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Activity Number:
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110
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Type:
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Contributed
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Date/Time:
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Monday, July 30, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #308333 |
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Title:
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Goodness-of-Fit Tests for Multinomial Logistic Regression
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Author(s):
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David Hosmer*+ and Morten W. Fagerland and Anna M. Bofin
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Companies:
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University of Massachusetts Amherst and Ullevål University Hospital and Norwegian University of Science and Technology
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Address:
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128 Worcester Road, Stowe, VT, 05672,
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Keywords:
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regression models ; generalized linear models ; fit tests ; simulations
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Abstract:
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We examine goodness-of-fit tests for multinomial logistic regression. One is based on a g by outcomes contingency table. The test statistic (Cg ) is obtained by calculating the usual Pearson chi-square statistic from this table. Simulations compare the properties of Cg to the Pearson chi-square test (X2) and its normalized test (z). The null distribution of Cg is approximated by the chi-square distribution with (g -2) × (c-1) degrees of freedom. X2 is compared to a chi-square with n × (c - 1) degrees of freedom, but shows erratic behavior. z adheres reasonably well to the standard normal distribution. Power simulations show that Cg and z have low power for a sample size of 100 observations, but satisfactory power for a sample size of 400. The tests are illustrated using data from a study of cytological criteria for the diagnosis of breast tumors.
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