This chapter introduces two explanatory Rasch models—the Linear Logistic Rasch Model (LLRM) and the Latent Regression Rasch Model (LRRM)—that extend descriptive Rasch models by incorporating item and person covariates, respectively. Using the generalized linear mixed model (GLMM) framework, both models integrate structural predictors into the measurement process by linking covariates to variations in item difficulty (LLRM) or person locations on the latent variable (LRRM). For the LLRM, dichotomous and polytomous applications are illustrated. The dichotomous example uses the Learning Stimulation Scale with an item covariate that distinguishes child from adult focused activities. Results indicate that child-related items are more frequently observed in homes. The polytomous example applies the LLRM to the Attitude Toward Censorship (ATC) Scale with sentiment analysis used to classify items by valence. Although positive-valence items were somewhat easier to endorse, valence was not a statistically significant predictor. The LRRM is demonstrated with the ATC Scale with education level and gender as person covariates. The results show that college graduates and male respondents express greater support for censorship with no significant interaction between education and gender. Overall, explanatory Rasch models have the potential to enhance interpretability by linking measurement parameters to substantive explanatory variables. Explanatory Rasch models can provide richer insights into educational and psychological assessments as compared to descriptive Rasch models alone.