Perform Regression Analysis — regression

This function performs regression analysis on multiply imputed data and pools the results using Rubin's Rules. It supports fixed-effects, random-effects, and mixed-effects models, each available in a linear variant (Gaussian / identity link) or a non-linear variant (generalized models with a family, e.g. logistic or Poisson).

Usage

regression_analysis(
  births,
  targets,
  cat_label,
  exposure_level_col,
  regression_formula,
  output_dir,
  model_type = "mixed",
  model_family = NULL
)

Arguments

births: A data frame containing the birth data with imputation identifiers.
targets: A character vector of target variables (health outcomes).
cat_label: A character vector of exposure categories (excluding reference).
exposure_level_col: A character string for the exposure level column name.
regression_formula: A formula object or character string for the regression model.
output_dir: A character string for the output directory path.
model_type: A character string selecting the effects structure. One of "mixed" (default, fixed + random effects), "random" (random-intercept only), or "fixed" (no random effects).
model_family: The error distribution / link for non-linear (generalized) models. Accepts NULL (default, a linear/Gaussian model), a family name such as "binomial" or "poisson", the special value "multinomial" (multi-level categorical outcome, fitted with nnet::multinom() for fixed effects or mclogit::mblogit() for random-/mixed-effects), a stats::family() object, or a family-generating function. When non-NULL, generalized models are fitted.

Value

A named list of data frames with pooled regression results for each target.

Details

The fitting engine is selected from the combination of model_type and model_family:

model_type	linear (model_family = NULL)	non-linear (model_family set)
`"fixed"`	`stats::lm()`	`stats::glm()`
`"random"`	`lme4::lmer()`	`lme4::glmer()`
`"mixed"`	`lme4::lmer()`	`lme4::glmer()`

Multi-level categorical outcomes are supported via multinomial logistic regression (model_family = "multinomial"): fixed-effects fits use nnet::multinom(), while random- and mixed-effects fits use mclogit::mblogit(). Multinomial results include a y.level column identifying the outcome category (relative to the reference level) that each pooled estimate refers to.