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The main purpose of this paper is to present new families of test statisticsfor studying the problem of goodness-of-fit of some data to a latent classmodel for binary data. The families of test statistics introduced are based onphi-divergence measures, a natural extension of maximum likelihood. We alsotreat the problem of testing a nested sequence of latent class models forbinary data. For these statistics, we obtain their asymptotic distribution. Weshall consider consistent estimators introduced in Felipe et al (2014) forsolving the problem of estimation. Finally, a simulation study is carried outin order to compare the efficiency, in the sense of the level and the power, ofthe new statistics considered in this paper for sample sizes that are not bigenough to apply the asymptotical results.

Phi-Divergence test statistics for testing the validity of latent class models for binary data