oglm: Ordinal Generalized Linear Models
Richard Williams, University of Notre Dame
Note: Those who are interested in oglm may also be interested in its older sibling, gologit2. Much of the material on the gologit2 page will also apply to oglm.
Readings. Allison (1999) showed that comparisons of logit and probit coefficients across groups was potentially problematic. Using Heterogeneous Choice Models To Compare Logit and Probit Coefficients Across Groups (revised March 2009; a final version is in the May 2009 Sociological Methods and Research) critiques Allison's proposed solution and shows how it can be improved upon using heterogeneous choice models that can be estimated by the author's Stata program oglm (Ordinal Generalized Linear Models). Download these zip files if you want to replicate the Simulations of Table 4 or the Other Analyses.
This 2010 Stata Journal paper, Fitting heterogeneous choice models with oglm, illustrates how oglm can be used to estimate heterogeneous choice and related models. It shows that two other models that have appeared in the literature (Allison's model for group comparisons and Hauser and Andrew's logistic response model with proportionality constraints) are special cases of a heterogeneous choice model and alternative parameterizations of it. The paper further argues that heterogeneous choice models may sometimes be an attractive alternative to other ordinal regression models, such as the generalized ordered logit model estimated by gologit2. Finally, the paper offers guidelines on how to interpret, test and modify heterogeneous choice models. If you want to replicate the analyses, you can download oglm_examples.do and lrpc.dta. I thank J. Scott Long, Robert Hauser and Megan Andrew for making their data sets available for this paper. (NOTE: Several additional variables not used in the paper can be found in the 74 MB lrpcfull.dta. More information on the OCG II data used in the lrpc files can be found at ICPSR.)
This paper from The Stata Journal discusses the closely related gologit2 program, which estimates many of the same models as oglm. Also, this July 2006 presentation (powerpoint or pdf; related handout) discusses "Interpreting and using heterogeneous choice & generalized ordered logit models." It raises several issues that users of gologit may not be aware of and argues that heterogeneous choice models (which can be estimated with oglm) can sometimes be an attractive alternative to gologit models.
I also highly recommend this working paper by Keele and Park. It reviews the literature on some of the models estimated by oglm , and also critiques these methods. I asked the authors how much I should be worried about these problems, and they told me that "I wouldn't worry that much in that the ordinal probit is quite a bit better overall. In political science people use fairly complicated specifications for the variance model. I think if you know pretty clearly that the heterogeneity is from some set of groups then the specification is a lot easier to get right." This chapter on SPSS Plum (which oglm is patterned after) is also quite good, but keep in mind that oglm and PLUM do some things differently. The oglm help file includes several examples and documents its options.
Overview. oglm estimates Ordinal Generalized Linear Models. When these models include equations for heteroskedasticity they are also known as heterogeneous choice/ location-scale / heteroskedastic ordinal regression models. oglm supports multiple link functions, including logit (the default), probit, complementary log-log, log-log and cauchit.
When an ordinal regression model incorrectly assumes that error variances are the same for all cases, the standard errors are wrong and (unlike OLS regression) the parameter estimates are biased. Heterogeneous choice/ location-scale models explicitly specify the determinants of heteroskedasticity in an attempt to correct for it. Further, these models can be used when the variance/variability of underlying attitudes is itself of substantive interest. Alvarez and Brehm (1995), for example, argued that individuals whose core values are in conflict will have a harder time making a decision about abortion and will hence have greater variability/error variances in their responses.
Several special cases of ordinal generalized linear models can also be estimated by oglm, including the parallel lines models of ologit and oprobit (where error variances are assumed to be homoskedastic), the heteroskedastic probit model of hetprob (where the dependent variable must be a dichotomy and the only link allowed is probit), the binomial generalized linear models of logit, probit and cloglog (which also assume homoskedasticity), as well as similar models that are not otherwise estimated by Stata. This makes oglm particularly useful for testing whether constraints on a model (e.g. homoskedastic errors) are justified, or for determining whether one link function is more appropriate for the data than are others.
Other features of oglm include support for linear constraints, making it possible, for example, to impose and test the constraint that the effects of x1 and x2 are equal. oglm works with several prefix commands, including by, nestreg, xi, svy and sw. Its predict command includes the ability to compute estimated probabilities. The actual values taken on by the dependent variable are irrelevant except that larger values are assumed to correspond to "higher" outcomes. Up to 20 outcomes are allowed. oglm was inspired by the SPSS PLUM routine but differs somewhat in its terminology, and labeling of links.
To install oglm : From within Stata, type
Suggested citations if using oglm in published work
oglm is not an official Stata command. It is a free contribution to the research community, like a paper. Please cite it as such.
Williams, Richard. 2009. "Using Heterogeneous Choice Models To Compare Logit and Probit Coefficients Across Groups." Sociological Methods & Research 37(4): 531-559. A pre-publication version can be found at https://www3.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf .
Williams, Richard. 2010. "Estimating heterogeneous choice models with oglm." Working paper. Last updated October 17, 2010. https://www3.nd.edu/~rwilliam/oglm/oglm_Stata.pdf . A final version is forthcoming in The Stata Journal.
I would appreciate an email notification if you use oglm in published work, as well as a citation of one or more of the sources listed above. Also feel free to email me if you have comments about the program or its documentation.