Goodness of Fit of Product Multinomial Regression Models to Sparse Data

Dianliang Deng () and Sudhir R. Paul ()
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Dianliang Deng: University of Regina
Sudhir R. Paul: University of Windsor

Sankhya B: The Indian Journal of Statistics, 2016, vol. 78, issue 1, No 4, 78-95

Abstract: 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.

Keywords: Pearson statistic; sparse data; multinomial model; family of power-divergence statistics; size; power; Primary 62H15; 62J12; Secondary 62F05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13571-015-0109-z

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