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Bootstrapping Goodness-of-Fit Measures in Categorical Data Analysis

Author

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  • ROLF LANGEHEINE

    (University of Kiel, Germany)

  • JEROEN PANNEKOEK

    (Statistics Netherlands)

  • FRANK VAN DE POL

    (Statistics Netherlands)

Abstract

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.

Suggested Citation

  • Rolf Langeheine & Jeroen Pannekoek & Frank Van De Pol, 1996. "Bootstrapping Goodness-of-Fit Measures in Categorical Data Analysis," Sociological Methods & Research, , vol. 24(4), pages 492-516, May.
    • Handle: RePEc:sae:somere:v:24:y:1996:i:4:p:492-516
    DOI: 10.1177/0049124196024004004
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    References listed on IDEAS

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    2. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 209-224, June.
    3. Paul S. Albert & Lisa M. McShane & Joanna H. Shih, 2001. "Latent Class Modeling Approaches for Assessing Diagnostic Error without a Gold Standard: With Applications to p53 Immunohistochemical Assays in Bladder Tumors," Biometrics, The International Biometric Society, vol. 57(2), pages 610-619, June.
    4. Huiping Xu & Bruce A. Craig, 2009. "A Probit Latent Class Model with General Correlation Structures for Evaluating Accuracy of Diagnostic Tests," Biometrics, The International Biometric Society, vol. 65(4), pages 1145-1155, December.
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