AMaximum-Likelihood Approach

The authors illustrate how to perform maximum-likelihood estimation in latent c lass ( L C ) analy sis when there are sampling weig hts. The methods are natural extensions of the approac hes proposed b y C log g and E liason ( 1 9 8 7 ) and M ag idson ( 1 9 8 7 ) for dealing with sampling weig hts in the log linear analy sis of freq uenc y tab les. F or the log -linear form of the L C model, the approac h c orresponds to a spec ial c ase of H ab erman’ s ( 1 9 7 9 ) log -linear L C model with c ell weig hts. This approac h c an also b e applied to the prob ab ility formulation of the L C model with c ell weig hts, whic h c an ac c ommodate many indic ators. The authors propose an effi c ient estimationmaximiz ation alg orithm for estimating the parameters for this formulation. A small simulation study shows that the prob ab ility estimates ob tained b y this approac h c ompare fav orab ly to other weig hting approac hes. S ev eral empiric al examples are prov ided to illustrate v arious possib le weig hting methods in L C analy sis.