Ordinal-level measures are very common in social science research. Researchers often analyze ordinal dependent variables using the proportional odds logistic regression model. However, this ‘‘traditional’’ method is one of many different types of logistic regression models available for the analysis of ordered response variables. In this article, the author identifies 12 distinct models that rely on logistic regression and fit within a framework of three major approaches with variations within each approach based on the application of the proportional odds assumption. This typology provides a degree of conceptual clarity that is missing in the extant literature on logistic regression models for ordinal outcomes. The author illustrates the similarities and differences among the different models with examples from the General Social Survey and the American National Election Study.
Agresti, Alan.1984. Analysis of Ordinal Categorical Data. New York: John Wiley.
2.
Albert, James H. and Siddhartha Chib.2001. ‘‘Sequential Ordinal Modeling With Applications to Survival Data.’’Biometrics57:829-36.
3.
Allison, Paul D.1984. Event History Analysis. Beverly Hills, CA: Sage.
4.
Allison, Paul D.1999. ‘‘Comparing Logit and Probit Coefficients Across Groups.’’Sociological Methods & Research28:186-208.
5.
Amemiya, Takeshi.1981. ‘‘Qualitative Response Models. ’’ Journal of Economic Literature19:1483-1536.
6.
Ananth, Cande V. and David G. Kleinbaum.1997. ‘‘Regression Models for Ordinal Responses: A Review of Methods and Applications.’’International Journal of Epidemiology26:1323-33.
7.
Anderson, J.A.1984. ‘‘Regression and Ordered Categorical Variables.’’Journal of the Royal Statistical Society, Series B (Methodological) 46:1-30.
8.
Bobo, Lawrence and James R. Kluegel.1993. ’’Opposition to Race-Targeting: Self-Interest, Stratification Ideology, or Racial Attitudes?’’American Sociological Review58:443-64.
9.
Boes, Stefan and Winkelmann, Rainer.2004. ‘‘Income and Happiness: New Results From Generalized Threshold and Sequential Models.’’ IZA Discussion Paper No. 1175 , Institute for the Study of Labor, Bonn, Germany.
10.
Brant, Rollin.1990. ‘‘Assessing Proportionality in the Proportional Odds Model for Ordinal Logistic Regression.’’ Biometrics46:1171-78.
11.
Branton, Regina P. and Bradford S. Jones.2005. ‘‘Reexamining Racial Attitudes: The Conditional Relationship Between Diversity and Socioeconomic Environment.’’American Journal of Political Science49:359-72.
12.
Clogg, Clifford C. and Edward S. Shihadeh.1994. Statistical Models for Ordinal Variables . Thousand Oaks, CA: Sage.
13.
Cook, Fay Lomax and Edith J. Barrett.1992. Support for the American Welfare State: The Views of Congress and the Public. New York: Columbia University Press.
14.
Cox, D.R.1972. ‘‘Regression Models and Life-Tables.’’Journal of the Royal Statistical Society, Series B (Methodological)34:187-220.
15.
Davis, James Allan and Tom W. Smith.2005. General Social Surveys, 1972-2004 [Machine-readable data file]. Chicago: National Opinion Research Center [Producer]; Storrs: University of Connecticut, Roper Center for Public Opinion Research [Distributor].
16.
DiPrete, Thomas A.1990. ‘‘Adding Covariates to Loglinear Models for the Study of Social Mobility.’’American Sociological Review55:757-73.
17.
Fienberg, Stephen E.1980. The Analysis of Cross-Classified Categorical Data. 2nd ed. Cambridge, MA: MIT Press.
18.
Fox, Cybelle.2004. ‘‘The Changing Color of Welfare? How Whites’ Attitudes Toward Latinos Influence Support for Welfare.’’ American Journal of Sociology110:580-625.
Fujimoto, Kayo.2005. ‘‘From Women’s College to Work: Inter-Organizational Networks in the Japanese Female Labor Market.’’ Social Science Research34:651-81.
21.
Fullerton, Andrew S. and Michael Wallace.2007. ‘‘Traversing the Flexible Turn: U.S. Workers’ Perceptions of Job Security, 1977-2002.’’Social Science Research36:201-21.
22.
Gilens, Martin.1999. Why Americans Hate Welfare. Chicago : University of Chicago Press.
23.
Goodman, Leo A.1983. ‘‘The Analysis of Dependence in Cross-Classifications Having Ordered Categories, Using Log-Linear Models for Frequencies and LogLinear Models for Odds.’’Biometrics39:149-60.
24.
Gould, William, Jeffrey Pitblado, and William Sribney .2003. Maximum Likelihood Estimation With Stata. 2nd ed. College Station, TX: Stata Press.
25.
Greenland, Sander.1994. ‘‘Alternative Models for Ordinal Logistic Regression.’’ Statistics in Medicine13:1665-77.
26.
Halaby, Charles N.1986. ‘‘Worker Attachment and Workplace Authority.’’American Sociological Review51:634-49.
27.
Hauser, Robert M. and Megan Andrew.2006. ‘‘Another Look at the Stratification of Educational Transitions: The Logistic Response Model With Partial Proportionality Constraints.’’Sociological Methodology36:1-26.
28.
Hout, Michael, Clem Brooks, and Jeff Manza.1995. ‘‘The Democratic Class Struggle in the United States, 1948-1992.’’ American Sociological Review60:805-28.
29.
Kahn, Lawrence M. and Kimio Morimune.1979. ‘‘Unions and Employment Stability: A Sequential Logit Approach.’’International Economic Review20:217-35.
30.
Liao, Tim Futing.1994. Interpreting Probability Models: Logit, Probit, and Other Generalized Linear Models. Thousand Oaks, CA: Sage.
31.
Liao, Tim Futing and Gillian Stevens.1994. ‘‘Spouses, Homogamy, and Social Networks.’’Social Forces73:693-707.
32.
Long, J. Scott.1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage .
33.
Long, J. Scott and Simon Cheng.2004. ’’Regression Models for Categorical Outcomes.’’ Pp. 259-84 in Handbook of Data Analysis, edited by Melissa Hardy and Alan Bryman.Thousand Oaks, CA: Sage.
34.
Long, J. Scott and Robert McGinnis.1981. ‘‘Organizational Context of Scientific Productivity.’’American Sociological Review46:422-42.
35.
Maddala, G.S.1983. Limited-Dependent and Qualitative Variables in Econometrics . Cambridge, UK: Cambridge University Press.
36.
Manor, Orly, Sharon Matthews, and Chris Power.2000. ‘‘Dichotomous or Categorical Response? Analysing Self-Rated Health and Lifetime Social Class. ’’ International Journal of Epidemiology29:149-57.
37.
Mare, Robert D.1980. ‘‘Social Background and School Continuation Decisions.’’Journal of the American Statistical Association75:295-305.
38.
McCullagh, Peter.1980. ‘‘Regression Models for Ordinal Data.’’Journal of the Royal Statistical Society, Series B42:109-42.
39.
McCullagh, Peter and John A. Nelder.1989. Generalized Linear Models. 2nd ed. New York: Chapman and Hall.
40.
McKelvey, Richard D. and William Zavoina.1975. ‘‘A Statistical Model for the Analysis of Ordinal Level Dependent Variables.’’Journal of Mathematical Sociology4:103-20.
41.
Mooney, Margarita.2003. ‘‘Migrants’ Social Ties in the U.S. and Investment in Mexico.’’ Social Forces81:1147-70.
42.
Mouw, Ted and Michael E. Sobel.2001. ‘‘Culture Wars and Opinion Polarization: The Case of Abortion.’’American Journal of Sociology106:913-43.
43.
O’Connell, Ann A.2006. Logistic Regression Models for Ordinal Response Variables . Thousand Oaks, CA: Sage.
44.
Peterson, Bercedis and Frank E. Harrell, Jr.1990. ‘‘Partial Proportional Odds Models for Ordinal Response Variables.’’Applied Statistics39:205-17.
45.
Powers, Daniel A. and Yu Xie.2000. Statistical Methods for Categorical Data Analysis. San Diego, CA: Academic Press.
46.
Rosenstone, Steven J. and John Mark Hansen.1993. Mobilization, Participation, and Democracy in America . New York: Macmillan.
47.
Sobel, Michael E.1997. ‘‘Modeling Symmetry, Asymmetry, and Change in Ordered Scales With Midpoints Using Adjacent Category Logit Models for Discrete Data.’’Sociological Methods & Research26:213-32.
48.
Train, Kenneth E.2003. Discrete Choice Methods With Simulation. Cambridge, UK: Cambridge University Press.
49.
University of Michigan, Center for Political Studies, American National Election Study. (2004). American National Election Study, 2004: Pre- And Post-Election Survey (ICPSR04245-v1) [Computer file]. Ann Arbor: University of Michigan, Center for Political Studies, American National Election Study [Producer]; Ann Arbor: Inter-university Consortium for Political and Social Research [Distributor].
50.
Williams, Richard.2006a. ‘‘Generalized Ordered Logit/Partial Proportional Odds Models for Ordinal Dependent Variables.’’ Stata Journal6:58-82.
51.
Williams, Richard.2006b. ’’OGLM: Stata Module to Estimate Ordinal Generalized Linear Models.’’http://econpapers.repec.org/software/bocbocode/s453402.htm .
52.
Williams, Richard.2009. ‘‘Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients Across Groups.’’Sociological Methods & Research37:531-559.
53.
Winship, Christopher and Robert D. Mare.1984. ‘‘Regression Models With Ordinal Variables.’’American Sociological Review49:512-25.
54.
Wright, Erik Olin, Janeen Baxter, and Gunn Elisabeth Birkelund.1995. ‘‘The Gender Gap in Workplace Authority: A Cross-National Study.’’American Sociological Review60:407-35.
