The LOGSELECT Procedure

The LOGSELECT procedure fits and performs model selection for logistic regression models in SAS Viya, including binary, binomial, and multinomial response models.

The models that PROC LOGSELECT supports can contain main effects that consist of both continuous and classification variables and interaction effects of these variables. The models can also include constructed effects such as splines. The procedure offers a number of effect-selection methods, including stepwise methods and modern LASSO methods. It also offers extensive capabilities for customizing the model selection by using a wide variety of selection and stopping criteria, from computationally efficient significance-level-based criteria to modern, computationally intensive validation-based criteria. PROC LOGSELECT also provides a variety of logistic regression diagnostics that are conditional on the selected model.

Logistic regression analysis is often used to investigate the relationship between discrete responses and a set of explanatory variables. The LOGSELECT procedure fits logistic regression models in the broader sense; the procedure permits several link functions and can handle ordinal and nominal response data that have more than two response categories (multinomial data).

The logistic model shares a common feature with a more general class of linear models: a function of the mean of the response variable is assumed to be linearly related to the explanatory variables. Because the mean implicitly depends on the stochastic behavior of the response and the explanatory variables are assumed to be fixed, the function g provides the link between the random (stochastic) component and the systematic (deterministic) component of the response variable Y. For this reason, Nelder and Wedderburn (1972) refer to as a link function. The LOGSELECT procedure fits a broad class of binary response models of the form

where the link functions that are available in PROC LOGSELECT and that are widely used in practice are the logit, probit, log-log, and complementary log-log functions, and the predicted probability of an event, , is the mean of the response variable. One advantage of the logit function over other link functions is that differences on the logistic scale are interpretable regardless of whether the data are sampled prospectively or retrospectively (McCullagh and Nelder 1989, Chapter 4).

If your response Y has more than two values and they can be ordered (for example, ), then the LOGSELECT procedure uses the preceding link functions and fits ordinal response models of the form

where are cumulative probabilities of the ordered response categories.

If your response Y has more than two values and they have no natural ordering, then the LOGSELECT procedure fits a generalized or baseline-category logit model, which has the form

where the are J–1 vectors of slope parameters. These models are a special case of the discrete choice or conditional logit models introduced by McFadden (1974).

Texts that discuss logistic regression include Agresti (2013); Allison (2012); Collett (2003); Cox and Snell (1989); Hosmer and Lemeshow (2013); Stokes, Davis, and Koch (2012).