# Latent Class Analysis

Latent Class Analysis (LCA) is a statistical technique that is used in factor, cluster, and regression techniques; it is a subset of structural equation modeling (SEM). LCA is a technique where constructs are identified and created from unobserved, or latent, subgroups, which are usually based on individual responses from multivariate categorical data. These constructs are then used for r further analysis. LCA models can also be referred to as finite mixture models.

**Questions Answered:**

**What subtypes of disease exist within a given test?**

**What domains are found to exist among the different categorical symptoms?**

**Assumptions in latent class analysis:**

**Non-parametric:**Latent class does not assume any assumptions related to linearity, normal distribution or homogeneity.**Data level:**The data level should be categorical or ordinal data.**Identified model:**Models should be justly identified or over identified and also the number of equations must be greater than the number of the estimated parameter.**Conditional independence:**Observations should be independent in each class.

**Key concepts and terms in LCA:**

**Latent classes:**Latent classes are those observed variables that are derived from the unobserved variables. Latent classes divide the cases into their respective dimensions in relation to the variable. For example, 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. The maximum likelihood estimates are those that have a higher chance of accounting for the observed results.**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:**One set of items is used to establish class memberships, and then additional covariates are used to model the variation in class memberships.

**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.

Latent Variable and Latent Structure Models (Quantitative Methodology Series)

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