mtram: Transformation Models for Clustered Data

In tram: Transformation Models

Transformation Models for Clustered Data

Description

Marginally interpretable transformation models for clustered data.

Usage

mtram(object, formula, data,
      grd = SparseGrid::createSparseGrid(type = "KPU", 
                dimension = length(rt$cnms[[1]]), k = 10), 
      tol = .Machine$double.eps, optim = mltoptim(auglag = list(maxtry = 5)),
      ...)

Arguments

object	A tram object.
formula	A formula specifying the random effects.
data	A data frame.
grd	A sparse grid used for numerical integration to get the likelihood.
tol	numerical tolerance.
optim	a list of optimisers as returned by mltoptim
...	Additional argument.

Details

A Gaussian copula with a correlation structure obtained from a random intercept or random intercept / random slope model (that is, clustered or longitudinal data can by modelled only) is used to capture the correlations whereas the marginal distributions are described by a transformation model. The methodology is described in Barbanti and Hothorn (2022) and examples are given in the mtram package vignette.

Only coef() and logLik() methods are available at the moment, see vignette("mtram", package = "tram") for worked examples.

Value

An object of class tram with coef() and logLik() methods.

References

Luisa Barbanti and Torsten Hothorn (2024). A Transformation Perspective on Marginal and Conditional Models, Biostatistics, 25(2), 402–428, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biostatistics/kxac048")}.

See Also

vignette("mtram", package = "tram")

Examples

  if (require("lme4")) {
      ### linear mixed model
      sleep_lmer <- lmer(Reaction ~ Days + (Days | Subject), 
                         data = sleepstudy, REML = FALSE)

      ### marginal transformation model
      sleep_LM <- Lm(Reaction ~ Days, data = sleepstudy)
      sleep_LMmer <- mtram(sleep_LM, ~ (Days | Subject), data = sleepstudy)

      ### the same
      logLik(sleep_lmer)
      logLik(sleep_LMmer)

      ### Lm / mtram estimate standardised effects
      sdinv <- 1 / summary(sleep_lmer)$sigma
      fixef(sleep_lmer) * c(-1, 1) * sdinv
      coef(sleep_LMmer)[c("(Intercept)", "Days")]
  }

tram documentation built on April 4, 2025, 2:26 a.m.