Probing, Plotting, and Interpreting Multilevel Interaction Effects

Provides a workflow for probing, plotting, and checking cross-level interaction effects in two-level mixed-effects models fitted with 'lme4' (Bates et al., 2015) . Implements simple slopes analysis following Aiken and West (1991, ISBN:9780761907121), Johnson-Neyman intervals following Johnson and Fay (1950) and Bauer and Curran (2005) , and grand- or group-mean centering as described in Enders and Tofighi (2007) . Tests and intervals use Satterthwaite degrees of freedom via 'lmerTest' (Kuznetsova et al., 2017) by default, with Kenward-Roger and between-cluster alternatives. Also provides confidence and new-cluster prediction intervals for simple slopes in random-slope models, contour plots of predicted outcomes over the predictor-by-moderator space, and leave-one-cluster-out influence diagnostics for the interaction.

mlmoderator

mlmoderator probes, plots, and checks cross-level interactions in two-level models fitted with lme4::lmer().

Function	What it does
`mlm_center()`	Grand-mean, group-mean, or within/between centring
`mlm_probe()`	Simple slopes at chosen moderator values
`mlm_jn()`	Johnson-Neyman boundaries (closed form or exact root-finding)
`mlm_plot()`	Interaction plot with confidence bands
`mlm_surface()`	Contour plot of predicted outcomes over predictor x moderator
`mlm_summary()`	Interaction test, simple slopes, and JN region together
`mlm_variance_decomp()`	Confidence intervals for the average slope vs. prediction intervals for a new cluster
`mlm_sensitivity()`	Leave-one-cluster-out influence (DFBETA) on the interaction

Degrees of freedom

Inference for a cross-level interaction draws its information from the clusters. All tests and intervals therefore use Satterthwaite degrees of freedom by default (via lmerTest), with Kenward-Roger ("kenward-roger") and a between-cluster rule ("between", J - q - 1) as alternatives, through the df_method argument. Versions before 0.3.0 used N - p, which is anti-conservative with few clusters; it remains available as df_method = "residual" for reproducing earlier results.

Installation

install.packages("mlmoderator")

Example

library(mlmoderator)
library(lme4)

data(school_data)
mod <- lmer(math ~ ses * climate + gender + (1 + ses | school),
            data = school_data)

mlm_summary(mod, pred = "ses", modx = "climate")
mlm_plot(mod, pred = "ses", modx = "climate")
plot(mlm_jn(mod, pred = "ses", modx = "climate"))
mlm_variance_decomp(mod, pred = "ses", modx = "climate")
mlm_sensitivity(mod, pred = "ses", modx = "climate")

vignette("hsb-workflow") works through a full analysis of the public High School and Beyond data.

Scope

The package describes and checks the fitted model. It does not address unmeasured confounding of the interaction, and it currently supports Gaussian lmer() models with the cluster defined by the first grouping factor.