icc_11 {quest}

Intraclass Correlation for Multilevel Analysis: ICC(1,1)

Description

icc_11 computes the intraclass correlation (ICC) based on a single rater with a single dimension, aka ICC(1,1). Traditionally, this is the type of ICC used for multilevel analysis where the value is interpreted as the proportion of variance accounted for by group membership. In other words, ICC(1,1) = the proportion of between-group variance; 1 - ICC(1,1) = the proportion of within-group variance.

Usage

icc_11(x, grp, how = "lme", REML = TRUE)

Arguments

x

numeric vector.

grp

atomic vector the same length as x providing the grouping variable.

how

character vector of length 1 specifying how the ICC(1,1) should be calculated. There are four options: 1) "lme" uses a linear mixed effects model with the function lme from the package nlme, 2) "lmer" uses a linear mixed effects modeling with the function lmer from the package lme4, 3) "aov" uses a one-way analysis of variance with the function aov, and 4) "raw" uses the observed variances, which provides a biased estimate of the ICC(1,1) and is not recommended (It is only included for teaching purposes).

REML

logical vector of length 1 specifying whether restricted maximum likelihood estimation (TRUE) should be used rather than traditional maximum likelihood estimation (FALSE). Only used for linear mixed effects models if how = "lme" or how = "lmer".

Value

numeric vector of length 1 providing ICC(1,1) and computed based on the how argument.

See Also

iccs_11 # ICC(1,1) for multiple variables, icc_all_by # all six types of ICCs by group, lme # how = "lme" function, lmer # how = "lmer" function, aov # how = "aov" function,

Examples

# BALANCED DATA (how = "aov" and "lme"/"lmer" do YES provide the same value)

str(InsectSprays)
icc_11(x = InsectSprays$"count", grp = InsectSprays$"spray", how = "aov")
icc_11(x = InsectSprays$"count", grp = InsectSprays$"spray", how = "lme")
icc_11(x = InsectSprays$"count", grp = InsectSprays$"spray", how = "lmer")
icc_11(x = InsectSprays$"count", grp = InsectSprays$"spray",
   how = "raw") # biased estimator and not recommended. Only available for teaching purposes.

# UN-BALANCED DATA (how = "aov" and "lme"/"lmer" do NOT provide the same value)

dat <- as.data.frame(lmeInfo::Bryant2016)
icc_11(x = dat$"outcome", grp = dat$"case", how = "aov")
icc_11(x = dat$"outcome", grp = dat$"case", how = "lme")
icc_11(x = dat$"outcome", grp = dat$"case", how = "lmer")
icc_11(x = dat$"outcome", grp = dat$"case", how = "lme", REML = FALSE)
icc_11(x = dat$"outcome", grp = dat$"case", how = "lmer", REML = FALSE)

# how = "lme" does not account for any correlation structure
lme_obj <- nlme::lme(outcome ~ 1, random = ~ 1 | case,
   data = dat, na.action = na.exclude,
   correlation = nlme::corAR1(form = ~ 1 | case), method = "REML")
var_corr <- nlme::VarCorr(lme_obj) # VarCorr.lme
vars <- as.double(var_corr[, "Variance"])
btw <- vars[1]
wth <- vars[2]
btw / (btw + wth)