Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total scores across classes, and discusses different approaches to item analysis by these models. The analysis by stochastically ordered mixed Rasch models is illustrated both on simulated data and on part of the data collected during development of a new Danish cognitive test called Children's Problem Solving (CHIPS). The main purpose of the analysis of responses to CHIPS items was to validate this theory by disclosure of evidence confirming that item responses fit a stochastically ordered mixed Rasch model but not a conventional Rasch model. (Contains 16 tables and 4 figures.)