An Alternative Method for Assessing Goodness-of-Fit for Logit Models

An inference strategy is presented to assess the goodness-of-fit for logit models. The conventional approach has emphasized likelihood ratio tests in which a distribution for the test statistic is assumed. A more recent development, the prediction success table, is based upon a ratio of predicted to observed choice patterns, yet it is primarily a descriptive index not placed within the context of an inference strategy/hypothesis-testing framework. An alternative method is put forward which uses residuals. Although problematic in a parametric context, residuals can be used in an approach which incorporates both a nonparametric randomization procedure and a sample reuse design. A test statistic is defined and compared to a reference distribution created under the assumption of random variation in the responses with variation in the explanatory variable(s). A numerical example is carried out to investigate the efficacy of using this approach.