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Alternative goodness-of-fit test in logistic regression models
The Deviance and the Pearson chi-square are two traditional goodness-of-fit tests in generalized linear models for which the logistic model is a special case. The effort involved in the computation of either the Deviance or Pearson chi-square statistic is enormous and this provides a reason for pros...
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2011
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| Summary: | The Deviance and the Pearson chi-square are two traditional goodness-of-fit tests in generalized linear models for which the logistic model is a special case. The effort involved in the computation of either the Deviance or Pearson chi-square statistic is enormous and this provides a reason for prospecting an alternative goodness-of-fit test in logistic regression models with discrete predictor variables. The Deviance is based on the log likelihood function while the Pearson chi-square derives from the discrepancies between observed and predicted counts. Replacing observed and predicted counts with observed proportions and predicted probabilities, respectively in a cross-classification data arrangement, the standard error of estimate is proposed as an alternative goodness-of-fit test in logistic regression models. The illustrative example returns favourable comparisons with Deviance and the Pearson chi-square statistics. |
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