Plumage damage scores (PDS) were assessed in laying hens of 2 genotypes (Lohmann Tradition and Lohmann Silver) at the 45th and 70th weeks of age, with scores ranging from zero (no damage) to 6 (completely denuded). This ordinally scaled categorical characteristic was recorded from different body regions of 365 hens that had experienced different housing environments (2 enrichment levels) during their rearing and laying periods. The so-called threshold model is an option for analyzing repeated ordered categorical data from individual animals. This model represents a generalized linear mixed model if the linear predictor additionally includes the animal as a random effect. This paper is intended to fill the gap between the theoretical aspects of generalized linear mixed models and their practical application in animal science. A cumulative probit model was adapted for analyzing plumage damage. The variation among birds was considered as a random effect for the analysis of cumulative probabilities. The numerical implementation of the methodology was done based on the NLMIXED procedure of the SAS statistical program. A threshold model with inhomogeneous residual variances for the latent variable was used because less plumage damages were observed up to the 45th week of age compared to the 70th week of age. Differences in PDS were evident between genotypes, age, and enrichment levels during housing periods. However, neither of the 2 enriched environments proved consistent superiority or inferiority across all traits. Major plumage damage (PDS larger than or equal to 5) was observed for the breast region in 56.6% of all birds with the Lohmann Tradition genotype and in 34.4% with the Lohmann Silver genotype when we look at the mean over all treatments. The most severe plumage damage was observed at the 70th week of age for the traits breast and housing environment without additional enrichment.