Abstract

ARAYA ALPIZAR, Carlomagno. An alternative to classical latent class models selection methods for sparse binary data: an illustration with simulated data. Rev. Mat [online]. 2016, vol.23, n.1, pp.199-220. ISSN 1409-2433.

Within the context of a latent class model with manifest binary variables, we propose an alternative method that solves the problem of estimating empirical distribution with sparse contingency tables and the chisquare approximation for goodness-of-fit will not be valid. We analyze sparse binary data, where there are many response patterns with very small expected frequencies in several data sets varying in degree of sparseness from 1 to 5 defined d = n/2p = n/R is a factor that is mentioned in almost all prior literature as being an important determinant of how well the distribution is represented by the chi-squared.The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. Results from the proposal presented compare the rates of Type I for traditional goodness-of-fit tests. We also show that with data density d ≤ 5, Pearson's statistic should not be used to select latent class models using the Patterns Method, given that this has the probability of Type I error being greater than 5%. By comparing the Patterns Method and the Parametric Bootstrap for data density d = 2, we show that the Patterns Method has more accurate Type I error probabilities since the likelihood ratio, Read-Cressie and Freeman-Tukey statistics afford values of α<0.05. In contrast, the Parametric Bootstrap provides values in these statistics that surpass 5%.

Keywords : sparse data; latent class; goodness-of-fit; binary data.

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