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.

data

data frame used to fit model. When NULL, the default, the model frame of model is used, so id must then be a variable of the model. The model frame holds the terms of the model rather than its variables (log(x) rather than x), so a model that transforms a variable needs data, as does a model with an offset() term.

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.

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")