A Mathematical Tool for Inference in Logistic Regression with Small-Sized Data Sets: A Practical Application on ISW-Ridge Relationships

摘要

The general approach to modeling binary data for the purpose of estimating thepropagation of an internal solitary wave (ISW) is based on the maximum likelihoodestimate (MLE) method. In cases where the number of observations in the data is small,any inferences made based on the asymptotic distribution of changes in the deviance may be unreliable for binary data (themodel's lack of fit is described in terms of a quantity known as the deviance). Thedeviance for the binary data is given by D. Collett (2003). may be unreliable for binary data.Logistic regression shows that theP-values for the likelihood ratio test and the scoretest are both<0.05. However, the null hypothesis is not rejected in the Wald test. Theseeming discrepancies inP-values obtained between the Wald test and the other two testsare a sign that the large-sample approximation is not stable. We find that the parametersand the odds ratio estimates obtained via conditional exact logistic regression aredifferent from those obtained via unconditional asymptotic logistic regression. Usingexact results is a good idea when the sample size is small and the approximateP-valuesare<0.10. Thus in this study exact analysis is more appropriate.