Untangle a two-way interaction in a fitted model

Produces post-hoc marginal means and/or slopes that describe how two interacting predictors jointly shape the fitted model. The behaviour adapts to the types of the two variables:

• categorical x categorical: estimated marginal means (emmeans::emmeans()) for every combination of the two factors, plus a faceted ggplot of those means with 95% error bars. Faceting is by any categorical predictor not listed in average.over. The plot is suppressed (with a warning) when the number of facets exceeds 8, unless overridePlot = TRUE.

• categorical x continuous: slopes of the continuous predictor at each level of the factor (emmeans::emtrends()), plus a faceted ggplot of predicted responses across n equally-spaced values of the continuous predictor. Faceting is by any categorical predictor not listed in average.over. The plot is suppressed (with a warning) when the number of facets exceeds 8, unless overridePlot = TRUE.

• continuous x continuous: slopes of each predictor at low, medium and high values of the other (emmeans::emtrends()), plus Johnson-Neyman intervals in both directions (interactions::johnson_neyman()).

Usage

untangle_interaction(
  model,
  interaction,
  average.over = NULL,
  standardized = FALSE,
  n = 100,
  overridePlot = FALSE
)

Arguments

model

A fitted model. Either an object returned by countGLM() or one of the package's individual fitters (poissonGLM(), negbinGLM(), tweedieGLM(), zeroinflPoissonGLM(), zeroinflNegbinGLM(), zeroinflTweedieGLM()), or a raw glm / glmmTMB fit. For countGLM objects the best-fitting component model is used and a message is printed.

interaction

The pair of interacting variables. Either a length-2 character vector (e.g. c("x7", "x8")) or a one-sided formula (e.g. ~ x7:x8 or ~ x7*x8).

average.over

Character vector of categorical predictor names that may be averaged over by emmeans. Default NULL means do not average over any categorical predictor; each level is reported separately.

standardized

Logical; set TRUE when the continuous predictors have been standardized to mean 0 and SD 1. In that case the low / medium / high values used for continuous x continuous slopes are c(-1, 0, 1) (standard deviations), and the interpretation text refers to a "one-standard-deviation increase" rather than a "one-unit increase". Default FALSE.

n

Integer; number of equally-spaced points used for the continuous predictor in the categorical x continuous emmeans grid backing the plot. Default 100.

overridePlot

Logical; when TRUE, the faceted plot in the categorical x categorical and categorical x continuous cases is built and returned even if the number of facets exceeds 8. Default FALSE.

Value

A list with class "untangle_interaction" whose contents depend on the interaction type:

type

One of "categorical-categorical", "categorical-continuous", "continuous-continuous".

variables

Character vector of the two predictor names.

emmeans

(cat x cat) data frame with columns for each factor, Mean, SE, df, Lower, Upper.

plot

(cat x cat) faceted ggplot of estimated means with 95% error bars. NULL when the number of facets exceeds 8 and overridePlot = FALSE.

emtrends

(cat x cont) data frame with Slope, SE, df, Lower, Upper at each level of the factor.

plot

(cat x cont) faceted ggplot of predicted responses vs the continuous predictor, coloured by the factor, with a 95% confidence ribbon. NULL when the number of facets exceeds 8 and overridePlot = FALSE.

emtrends_<v1>, emtrends_<v2>

(cont x cont) data frames of slopes of each predictor at low/medium/high values of the other.

johnson_neyman_<v1>_by_<v2>, johnson_neyman_<v2>_by_<v1>

(cont x cont) Johnson-Neyman objects from interactions::johnson_neyman(). NULL if the call failed (e.g. unsupported model class).

interpretation

A plain-language description, also printed.

Details

By default, the function never averages over categorical predictors outside the interaction of interest: results are reported separately for each level. Predictors listed in average.over are averaged over instead. Continuous predictors outside the interaction are always held at their mean (the emmeans default) and therefore implicitly averaged in a linear sense.

emmeans and interactions are declared in Suggests; both must be installed before calling this function.

All emmeans summaries are returned on the response scale when a known link is present. Slopes from emtrends are returned on the linear predictor (link) scale — on a log link, a positive slope means the expected response grows multiplicatively with the predictor.

See also

interpret_coef(), emmeans::emmeans(), emmeans::emtrends(), interactions::johnson_neyman()

Examples

if (FALSE) { # \dontrun{
fit <- poissonGLM(y ~ x1 * x2 + x3, data = df)
untangle_interaction(fit, c("x1", "x2"))
untangle_interaction(fit, ~ x1:x2, average.over = "x3")
untangle_interaction(fit, c("x7", "x8"), standardized = TRUE)
} # }