Abstract
Methods for group comparisons using predicted probabilities and marginal effects on probabilities are developed for regression models for binary outcomes. Unlike approaches based on the comparison of regression coefficients across groups, the methods we propose are unaffected by the scalar identification of the coefficients and are expressed in the natural metric of the outcome probability. While we develop our approach using binary logit with two groups, we consider how our interpretive framework can be used with a broad class of regression models and can be extended to any number of groups.
References
|
Agresti, A. 2013. Categorical Data Analysis. 3rd ed. New York: Wiley. Google Scholar | |
|
Ai, C., Norton, E. C.. 2003. “Interaction Terms in Logit and Probit Models.” Economics Letters 80:123–29. Google Scholar | ISI | |
|
Allison, P. D. 1999. “Comparing Logit and Probit Coefficients across Groups.” Sociological Methods & Research 28:186–208. Google Scholar | SAGE Journals | ISI | |
|
Amemiya, T. 1981. “Qualitative Response Models: A Survey.” Journal of Economic Literature 19:1483–536. Google Scholar | ISI | |
|
Bender, R., Kuss, O.. 2010. “Methods to Calculate Relative Risks, Risk Differences, and Numbers Needed to Treat from Logistic Regression.” Journal of Clinical Epidemiology 63:7. Google Scholar | Medline | |
|
Bishop, Y., Fienberg, S., Holland, P.. 1975. Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press. Google Scholar | |
|
Breen, R., Holm, A., Karlson, K. B.. 2014. “Correlations and Nonlinear Probability Models.” Sociological Methods & Research 43:571–605. Google Scholar | SAGE Journals | ISI | |
|
Breen, R., Karlson, K. B.. 2013. Counterfactual Causal Analysis and Nonlinear Probability Models. Dordrecht, the Netherlands: Springer. Google Scholar | |
|
Buis, M. L. 2010. “Stata tip 87: Interpretation of Interactions in Non-linear Models.” The Stata Journal 10:305–8. Google Scholar | SAGE Journals | ISI | |
|
Burbidge, J. B., Magee, L., Robb, A. L.. 1988. “Alternative Transformations to Handle Extreme Values of the Dependent Variable.” Journal of the American Statistical Association 83:123–27. Google Scholar | ISI | |
|
Chow, G. 1960. “Tests of Equality between Sets of Coefficients in Two Linear Regressions.” Econometrica 28:591–605. Google Scholar | ISI | |
|
Greenland, S. 1987. “Interpretation and Choice of Effect Measures in Epidemiologic Analyses.” American Journal of Epidemiology 125:761–68. Google Scholar | Medline | ISI | |
|
Health and Retirement Study . 2006. Public Use Dataset. Ann Arbor, MI.: Produced and Distributed by the University of Michigan with Funding from the National Institute on Aging (grant number NIA U01AG009740). Google Scholar | |
|
Hummer, R. A., Benjamins, M. R., Rogers, R. G.. 2004. “Racial and Ethnic Disparities in Health and Mortality among the U.S. Elderly Population.” Pp 53–94 in Critical Perspectives on Racial and Ethnic Differences in Health in Late Life, edited by Anderson, Norman B., Bulatao, Rodolfo A., Cohen, Barney. Washington, DC: National Academies Press. Google Scholar | |
|
Kendler, K. S., Gardner, C. O.. 2010. “Interpretation of Interactions: Guide for the Perplexed.” The British Journal of Psychiatry 197:170–71. Google Scholar | Medline | ISI | |
|
Kuha, J., Mills, C.. 2018. “On Group Comparisons with Logistic Regression Models.” Sociological Methods & Research 1–28. Google Scholar | |
|
Landerman, L. R., Mustillo, S. A., Land, K. C.. 2011. “Modeling Repeated Measures of Dichotomous Data: Testing Whether the Within-person Trajectory of Change Varies across Levels of Between-person Factors.” Social Science Research 40:1456–64. Google Scholar | Medline | |
|
Leeper, T. J . 2018. Margins: An R Port of Statas Margins Command. R package version 0.3.23. Google Scholar | |
|
Liao, T. F. 2002. Statistical Group Comparison. Vol. 29. New York: Wiley. Google Scholar | |
|
Long, J. S. 1997. Regression Models for Categorical and Limited Dependent Variables, vol. 7 of Advanced Quantitative Techniques in the Social Sciences. Thousand Oaks, CA: Sage. Google Scholar | |
|
Long, J. S. 2005. Group Comparisons in Nonlinear Models Using Predicted Outcomes. Working paper, Department of Sociology, Indiana University. Google Scholar | |
|
Long, J. S. 2009. Group Comparisons in Logit and Probit Using Predicted Probabilities. Working paper, Department of Sociology, Indiana University. Google Scholar | |
|
Long, J. S., Freese, J.. 2006. Regression Models for Categorical Dependent Variables Using Stata. 2nd ed. College Station, TX: Stata Press. Google Scholar | |
|
Long, J. S., Freese, J.. 2014. Regression Models for Categorical Dependent Variables Using Stata. 3rd ed. College Station, TX: Stata Press. Google Scholar | |
|
Maddala, G. 1983. Limited-dependent and Qualitative Variables in Econometrics. Cambridge, MA: Cambridge University Press. Google Scholar | |
|
Markides, K. S., Rudkin, L., Angel, R. J., Espino, D. V.. 1997. “Health status of Hispanic elderly.” Pp 285–300. in Racial and Ethnic Differences in the Health of Older Americans, edited by Martin, L. G., Soldo, B. J., Washington DC: National Academy Press. Google Scholar | |
|
McKelvey, R. D., Zavoina, W.. 1975. “A Statistical Model for the Analysis of Ordinal Level Dependent Variables.” Journal of Mathematical Sociology 4:103–20. Google Scholar | ISI | |
|
Mood, C. 2010. “Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do about It.” European Sociological Review 26: 1–16. Google Scholar | |
|
Mustillo, S., Landerman, L. R., Land, K. C.. 2012. “Modeling Longitudinal Count Data: Testing for Group Differences in Growth Trajectories Using Average Marginal Effects.” Sociological Methods & Research 41:467–87. Google Scholar | SAGE Journals | ISI | |
|
Norton, E. C., Miller, M. M., Kleinman, L. C.. 2013. Computing Adjusted Risk Ratios and Risk Differences in Stata. Stata Journal 13:492–509. Google Scholar | Abstract | ISI | |
|
Norton, E. C., Wang, H., Ai, C.. 2004. “Computing Interaction Effects and Standard Errors in Logit and Probit.” The Stata Journal 4:154–67. Google Scholar | Abstract | |
|
Þxpert Panel on the Identification, Evaluation, and Treatment of Overweight in Adults . 1998. “Clinical guidelines on the identification, evaluation, and treatment of overweight and obesity in adults: executive summary.” The American Journal of Clinical Nutrition 68: 899–917. Google Scholar | Medline | |
|
RAND . 2014. RAND HRS Data, Version N. Santa Monica, CA: Produced by the RAND Center for the Study of Aging, with funding from the National Institute on Aging and the Social Security Administration. Google Scholar | |
|
StataCorp . 2017a. Stata 15 Base Reference Manual. College Station, TX: Stata Press. Google Scholar | |
|
StataCorp . 2017b. Stata 15 Survey Data Reference Manual. College Station, TX: Stata Press. Google Scholar | |
|
Williams, R. 2009. “Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients across Groups.” Sociological Methods and Research 37:531–59. Google Scholar | SAGE Journals | ISI | |
|
Zhang, Q., Wang, Y., Huang, E. S.. 2009. “Changes in Racial/Ethnic Disparities in the Prevalence of Type 2 Diabetes by Obesity Level among US Adults.” Ethnicity & Health 14:439–57. Google Scholar | Medline | ISI |
