The probabilistic reduction approach to specifying multinomial logistic regression models in health outcomes research

Abstract

The paper provides a novel application of the probabilistic reduction (PR) approach to the analysis of multi-categorical outcomes. The PR approach, which systematically takes account of heterogeneity and functional form concerns, can improve the specification of binary regression models. However, its utility for systematically enriching the specification of and inference from models of multi-categorical outcomes has not been examined, while multinomial logistic regression models are commonly used for inference and, increasingly, prediction. Following a theoretical derivation of the PR-based multinomial logistic model (MLM), we compare functional specification and marginal effects from a traditional specification and a PR-based specification in a model of post-stroke hospital discharge disposition and find that the traditional MLM is misspecified. Results suggest that the impact on the reliability of substantive inferences from a misspecified model may be significant, even when model fit statistics do not suggest a strong lack of fit compared with a properly specified model using the PR approach. We identify situations under which a PR-based MLM specification can be advantageous to the applied researcher.

Keywords:

• heterogeneity
• interaction effects
• marginal effects
• model specification
• multinomial logistic regression
• probabilistic reduction approach

Notes

1. Heterogeneity and differences due to ethnic and racial disparity has been a significant topic in the health outcomes research literature [13,17,25,26].

2. An inverse conditional distribution that does fit the shape of the data and explored by Bergtold et al. [4] was the Weibull distribution. The Weibull distribution has two parameters (scale and location). If the scale parameter is not consistent across j, then this distribution will not provide a tractable option for defining an operational statistical model as no clear mapping between the parameters of the inverse conditional distribution and the multinomial logistic regression model (e.g. can be established, making estimation extremely difficult. For the given empirical problem, when the Weibull distribution was fit to patient age for the different hospital discharge categories, the scale parameter varied between the j categories (i.e. from 4 to 8). Thus, a more flexible approach was deemed the optimal modeling strategy to pursue.