[R-sig-ME] Statistical significance of random-effects (lme4 or others)

[Simon Harmel]

Dear All,

Most MLM packages (e.g., HLM, SPSS, SAS, STATA) provide a p-value for the
variance components.

My understanding based on (
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#testing-significance-of-random-effects)
is that this is not possible to achieve in R, right?

If not, for my 4 models below, I assume I need to compare, using anova(),
each model against its OLS equivalent to obtain a likelihood ratio test
p-value for each model's variance component, correct?

hsb <- read.csv('
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')

library(lme4)
m1 <- lmer(math ~ 1 + (1|sch.id), data = hsb)
m2 <- lmer(math ~ meanses + (1|sch.id), data = hsb)
m3 <- lmer(math ~ ses + (ses | sch.id), data = hsb)
m4 <- lmer(math~ ses * meanses + (ses | sch.id ), data = hsb)

ols1 <- lm(math ~ 1, data = hsb)
ols2 <- lm(math ~ meanses, data = hsb)
ols3 <- lm(math ~ ses, data = hsb)
ols4 <- lm(math ~ ses * meanses, data = hsb)

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