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Goodness of Fit of Product Multinomial Regression Models to Sparse Data

Author

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  • Dianliang Deng

    (University of Regina)

  • Sudhir R. Paul

    (University of Windsor)

Abstract

Tests of goodness of fit of sparse multinomial models with non-canonical links is proposed by using approximations to the first three moments of the conditional distribution of a modified Pearson Chi-square statistic. The modified Pearson statistic is obtained using a supplementary estimating equation approach. Approximations to the first three conditional moments of the modified Pearson statistic are derived. A simulation study is conducted to compare, in terms of empirical size and power, the usual Pearson Chi-square statistic, the standardized modified Pearson Chi-square statistic using the first two conditional moments, a method using Edgeworth approximation of the p-values based on the first three conditional moments and a score test statistic. There does not seems to be any qualitative difference in size of the four methods. However, the standardized modified Pearson Chi-square statistic and the Edgeworth approximation method of obtaining p-values using the first three conditional moments show power advantages compared to the usual Pearson Chi-square statistic, and the score test statistic. In some situations, for example, for small nominal level, the standardized modified Pearson Chi-square statistic shows some power advantage over the method using Edgeworth approximation of the p-values using the first three conditional moments. Also, the former is easier to use and so is preferable. Two data sets are analyzed and a discussion is given.

Suggested Citation

  • Dianliang Deng & Sudhir R. Paul, 2016. "Goodness of Fit of Product Multinomial Regression Models to Sparse Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 78-95, May.
    • Handle: RePEc:spr:sankhb:v:78:y:2016:i:1:d:10.1007_s13571-015-0109-z
    DOI: 10.1007/s13571-015-0109-z
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    References listed on IDEAS

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    1. S. R. Paul & D. Deng, 2000. "Goodness of fit of generalized linear models to sparse data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 323-333.
    2. Kim, Sung-Ho & Choi, Hyemi & Lee, Sangjin, 2009. "Estimate-based goodness-of-fit test for large sparse multinomial distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1122-1131, February.
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    Cited by:

    1. Farzana Afroz & Matt Parry & David Fletcher, 2020. "Estimating overdispersion in sparse multinomial data," Biometrics, The International Biometric Society, vol. 76(3), pages 834-842, September.

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