ncv_tests {mlmhelpr}

Non-constant Variance Tests at Level-1 (experimental)

Description

Computes three different Non-constant variance tests: the H test as discussed in Raudenbush and Bryk (2002, pp. 263-265) and Snijders and Bosker (2012, p. 159-160), an approximate Levene's test discussed by Hox et al. (2018, p. 238), and a variation of the Breusch-Pagan test.

For the H test, the user must specify the level-1 formula. This test computes a standardized measure of dispersion for each level-2 group and detects heteroscedasticity in the form of between-group differences in the level-one residuals variances. The standardized measure of dispersion is based on estimated ordinary least squares residuals in each group.

The Levene's test computes a oneway analysis of variance of the level-2 grouping variable on the squared residuals of the model. This test examines whether the variance of the residuals is the same in all groups.

The Breusch-Pagan test regresses the squared residuals on the fitted model. A likelihood ratio test is used to compare this model with a with a null model that regresses the squared residuals on an empty model with the same random effects. This test examines whether the variance of the residuals depends on the predictor variables.

Usage

ncv_tests(model, formula = NULL, verbose = FALSE)

Arguments

model

a mixed model produced using the lme4 package and the lmer() function. This is an object of class merMod and subclass lmerMod. Currently, only supports 2-level models.

formula

level-1 formula to compute H test. Formula should be of the form y \sim x_1 + ... + x_n \; | \; g where y is the response, x_1 + ... + x_n are the covariates, and g is the grouping factor, see lme4::lmList for details.

verbose

return additional statistics including d-values and outliers from H test; adjusted R-squared, ANOVA results, and mean residual by cluster for Levene test; and likelihood ratio test for B-P test.

Value

A list containing results from the three non-constant variance tests.

References

Hox JJ, Moerbeek M, van de Schoot R (2018). Multilevel Analysis: Techniques and Applications. Taylor and Francis. ISBN 9781138121362.

Raudenbush SW, Bryk AS (2002). Hierarchical Linear Models: Applications and Data Analysis Methods. SAGE. ISBN 9780761919049.

Singer JD, Willett JB (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press. ISBN 978-0-19-515296-8.

Examples

fit <- lme4::lmer(mathach ~ 1 + ses + catholic + (1|id), data=hsb, REML=FALSE)

ncv_tests(fit)

# extract outliers from H test
test <- ncv_tests(fit, formula = mathach ~ 1 + ses | id, verbose = TRUE)
test$H_test$outliers