Categorical predictors and supported variable types

wsMed supports binary and multicategory between-subject covariates and one categorical moderator in models with numeric outcomes and mediators.

Supported roles

Outcomes, mediators, and within-subject covariates must be numeric measures analyzed by the continuous-response SEM. Binary or ordinal response models, thresholds, and categorical links are not implemented. Storing a binary outcome as numbers does not turn the estimator into a categorical-response model. Between-subject covariates and the single moderator may instead be unordered factors. Ordered factors are rejected by wsmed_fit(); explicitly convert them to unordered factors only if a nominal interpretation is intended.

Declaring categories

In both the one-call and staged workflows, use base::factor() to declare categorical between-subject covariates and moderators in the input data. Specify levels explicitly: the first level is the reference group. For a binary predictor, factor(x, levels = c(0, 1)) selects 0 as the reference; reversing the levels selects 1. Use unordered factors for nominal categories. Every declared factor level must have observations in the supplied data.

The existing default recognition rules are retained for compatibility. wsmed_fit() treats numeric predictors, including 0/1 columns, as continuous. The one-call wsMed() and PrepareData() interfaces retain automatic detection: factors, character columns, and numeric columns whose observed values are exactly 0 and 1 are categorical. Other numeric columns are continuous unless C_type or W_type overrides detection. Explicit factors provide the same categorical interpretation and reference coding in both interfaces without relying on automatic recognition. The one-call type arguments remain available to override its default rules.

Reference coding and comparisons

A factor with K levels is represented by K - 1 treatment indicators. The first factor level is the reference; stats::relevel() changes it before fitting. Indicators are not mean-centered. Coding does not depend on the global contrasts option. Between-subject indicators use Cb* names and moderator indicators use W* names. The C_info and W_info attributes of prepared data record their mappings. Labels such as low vs high identify the reference and comparison level: the indicator is 0 at low and 1 at high, so its coefficient is high minus low.

wsmed_effects() accepts original factor labels in at; by default it extracts every level. wsmed_contrasts() compares effects using their joint draws, preserving covariance. Do not subtract the endpoints of separate confidence intervals to obtain an interval for a difference. Marginally standardized conditional effects use the common model-implied outcome-difference SD, not separate within-category SDs; factor labels and dummy indicators retain their coding. See standardize_moderation(). Generated models account for the dependence of endogenous products on upstream mediator disturbances. Reference changes preserve the implied marginal scales of the same fitted model. MI pools marginal variance estimates jointly with coefficients; compare the same completed datasets when checking recoding. Refit saved models from before this covariance correction.

Missing values

The staged default missing = "error" rejects missing analysis values. Listwise deletion and multiple imputation are available for incomplete categorical predictors. FIML is allowed with fully observed categorical predictors but wsmed_fit() rejects missing categorical predictors; the one-call interface should follow the same restriction. MI imputes the raw variables before constructing dummy variables and interactions. The staged mi$method argument selects the method for numeric variables (default "pmm"). Factors use logistic regression for two levels and multinomial logistic regression for more than two levels. This differs from the lower-level ImputeData() method argument. MI supports Monte Carlo inference only.

Examples

data(example_data)
dat <- example_data
dat$Group <- factor(dat$Group, levels = c("low", "med", "high"))
prepared <- PrepareData(dat, M_C1 = "A1", M_C2 = "A2",
                        Y_C1 = "D1", Y_C2 = "D2",
                        W = "Group", W_type = "categorical")
attr(prepared, "W_info")
#> $raw
#> [1] "Group"
#> 
#> $dummy_names
#> [1] "W1" "W2"
#> 
#> $dummy_map
#> $dummy_map$W1
#> [1] "low vs med"
#> 
#> $dummy_map$W2
#> [1] "low vs high"
#> 
#>