**Fitting Log-Linear Models to Contingency Tables From Surveys With Complex Sampling Designs: An Investigation of the Clogg-Eliason Approach**, Sociological Methods & Research 2010 39: 83-108.

## Fitting Log-Linear Models to Contingency Tables From Surveys With Complex Sampling Designs: An Investigation of the Clogg-Eliason Approach

August 12, 2010## Jeroen K. Vermunt and Jay Magidson Latent Class Analysis With Sampling Weights: A Maximum-Likelihood Approach Sociological Methods & Research 2007 36: 87-111.

February 7, 2010The authors illustrate how to perform maximum-likelihood estimation^{ }in latent class (LC) analysis when there are sampling weights.^{ }The methods are natural extensions of the approaches proposedby Clogg and Eliason (1987) and Magidson (1987) for dealing^{ }with sampling weights in the log-linear analysis of frequency^{ }tables. For the log-linear form of the LC model, the approachcorresponds to a special case of Haberman’s (1979) log-linear^{ }LC model with cell weights. This approach can also be applied^{ }to the probability formulation of the LC model with cell weights,which can accommodate many indicators. The authors propose an^{ }efficient estimation-maximization algorithm for estimating the^{ }parameters for this formulation. A small simulation study shows^{ }that the probability estimates obtained by this approach compare^{ }favorably to other weighting approaches. Several empirical examples^{ }are provided to illustrate various possible weighting methods^{ }in LC analysis.

**Key Words:** latent class analysis • mixture model • complex sampling • log-linear analysis • EM algorithm