the model does not use needs data. Since 0.16.0, data that are given are matched to the observations of the fit: rows with row names of their own by name, in any order; rows that only number themselves (a tibble, a data.table, a data frame whose row names were reset) by the row numbers of the fit, or in the order of the fit when they hold one row per observation. The rows the fit dropped may be there or not. Data whose rows cannot be shown to hold the observations of the fit are refused; see test_results.

id

individual identifier column.

Value

An object of class htest.

Details

The statistic is Breusch and Pagan (1980) equation 5, \(LM = nT / (2(T-1)) [ \sum_i (\sum_t e_{it})^2 / \sum_{it} e_{it}^2 - 1 ]^2\), which follows a chi-square distribution with one degree of freedom under the null of no individual effect. The bracketed ratio is close to one under the null and the statistic measures its squared departure from one. Before 0.11.0 the "- 1" and the square were absent and the scaling used T^2 rather than nT, which left the statistic sitting at the critical value: it rejected about a third of the time when no individual effect was present.

Supported models

It accepts an lm and a glm with the Gaussian family and the identity link, unweighted or with positive weights, a fitWLS() fit and, since 0.16.0, a rank-deficient fit, which it tests on the estimable part of its design: it gives the value of the same model fitted without the aliased columns. It refuses a glm of another family or link, a survey::svyglm() fit, a fit with a zero weight, a coefficient that is not finite for another reason, and data that lack rows or variables of the fit. The model is a pooled lm of the panel, with the units and the periods as columns of data; a plm::plm() fit is not an lm and is refused. Which model each test accepts, and why, is set out in test_results, under Supported models.

References

Breusch, T. S., & Pagan, A. R. (1980). The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics. Review of Economic Studies, 47(1), 239–253.

Examples

 df <- data.frame(id = rep(1:5, each = 4), time = rep(1:4, 5), x = runif(20), y = rnorm(20))
 m <- lm(y ~ x, data = df)
 performBPRandomEffectsTest(m, df, "id")