This is a common problem with logistic models. Unlike in ordinary least-squares regression for modeling a normally distributed response, when a logistic model perfectly or nearly perfectly predicts the response (that is, separates the response levels), unique maximum likelihood estimates do not exist. Some model parameters are actually infinite. This is a common result of the data being sparse, meaning that not all response levels are observed in each of the predictor settings, which often happens with small data sets or when the event is rare.
One possible solution to the separation problem is to make the model fit less perfectly by reducing the number of variables or effects in the model, categorizing continuous variables, or merging categories of categorical (CLASS) variables. It is often difficult to know exactly which variables cause the separation, but variables that exhibit large parameter estimates or standard errors are likely candidates.
Because separation often happens with small data sets, another possible solution is to use exact logistic regression, which is available via the EXACT statement in PROC LOGISTIC. However, exact methods are very computationally intensive and can take great amounts of time and/or memory even for moderate sized problems. A penalized likelihood method by Firth can often converge to a solution even though a unique solution by maximum likelihood does not exist in separation cases. Firth's method is available, beginning in SAS 9.2, by specifying the FIRTH option in the MODEL statement.
扫码加好友，拉您进群
全部版块
我的主页
收藏
