Fits generalized linear models where the parameters are subject to linear constraints. The model is specified by giving a symbolic description of the linear predictor, a description of the error distribution, and a matrix of constraints on the parameters.

In statistical modeling, there is a wide variety of regression models for categorical dependent variables (nominal or ordinal data); yet, there is no software embracing all these models together in a uniform and generalized format. Following the methodology proposed by Peyhardi, Trottier, and Guédon (2015) <doi:10.1093/biomet/asv042>, we introduce 'GLMcat', an R package to estimate generalized linear models implemented under the unified specification (r, F, Z). Where r represents the ratio of probabilities (reference, cumulative, adjacent, or sequential), F the cumulative cdf function for the linkage, and Z, the design matrix. The package accompanies the paper "GLMcat: An R Package for Generalized Linear Models for Categorical Responses" in the Journal of Statistical Software, Volume 114, Issue 9 (see <doi:10.18637/jss.v114.i09>).

Provides Generalized Inferences based on exact distributions and exact probability statements for mixed effect models, provided by such papers as Weerahandi and Yu (2020) <doi:10.1186/s40488-020-00105-w> under the widely used Compound Symmetric Covariance structure. The package returns the estimation of the coefficients in random and fixed part of the mixed models by generalized inference.

Recursive partitioning based on (generalized) linear mixed models
    (GLMMs) combining lmer()/glmer() from 'lme4' and lmtree()/glmtree() from 
    'partykit'. The fitting algorithm is described in more detail in Fokkema,
    Smits, Zeileis, Hothorn & Kelderman (2018; <DOI:10.3758/s13428-017-0971-x>).
    For detecting and modeling subgroups in growth curves with GLMM trees see
    Fokkema & Zeileis (2024; <DOI:10.3758/s13428-024-02389-1>).

Fits generalized linear models (GLMs) when there is missing data in both the response and categorical covariates. The functions implement likelihood-based methods using the Expectation and Maximization (EM) algorithm and optionally apply Firth’s bias correction for improved inference. See Pradhan, Nychka, and Bandyopadhyay (2025) <https:>, Maiti and Pradhan (2009) <doi:10.1111/j.1541-0420.2008.01186.x>, Maity, Pradhan, and Das (2019) <doi:10.1080/00031305.2017.1407359> for further methodological details.