Latent class model
The latent class analysis (English Latent Class Analysis LCA) is a classification method, can be assigned to latent variable with the observable discrete variables. It is based on a special latent variable model where the manifest and the latent variables are categorical and not metric. This is called latent classes because there are discrete latent variables. The latent class analysis is a special type of structural equation model. It is used to detect groups or subgroups of cases in multivariate categorical data. Such subgroups are called latent classes. With the LCA typologies are developed that can be tested empirically. The latent class analysis can not directly measurable concepts such as Milieu, lifestyles, leisure activities, etc., represent empirically directly measurable variables to types.
The latent class analysis is superior to classical cluster analysis method, particularly if only a few observed characteristics or attribute characteristics are present.
The method finds its application among others in the field of economics (especially market research ).
Example: Determination of segment-specific utility functions
Aim is to identify segment-specific utility functions and the reliable assignment of segments.
Background and meaning of the latent -class method: estimates of individual utility functions based usually on inadequate information base ( symptoms of fatigue of respondents in many surveys). This is hardly possible individual estimates. Remedy is managed by aggregated process, but this can be justified only for high agreement of the respondents. This high level of agreement is found in segments.
Approach of the latent -class method: instead of a single utility function (as used, for example, conjoint analysis ) is estimated own utility function for each segment. Each respondent belongs to each segment with a probability equal to zero. By this time being ambiguous assignment to segments erroneous assignments are avoided. By an iterative process using a special algorithm, segment-specific utility functions and probability are determined to segment membership. The number of segments ( latent classes ) should not be specified ex ante, since the basic assumption prevails that it is " true number of segment-specific utility functions " is one. In practice this is hardly possible. Rather, the solution algorithm for different numbers of segments and repeatedly determined on the basis of an information criterion ( CAIC ).
Assessment of the procedure: beneficial is the high efficiency of the method is especially considering that there is little data per respondent are required. Internal validity, cross-over and predictive validity in this method proved to be quite high. A measure of the validity of the content has, for example, the likelihood ratio index that is between 0 and 1. Is he, for example, 0.7, the data has been mapped very well by the utility function. The allocation to segments may incidentally be significantly improved if the number of interviews per respondent increases.