Sociological Methods & Research · 1996 · 235 citations · 32 references
Public HealthBiostatisticsCategorical Data AnalysisStatistical ModelingStatisticsBootstrap MethodsGoodness-of-fit For Categorical ModelsInferential StatisticsLog-linear ModelsModel FittingStatistical InferenceBootstrap EstimationChi-square TestGoodness-of-fitGoodness-of-fit AssessmentGoodness-of-fit IndicesGoodness-of-fit TestsSparse Data HandlingSparse Models
When sparse data have to be fitted to a log-linear or latent class model, one cannot use the theoretical chi-square distribution to evaluate model fit, because with sparse data the observed cross-table has too many cells in relation to the number of observations to use a distribution that only holds asymptotically. The choice of a theoretical distribution is also difficult when model-expected frequencies are 0 or when model probabilities are estimated 0 or 1. The authors propose to solve these problems by estimating the distribution of a fit measure, using bootstrap methods. An algorithm is presented for estimating this distribution by drawing bootstrap samples from the model-expected proportions, the so-called nonnaive bootstrap method. For the first time the method is applied to empirical data of varying sparseness, from five different data sets. Results show that the asymptotic chi-square distribution is not at all valid for sparse data.
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