mlmhelpr (version 0.1.1)

icc: Intraclass Correlation (ICC)

Description

The icc function calculates the intraclass correlation (ICC) for multilevel models. The ICC represents the proportion of group-level variance to total variance. The ICC can be calculated for two or more levels in random-intercept models (Hox et al, 2018).

Note: For models with random slopes, it is generally advised to interpret with caution. According to Kreft and De Leeuw (1998, p. 63), "The concept of intra-class correlation is based on a model with a random intercept only. No unique intra-class correlation can be calculated when a random slope is present in the model." However, Snijders and Bosker (2012) offer a calculation to derive this value (equation 7.9). This equation is implemented here.

The icc function calculates the intraclass correlation for linear mixed-effects models estimated with the lme4::lmer function or generalized linear mixed-effect model estimated with the lme4::glmer function with family = binomial(link="logit"). For logistic models, the estimation method follows Hox et al. (2018, p. 107) recommendation of setting the level-1 residual variance to \(\frac{\pi^2}{3}\). For a discussion different methods for estimating the intraclass correlation for binary responses, see Wu et al. (2012).

Usage

icc(model)

Value

A data frame with random effects and their intraclass correlations.

Arguments

model

A model produced using the lme4::lmer() or lme4::glmer() functions. This is an object of class merMod and subclass lmerMod or glmerMod.

References

hox2018mlmhelpr

kreft1998mlmhelpr

snijders2012mlmhelpr

Wu2012mlmhelpr

Examples

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

icc(fit)

# Logistic Example
  # Create binary outcome
hsb$binary_math <- ifelse(hsb$mathach <= 13, 0, 1)

fitb <- lme4::glmer(binary_math ~ 1 + ses + catholic + (1|id),
data=hsb, family = binomial(link="logit"))

icc(fitb)