Factor mixture models are a combination of latent class and common factor models, used to explore unobserved population heterogeneity. These models allow for the analysis of both categorical and continuous observed variables within classes, and can incorporate covariates to explain differences between subpopulations. The models are flexible in terms of the number of latent classes and the structure of the covariance matrix and mean vector of the observed variables within each class. They are particularly useful for data from heterogeneous populations where the sources of heterogeneity are not known beforehand. The article discusses the characteristics of factor mixture models in comparison to other methods for analyzing heterogeneous data. It highlights the flexibility of factor mixture models in handling both categorical and continuous variables, as well as the ability to incorporate covariates in different ways. The models are described in detail, including the general factor mixture model and the different ways to include covariates. A step-by-step analysis of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point. The article also discusses the different ways to specify effects of covariates X and class variable C, including class-specific effects. It emphasizes the importance of measurement invariance in ensuring that observed variables are comparable across subpopulations. The article outlines the different levels of factorial invariance and their implications for measurement invariance. It also discusses the different ways to include covariate effects, such as direct effects on observed variables, indirect effects through latent continuous variables, and effects on the latent class variable. The article concludes with a step-by-step analysis of LSAY data at a single time point, illustrating how factor mixture models can be used to investigate population heterogeneity. The analysis includes the fitting of four models with increasing restrictions on the model for the observed means within class, and a post hoc comparison with respect to background variables. The article emphasizes the importance of including only those variables as covariates in the factor mixture models that are expected to have a significant effect, and using all other background variables in post hoc analyses. The simulation study by Lubke and Muthén (2003) is cited to support the inclusion of covariates with medium to large effects on class membership.Factor mixture models are a combination of latent class and common factor models, used to explore unobserved population heterogeneity. These models allow for the analysis of both categorical and continuous observed variables within classes, and can incorporate covariates to explain differences between subpopulations. The models are flexible in terms of the number of latent classes and the structure of the covariance matrix and mean vector of the observed variables within each class. They are particularly useful for data from heterogeneous populations where the sources of heterogeneity are not known beforehand. The article discusses the characteristics of factor mixture models in comparison to other methods for analyzing heterogeneous data. It highlights the flexibility of factor mixture models in handling both categorical and continuous variables, as well as the ability to incorporate covariates in different ways. The models are described in detail, including the general factor mixture model and the different ways to include covariates. A step-by-step analysis of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point. The article also discusses the different ways to specify effects of covariates X and class variable C, including class-specific effects. It emphasizes the importance of measurement invariance in ensuring that observed variables are comparable across subpopulations. The article outlines the different levels of factorial invariance and their implications for measurement invariance. It also discusses the different ways to include covariate effects, such as direct effects on observed variables, indirect effects through latent continuous variables, and effects on the latent class variable. The article concludes with a step-by-step analysis of LSAY data at a single time point, illustrating how factor mixture models can be used to investigate population heterogeneity. The analysis includes the fitting of four models with increasing restrictions on the model for the observed means within class, and a post hoc comparison with respect to background variables. The article emphasizes the importance of including only those variables as covariates in the factor mixture models that are expected to have a significant effect, and using all other background variables in post hoc analyses. The simulation study by Lubke and Muthén (2003) is cited to support the inclusion of covariates with medium to large effects on class membership.