AIC for mixed models: cAIC

Model selection was performed using the conditional Akaike information criterion (cAIC). This measure of the quality of fit penalised by the number of parameters corrected (Burnham and Anderson, 2002) was specially developed for mixed models (Greven and Kneib, 2010; Säfken et al., 2018 preprint).

Greven S, Kneib T (2010) On the behaviour of marginal and conditional Akaike Information Criteria in linear mixed models. Biometrika 97: 773-789
Säfken B, Rügamer D, Kneib T, Greven S (2018) Conditional model selection in mixed-effects models with cAIC4. arXiv 1803.05664v2: 1-31

library(cAIC4)

datax <- data.frame(y=rnorm(100), x1=rnorm(100),
                    x2=rnorm(100), x3=rnorm(100), x4=rnorm(100), x5=sample(x=c("A", "B"), size=100, replace = TRUE))

g0 <- lmer(y ~ x1+x2+x3+x4 + (1 | x5), data=datax)

cAIC(g0)
cAIC(g0)$caic


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