Latent class analysis is a multivariate statistical analysis technique that is used in factor, cluster and regression techniques. Latent class analysis is a technique where constructs are created from the number of other unobserved variables and these constructs are further used for regression analysis. Latent class analysis is commonly used to classify the case into latent classes. Latent class analysis supports nominal, ordinal and continuous data. Structural equation modeling is the major type of latent class analysis.
Key concepts and terms in latent class analysis:
Latent classes: In latent class analysis, latent classes are those observed variables that are derived from the unobserved variables. Latent classes divide the cases into their dimensions related to the variable. For example, in latent class analysis, cluster analysis groups similar cases and puts them into one group. The numbers of clusters in the cluster analysis are called the latent classes. In SEM, the number of constructs is called the latent classed.
Models in latent class analysis: To calculate the probability that a case will fall in a particular latent class, the maximum likelihood method is used.
Number of latent classes: In latent class analysis, to determine the number of latent classes, there are two methods available. The first method is iterative goodness of fit method. In this method, if we add one more class in the data, the goodness of fit model will increase, using chi-square statistics. Bootstrapping is the second method in latent class analysis used to determine the number of classes.
Classifications of cases: In latent class analysis, Bayes’ theorem is applied on the latent vector and accordingly vectors are classified into classes.
Latent class cluster analysis: Latent class cluster analysis is a different form of the traditional cluster analysis algorithms. The old cluster analysis algorithms were based on the nearest distance, but latent class cluster analysis is based on the probability of classifying the cases.
Latent class factor analysis: Latent class factor analysis is different from the traditional factor analysis. Traditional factor analysis was based on the rotated factor matrix. In latent class factor analysis, the factor is based on the class. One class shows one factor.
Latent class regression analysis: In latent class regression analysis, one set of items is used as in all latent class analysis, to establish class memberships, and then additional covariates are used to model the variation in class memberships.
Measure of model of fit in latent class analysis:
Model Chi-square: In latent class analysis, model chi-square is also called the likelihood ratio of chi-square with chi-square distribution with S-p-1 degree of freedom—where S is equal to the total number of different response patterns and p is equal to the parameter estimated in the model.
Difference chi-square: In Latent class analysis, the original model is compared with the two nested models. The nested model is the modified model from the original model.
Goodness of fit measure: In latent class analysis, the goodness of fit is measured from the BIC, AIC and CAIC criteria. A lower value of these statistics shows the better comparison of the model. There is another goodness of fit measure in latent class analysis that is also used in SEM. Incremental fit indexes and absolute fit indexes are used in latent class analysis to measure the goodness of fit.
Wald statistics: In latent class analysis, Wald statistics is used to access the statistical significance of the estimated parameter.
Assumptions in latent class analysis:
- Non-parametric: Latent class analysis is a non-parametric test. Hence latent class analysis does not assume any assumptions related to linearity, normal distribution or homogeneity.
- Data level: In latent class analysis, the data level should be categorical or ordinal data.
- Identified model: In latent class analysis, models should be justly identified or over identified and also the number of equations in the latent class analysis must be greater than the number of the estimated parameter.
- Conditional independence: In latent class analysis, observations should be independent in each class.
Latent Class Analysis Resources
Biemer, P. P., & Wiesen, C. (2002). Measurement error evaluation of self-reported drug use: A latent class analysis of the U.S. National Household Survey on Drug Abuse. Journal of the Royal Statistical Society, 165(1), 97-119.
Chung, H., Flaherty, B. P., & Schafer, J. L. (2006). Latent class logistic regression: Application to marijuana use and attitudes among high school seniors. Journal of the Royal Statistical Society, 169(4), 723-743.
Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 311-359). New York: Plenum Press.
Clogg, C. C., & Goodman, L. A. (1984). Latent structure analysis of a set of multidimensional contingency tables. Journal of the American Statistical Association, 79(388), 762-771.
Croon, M. A. (1991). Investigating Mokken scalability of dichotomous items by means of ordinal latent class analysis. British Journal of Mathematical and Statistical Psychology, 44(2), 315-331.
Dayton, C. M. (1998). Latent class scaling analysis. Thousand Oaks, CA: Sage Publications.
Flaherty, B. P. (2002). Assessing the reliability of categorical substance use measures with latent class analysis. Drug and Alcohol Dependence, 69(1), 7-20.
Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61(2), 215-231.
Hagenaars, J. A. (1993). Loglinear models with latent variables. Newbury Park, CA: Sage Publications.
Kolb, R. R., & Dayton, C. M. (1996). Correcting for nonresponse in latent class analysis. Multivariate Behavioral Research, 31(1), 7-32.
Lanza, S. T., Collins, L. M., Lemmon, D. R., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis. Structural Equation Modeling, 14(4), 671-694.
Lazarsfeld, P. F., & Henry, N. W. (1968). Latent Structure Analysis. Boston: Houghton Mifflin.
Loken, E. (2004). Using latent class analysis to model temperament types. Multivariate Behavioral Research, 39(4), 625-652.
McCutcheon, A. L. (1987). Latent class analysis. Newbury Park, CA: Sage Publications.
Mooijaart, A., & van der Heijden, P. G. (1992). The EM algorithm for latent class analysis with equality constraints. Psychometrika, 56(4), 699-716.
Vermunt, J. K., & Magidson, J. (2002). Latent class cluster analysis. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class models (pp. 89-106). Cambridge, UK: Cambridge University Press.
