Many variables of interest are ordinal. That is, you can rank the values, but the real distance between categories is unknown. Diseases are graded on scales from least severe to most severe. Survey respondents choose answers on scales from strongly agree to strongly disagree. Students are graded on scales from A to F.

From the observed and expected frequencies, you can compute the usual Pearson and Deviance goodness- of- fit measures.

The Pearson goodness- of- fit statistic is

The deviance measure is

Both of the goodness- of- fit statistics should be used only for models that have reasonably large expected values in each cell. If you have a continuous independent variable or many categorical predictors or some predictors with many values, you may have many cells with small expected values. SPSS warns you about the number of empty cells in your design. In this situation, neither statistic provides a dependable goodness- of- fit test. If your model fits well, the observed and expected cell counts are similar, the value of each statistic is small, and the observed significance level is large. You reject the null hypothesis that the model fits if the observed significance level for the goodnessof- fit statistics is small. Good models have large observed significance levels.

[此贴子已经被作者于2006-5-17 13:14:53编辑过]