icc {mlmhelpr}

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)

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.

Value

A data frame with random effects and their intraclass correlations.

References

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

Kreft, Ita, de Leeuw, Jan (1998). Introducing Multilevel Modeling. Sage Publications. ISBN 0761951405.

Snijders TAB, Bosker RJ (2012). Multilevel Analysis. SAGE. ISBN 9781849202015.

Wu S, Crespi CM, Wong WK (2012). “Comparison of Methods for Estimating the Intraclass Correlation Coefficient for Binary Responses in Cancer Prevention Cluster Randomized Trials.” Contemporary Clinical Trials, 33(5), 869–880. ISSN 1559-2030, doi:10.1016/j.cct.2012.05.004.

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)