Title: Regularized Moderated Nonlinear Factor Analysis: The R Package mnlfa

Author: Alexander Robitzsch

Affiliation: Leibniz Institute for Science and Mathematics Education, Kiel,
Germany; Centre for International Student Assessment, Germany

Abstract:
In this talk, the R package mnlfa for estimating regularized moderated
nonlinear factor analysis (RMNLFA) is introduced. In this package,
multidimensional factor analysis models with normally distributed latent
variables are implemented. The item responses can be continuous (i.e.,
conditionally normally distributed) or categorical (i.e., dichotomous,
ordinal, or nominal). All item and model parameters can be specified as linear
functions of (possibly transformed) moderator variables in which
regularization (i.e., lasso, SCAD, group lasso) is allowed. The RMNLFA model
is estimated using penalized marginal maximum likelihood estimation by
applying an EM algorithm with coordinate descent optimization. We illustrate
the RMNLFA model for assessing differential item functioning of dichotomous
items and a continuous moderator.