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Latent Class Analysis and Latent Transition Analysis |
Home  Research Areas LCA & LTA
We are pleased to announce that the book Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences, by L. M. Collins and S. T. Lanza, is now available for pre-order from the publisher (Wiley) and other online vendors.
Both latent class analysis (LCA) and latent transition analysis (LTA) are latent variable models. You are probably familiar with latent variable models such as factor analysis. In factor analysis, a covariance matrix is analyzed statistically in order to shed light on the underlying latent structure. In the factor model the latent variable is continuous, and latent variable scores form a continuous distribution. LCA and LTA are conceptually similar to the factor model, but operationally different. In LCA and LTA the latent variable is discrete, and divides a population up into mutually exclusive and exhaustive categories. For example, whereas a factor might produce a continuous distribution of latent achievement scores, in LCA the latent variable would divide a population into discrete latent classes, such as 'highly proficient,' 'adequate,' and 'not proficient.' In LCA and LTA, a contingency table is analyzed with the objective of shedding light on the underlying latent structure.
In LCA, the latent variable is static or unchanging (at least for purposes of the study) and therefore typically measured at a single occasion. In other words, if you have cross-sectional data, you will probably be interested in LCA. In order to perform a LCA, you will have to specify the number of latent classes. Most people compare the fit of models with different numbers of latent classes. Each LCA produces parameter estimates corresponding to the class-membership probabilities and the probability of each possible item response conditional on latent class membership. Different latent classes are characterized by different patterns of responses. Just as in factor analysis where it is up to the investigator to assign labels to factors by interpreting the size and direction of factor loadings, in LCA it is the investigator's job to assign labels to latent classes. For example, individuals in a latent class labeled 'highly proficient' would probably be likely to pass most test items, whereas individuals in a latent class labeled 'not proficient' would probably be likely to fail most test items.
LTA is an extension of LCA that enables the investigator to model a dynamic, or changing, latent variable. In other words, here we are modeling change over time in the categories of the latent variable, referred to in this context as latent statuses. You must have longitudinal data in order to use LTA. LTA produces parameter estimates corresponding to the proportion of individuals in each latent status at Time 1 and the probability of each possible item response conditional on latent status membership. LTA also produces a transition probability matrix, consisting of estimates of the probability of latent status membership at time t+1 conditional on latent status membership at time t. An example of one element of the transition probability matrix would be the probability of membership in the 'highly proficient' latent status at Time 2 conditional on the probability of membership in the 'not proficient' latent status at Time 1. This often very interesting matrix summarizes the change over time in latent status membership exhibited by the sample.
Refer to the Resources listed below for more detailed information about LCA and LTA.
Software Downloads:
The Methodology Center distributes, free of charge, a suite of programs for LCA and LTA as add-on procedures for SAS. These procedures, PROC LCA (for latent class analysis) and PROC LTA (for latent transition analysis), were developed for SAS Version 9.1 for Windows.
The Methodology Center also distributes WinLTA, a free-standing Windows application for LCA and LTA. Although we no longer support this program, researchers without access to SAS may wish to download WinLTA free of charge.
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