I am attempting to use the stepwise selection method to formulate a parsimonious model from 30 covariates, a dichotomous outcome, and 177 observations. SLENTRY=SLSTAY=0.1 and the initial, univariate Chi-square scores show 10 variables meeting the entry criterion. However, two predictors with the largest Chi-square scores each terminate the stepwise process because they both fail (P>0.6) the predictor retention criterion, once entered and the output states "Model building terminates because the last effect entered is removed by the Wald statistic criterion". If I exclude these two predictors from the stepwise selection, the model proceeds as expected until no additional predictors meet the entry criterion. I have two questions: 1) Why does a predictor with a very large Chi-square score, and p=0.0007, fail to be retained in the stepwise model? and 2) Is it statistically-defensible to exclude predictors from the stepwise process with large Chi-square scores and proceed as I have described above? All advice and citations accepted with gratitude.
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