Many variables crucial to the social sciences are not directly observed but instead are latent and measured indirectly. When an external variable of interest affects this measurement, estimates of its relationship with the latent variable will then be biased. Such violations of “measurement invariance” may, for example, confound true differences across countries in postmaterialism with measurement differences. To deal with this problem, researchers commonly aim at “partial measurement invariance”; that is, to account for those differences that may be present and important. To evaluate this importance directly through sensitivity analysis, the “EPC-interest” was recently introduced for continuous data. However, latent variable models in the social sciences often use categorical data. The current paper therefore extends the EPC-interest to latent variable models for categorical data and demonstrates its use in example analyses of U.S. Senate votes as well as respondent rankings of postmaterialism values in the World Values Study.