What Are Latent Classes or Latent Segments?
Latent classes represent unobservable (latent) subgroups, types, or segments within a dataset. Members of the same latent class exhibit homogeneity concerning certain criteria, while members of different classes differ significantly. Formally, latent classes correspond to say K distinct categories of a nominal latent variable.
How Did the Field of Latent Class Analysis Develop?
Latent class (LC) analysis was first introduced by Lazarsfeld (1950) to explain respondent heterogeneity in dichotomous survey responses. Much later, Goodman (1974a, 1974b) extended the methodology to nominal response variables and developed the maximum likelihood estimation algorithm still used in LatentGOLD® and other LC software.
LC models evolved alongside finite mixture (FM) models, which emerged from the work of Day (1969) and Wolfe (1965, 1967, 1970). Both approaches aim to identify differences across unobserved subgroups. Today, the terms latent class analysis and finite mixture modeling are often used interchangeably to describe statistical models where parameters vary across hidden segments (Vermunt and Magidson, 2004).
Expanding Applications of LC Models
Over the past 25 years, LC models have rapidly gained traction across various disciplines. Initially recognized as a clustering method for individuals based on categorical response variables, LC modeling is now a comprehensive tool for addressing heterogeneity in data. It is widely applied in cluster analysis, longitudinal data analysis, multilevel modeling, and choice modeling (Vermunt and Paas, 2017).
Advances in computing power and efficient algorithms—implemented in software like LatentGOLD®—now allow for the estimation of LC models with large datasets, numerous observed indicators, and multiple explanatory variables. Numerous extensions and enhancements have been developed, including:
- Mixed-scale response variables, including nominal, ordinal, (censored/truncated) continuous, and (truncated) count data (Vermunt and Magidson, 2002).
- Multiple ordered categorical latent variables, known as discrete factors (DFactors) (Vermunt and Magidson, 2005).
- Categorical and numeric covariates for predicting class membership, as well as for accommodating measurement non-invariance.
- Relaxation of the local independence assumption for greater model flexibility.
- Tools for handling sparse data tables (e.g., bootstrap p-values), boundary solutions (e.g., Bayes constants), and local maxima (e.g., multiple start sets).
- Advanced LC modeling extensions, including LC regression, LC growth models, and latent Markov (latent transition) models (Vermunt, Tran, and Magidson, 2008).
- Multilevel LC models for hierarchical data structures (Vermunt, 2003, 2010b).
- Three-step modeling approaches to separate measurement and structural components (Vermunt, 2010a; Vermunt and Magidson, 2021).
- LC tree models, which generate hierarchically linked latent classes, similar to hierarchical clustering (van den Bergh et al., 2017, 2018).
How Do Latent Class Models Differ from Other Latent Variable Models?
LC models are latent variable models, but differ from “traditional” latent variable approaches—such as factor analysis, structural equation modeling, and random-effects regression—by using categorical rather than continuous latent variables. However, LC models can also be combined with these approaches, leading to mixture factor analysis, mixture structural equation models, and LC mixed regression and growth models, among others.
Comparison of LC Analysis with Traditional Cluster Analysis
1. Assumptions
Traditional clustering methods (e.g., K-Means, hierarchical clustering) rely on implicit assumptions, such as local independence and equal within-class variances, which may not accurately reflect real-world data. LC cluster analysis allows these assumptions to be tested and relaxed as needed, resulting in simpler and more interpretable segmentations (Magidson and Vermunt, 2002a, 2002b). Additionally, LC cluster analysis accounts for uncertainty in cluster membership, a factor that traditional clustering methods ignore (Vermunt and Magidson, 2025).
2. Support for Different Scale Types
LatentGOLD® offers flexibility in handling various variable scale types within cluster models, including binary, nominal, ordinal, continuous, and count variables—even in the presence of missing values. It automatically selects appropriate distributions and, with its Choice options, supports specialized data types such as ranking and discrete choice data.
3. Covariate-Based Profiling
While traditional clustering often uses post-hoc discriminant analysis or cross-tabs for cluster description, LatentGOLD® integrates covariates as part of the LC model, enabling simultaneous classification and descriptive profiling. It also supports covariate-based classification without indicators and interfaces with SI-CHAID® for enhanced profiling (Magidson and Vermunt, 2005). Popular nowadays are three-step approaches which correct for classification errors (Vermunt, 2010a; Vermunt and Magidson, 2021).
4. Optimal Cluster Determination
While traditional methods rely on rules of thumb for determining the number of clusters, LC models offer statistical measures for class enumeration. LatentGOLD® provides such formal model-based assessments, including information criteria and bootstrap-based likelihood-ratio tests.
Comparison of LC Analysis with Traditional Regression Analysis
1. Accounting for Heterogeneity
Traditional regression and choice models assume uniformity across populations. LC regression and choice models explore whether unobserved segments explain model heterogeneity. LatentGOLD® Advanced/Syntax also supports continuous heterogeneity (CFactors) (Popper, Kroll, and Magidson, 2014).
2. Flexible Dependent Variable Scale Types
LatentGOLD®’s mixture regression operates within the Generalized Linear Modeling (GzLM) framework, accommodating dichotomous, nominal, ordinal, continuous, and count-dependent variables, with corresponding logistic, multinomial logistic, ordinal logistic, linear normal, and loglinear Poisson models.
3. Repeated Measures
LatentGOLD® supports repeated measures for latent class variants of growth, conjoint, Rasch, survival, and other models. Its non-parametric random-coefficient approach avoids assuming multivariate normality, offering faster performance for non-normal outcomes with detailed outputs on coefficients and effects.
4. Multilevel Segmentation
LatentGOLD® Advanced/Syntax enables the simultaneous segmentation of units at multiple levels within a hierarchical structure. For example, it can classify both individuals and countries, supporting applications such as global market analysis (Bijmolt, Paas, and Vermunt, 2004; Vermunt, 2003, 2010b).
5. Dealing with Scale Use Heterogeneity and Response Styles
Examples of LC models which account for response styles when dealing with ordinal or numeric responses include Popper, Kroll, and Magidson (2004) and Morren, Gelissen, and Vermunt (2011). Moreover, when dealing with first choice, ranking, or best-worst/maxdif responses from choice experiments, LC analysis allows simultaneously accounting for preference and scale heterogeneity (Magidson and Vermunt, 2007, 2024).
References to Work by Magidson and Vermunt
(see also www.jeroenvermunt.nl)
Bijmolt, T.H., Paas, L.J., and Vermunt, J.K. (2004). Country and consumer segmentation: Multi-level latent class analysis of financial product ownership. International Journal of Research in Marketing, 21, 323-340.
Magidson, J., and Vermunt, J.K. (2002a). Latent class models for clustering: A comparison with K-means. Canadian Journal of Marketing Research, 20, 36-43.
Magidson, J., and Vermunt, J.K. (2002b). Latent class modeling as a probabilistic extension of K-means clustering. Quirk’s Marketing Research Review, March 2002, 20 & 77-80.
Magidson, J., and Vermunt, J.K. (2005). An extension of the CHAID tree-based segmentation algorithm to multiple dependent variables. In: C. Weihs und W. Gaul (eds.), Classification: The Ubiquitous Challenge, 240-247. Heidelberg: Springer.
Magidson, J., and Vermunt, J.K. (2007). Removing the scale factor confound in multinomial logit choice models to obtain better estimates of preference. Sawtooth Software Conference Proceedings, October 2007, 139-154.
Magidson, J., and Vermunt, J.K. (2024). Extracting meaning segments from HB utilities. Proceeding of the Analytics and Insights Summit (formerly known as Sawtooth Software Conference), September 2024, 321-344.
Morren, M., Gelissen, J.P.T.M., and Vermunt, J.K. (2011). Dealing with extreme response style in cross-cultural research: A restricted latent class factor analysis approach. Sociological Methodology, 41, 13-47.
Popper, R., Magidson J., and Kroll J. (2004). Application of latent class models to food product development: a case study, Sawtooth Software Conference Proceedings.
Van den Bergh, M., Schmittmann, V.D., and Vermunt, J.K. (2017). Building latent class trees, with an application to a study of social capital. Methodology, 13(Supplement), 13–22.
Van den Bergh, M., van Kollenburg, G.H., and Vermunt, J.K. (2018). Deciding on the starting number of classes of a latent class tree, Sociological Methodology, 48, 303-336.
Vermunt, J.K., and Magidson, J. (2002). Latent class cluster analysis. In: J.Hagenaars and A.McCutcheon (eds.), Applied latent class analysis, 89-106. Cambridge, UK: Cambridge University Press.
Vermunt, J.K. (2010a). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18, 450-469.
Vermunt, J.K (2010b). Mixture models for multilevel data sets. In: J. Hox and J.K. Roberts (eds.), Handbook of Advanced Multilevel Analysis, 59-81. New York: Routledge.
Vermunt, J.K., and Magidson, J. (2004). Latent class analysis. In: M.S. Lewis-Beck, A. Bryman, and T.F. Liao (eds.), The Sage Encyclopedia of Social Sciences Research Methods, 549-553. Thousand Oaks, CA: Sage Publications.
Vermunt, J.K., and Magidson, J. (2005). Factor Analysis with categorical indicators: A comparison between traditional and latent class approaches. In: A. Van der Ark, M.A. Croon, and K. Sijtsma (eds.), New Developments in Categorical Data Analysis for the Social and Behavioral Sciences, 41-62. Mahwah: Erlbaum.
Vermunt, J.K., and Magidson, J. (2021). How to perform three-step latent class analysis in the presence of measurement non-invariance or differential item functioning, Structural Equation Modeling, 28, 356-364.
Vermunt, J.K., and Magidson, J. (2025). Linear logistic scoring equations for latent class and latent profile models: A simple method for classifying new cases. Structural Equation Modeling, 32, 541-549.
Vermunt, J.K., and Paas, L.J. (2017). Mixture models. In: P.S.H Leeflang, J.E. Wieringa, T.H.A. Bijmolt, and K.H. Pauwels (eds.), Advanced Methods for Modeling Markets, 383-403. Cham, Switzerland: Springer.
Vermunt, J.K., Tran, B., and Magidson, J. (2008). Latent class models in longitudinal research. In: S. Menard (ed.), Handbook of Longitudinal Research: Design, Measurement, and Analysis, 373-385. Burlington, MA: Elsevier.