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Reporting logistic regression analysis – should we focus on probabilities instead of odds ratios?
Curt Hagquist
Building: Holme Building
Room: Withdrawing Room
Date: 2014-12-10 01:30 PM – 03:00 PM
Last modified: 2014-10-31
Abstract
Introduction: While most studies based on logistic regression analysis seem to report the results using odds ratios solely, focusing on marginal probabilities represents another way to communicate the outcomes. The purpose of the paper is to compare these two approaches, using a logistic regression analysis of the association between different family types and adolescent binge drinking as an illustrative example.
Methods: Data were collected in the fall of 2009 by Statistics Sweden in a national cross-sectional study. 91627 Swedish students in grade 9 (15 years old) completed a questionnaire in schools.
Binary logistic regression was conducted to analyse the association between four family types and binge drinking (monthly vs less/never). Odds ratios as well as marginal effects (changes in probabilities) were estimated using the STATA 13.1 software and the user written STATA program SPost13.
Results: The students’ binge drinking was significantly higher in all non-intact family types compared to intact families, which was indicated by significant odds ratios. The odds for being a binge drinker was 1.9 times higher for students living with only one parent compared to students in intact families; 1.7 times higher for students in shared residency and 1.4 times higher for students in joint physical custody.
The average marginal effects on binge drinking varied significantly between some family types, indicated by the changes in probabilities. The average effect of being with only one parent instead of living with both parents was to increase the probability of binge drinking by 0.132. The corresponding changes in probability values for shared residency and joint physical custody were 0.105 and 0.068 respectively.
Conclusions: Although the odds ratios clearly indicate that living in non-intact families increases the odds of binge drinking, the actual magnitude may be hard to grasp intuitively. In contrast, the marginal probabilities are more intuitive and easy to interpret. On the other hand, estimating marginal probabilities in the case with multiple independent variables doesn’t enable holding the other variables constant. Instead the values of the other variables have to be specified and interpreted either as marginal effects at the mean or as average marginal effects. In reporting results from logistic regression analysis marginal probabilities add valuable information that is complementing but not replacing the information provided by odds ratios.
Methods: Data were collected in the fall of 2009 by Statistics Sweden in a national cross-sectional study. 91627 Swedish students in grade 9 (15 years old) completed a questionnaire in schools.
Binary logistic regression was conducted to analyse the association between four family types and binge drinking (monthly vs less/never). Odds ratios as well as marginal effects (changes in probabilities) were estimated using the STATA 13.1 software and the user written STATA program SPost13.
Results: The students’ binge drinking was significantly higher in all non-intact family types compared to intact families, which was indicated by significant odds ratios. The odds for being a binge drinker was 1.9 times higher for students living with only one parent compared to students in intact families; 1.7 times higher for students in shared residency and 1.4 times higher for students in joint physical custody.
The average marginal effects on binge drinking varied significantly between some family types, indicated by the changes in probabilities. The average effect of being with only one parent instead of living with both parents was to increase the probability of binge drinking by 0.132. The corresponding changes in probability values for shared residency and joint physical custody were 0.105 and 0.068 respectively.
Conclusions: Although the odds ratios clearly indicate that living in non-intact families increases the odds of binge drinking, the actual magnitude may be hard to grasp intuitively. In contrast, the marginal probabilities are more intuitive and easy to interpret. On the other hand, estimating marginal probabilities in the case with multiple independent variables doesn’t enable holding the other variables constant. Instead the values of the other variables have to be specified and interpreted either as marginal effects at the mean or as average marginal effects. In reporting results from logistic regression analysis marginal probabilities add valuable information that is complementing but not replacing the information provided by odds ratios.