Latent class analysis

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The latent class analysis (engl. Latent class analysis , LCA ) is a classification method , the observable discrete variables to latent variables can be assigned. It is based on a special latent variable model in which the manifest and latent variables are categorical and not metric. We speak of latent classes because they are discrete latent variables. Latent class analysis is a special type of structural equation model . It is used to find groups or subsets of cases in multivariate categorical data. Such subgroups are called latent classes. With the LCA, typologies are developed that can be empirically verified. With the latent class analysis, concepts that cannot be measured directly, such as B. milieu, lifestyles, leisure time behavior etc., empirically mapped to typologies using directly measurable variables.

The latent class analysis is superior to classical cluster analysis methods , especially if there are only a few observed properties or characteristics.

The method is used, among other things, in the field of economics (especially market research).

Application example: Determination of segment-specific utility functions

The aim is to determine segment-specific utility functions and the reliable allocation of segments.

Background and purpose of the latent class method: Estimates of individual utility functions are based on i. d. Usually based on insufficient information (symptoms of fatigue of the respondents after too many surveys). This means that individual estimates are hardly possible. Remedial action is taken through aggregated procedures, but this can only be justified if there is a high degree of agreement among the respondents. This high degree of agreement can be found in segments.

Procedure of the latent class method: instead of a uniform utility function (such as that used in conjoint analysis ), a separate utility function is estimated for each segment. Every respondent belongs to every segment with a non-zero probability. This initially ambiguous assignment to segments prevents incorrect assignments. Using an iterative process using a special algorithm, segment-specific utility functions and the probability of segment affiliation are determined. The number of segments ( latent classes ) should actually be specified ex ante, since the basic assumption prevails that there is a "true number of segment-specific utility functions". In practice, however, this is hardly possible. Rather, the solution algorithm is repeated for different numbers of segments and determined using an information criterion (CAIC).

Evaluation of the procedure: the high efficiency of the procedure is advantageous, especially considering that only a small amount of data is required per respondent. Internal validity, cross-over validity and prognostic validity proved to be quite high with this method. The likelihood quotient index, which lies between 0 and 1, provides a measure of the validity of the content. Is he z. B. at 0.7, the data were mapped very well by the utility function. The allocation to segments can be significantly improved if the number of surveys per respondent increases.

literature

  • H.-J. Andreß, JA Hagenaars, S. Kühnel: Analysis of tables and categorical data. Berlin 1997.
  • AK Formann: The Latent Class Analysis. Weinheim 1984.
  • W. Kempf, R Langeheine: Item Response Models in Social Science Research. Berlin 2012.
  • PF Lazarsfeld: The logical and mathematical foundations of latent structure analysis. In: SA Stouffler, L. Guttman, EA Suchman, PF Lazarsfeld, SA Star, JA Clausen (eds.): Studies in social psychology in World War II. Volume IV: Measurement and Prediction. Princeton, 1950, pp. 362-412.
  • J. Rost: Applications of latent trait and latent class models in the social sciences. Munster 1997.
  • Thorsten Teichert : The latent-class method for segmenting choice-based conjoint data - findings from an empirical application. In: Marketing ZFP. Issue 3, 3rd quarter 2000.