Group comparisons in logit and probit using predicted probabilities 1
Group comparisons in logit and probit using predicted probabilities 1
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使用预测概率 1 进行 Logit 和 Probit 的组比较
DOI：
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发表时间：
2009
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通讯作者：
J. S. Long
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作者：
J. S. Long
二元结果的回归模型中的组比较由于这些模型固有的识别问题而变得复杂。传统的组间系数相等检验混淆了回归系数的大小和剩余变异。如果组间的剩余变异量不同，则测试可能导致不正确的结论（Allison 1999）。Allison提出了一种检验回归系数相等的方法，通过添加一些变量的回归系数在不同组间相同的假设，消除了组间差异对残差的影响。在实践中，研究人员不太可能对这种假设有经验或理论依据，在这种情况下，艾利森的测试也可能导致错误的结论。这里建议的另一种方法是使用预测概率。由于预测概率不受残差变化的影响，因此可以将跨组预测概率相等性的检验用于组比较，而无需假设某些变量的回归系数相等。使用预测概率要求研究人员在比较群体时以不同的方式思考。通过对回归系数相等性的检验，一个单一的检验可以让研究人员很容易地得出结论，一个变量的影响在不同的群体中是否相等。测试预测概率的相等性需要多次测试，因为预测中的组差异随模型中变量的水平而变化。研究人员必须在多个变量的水平上检查群体的预测差异，通常需要更复杂的结论来说明群体在变量的影响上是如何不同的。我感谢保罗·艾利森、肯·博伦、雷夫·斯托尔岑伯格、普拉文·特里维迪和里奇·威廉姆斯的评论。
The comparison of groups in regression models for binary outcomes is complicated by an identification problem inherent in these models. Traditional tests of the equality of coefficients across groups confound the magnitude of the regression coefficients with residual variation. If the amount of residual variation differs between groups, the test can lead to incorrect conclusions (Allison 1999). Allison proposes a test for the equality of regression coefficients that removes the effect of group differences in residual variation by adding the assumption that the regression coefficients for some variables are identical across groups. In practice, a researcher is unlikely to have either empirical or theoretical justification for this assumption, in which case the Allison’s test can also lead to incorrect conclusions. An alternative approach, suggested here, uses predicted probabilities. Since predicted probabilities are unaffected by residual variation, tests of the equality of predicted probabilities across groups can be used for group comparisons without assuming the equality of the regression coefficients of some variables. Using predicted probabilities requires researchers to think differently about comparing groups. With tests of the equality of regression coefficients, a single test lets the researcher conclude easily whether the effects of a variable are equal across groups. Testing the equality of predicted probabilities requires multiple tests since group differences in predictions vary with the levels of the variables in the model. A researcher must examine group differences in predictions at multiple levels of the variables often requiring more complex conclusions on how groups differ in the effect of a variable. 1I thank Paul Allison, Ken Bollen, Rafe Stolzenberg, Pravin Trivedi, and Rich Williams for their comments.