### Thursday, March 02, 2006

## st: Updates to oglm, gologit2

Thanks to Kit Baum, updates to oglm and gologit2 are now available at SSC. There are two main changes.

First, those of you who have been longing for the day when a Stata program would support the Cauchit link will be pleased to know that your wait is finally over. Both programs now support cauchit, along with logit, probit, complementary log-log and log-log. The nature of your data and/or the conventional practices in your discipline may determine which link is most appropriate for your analysis.

Second, and more critically, oglm is much more powerful and will hopefully be more than just a niche program now. oglm can now estimate what has been variously called heterogeneous choice/ location-scale / heteroskedastic ordinal regression models. (Like ologit and oprobit, oglm used to just do the location part of location-scale, i.e. you had to assume errors were homoskedastic.) Such models allow you to correct for heteroskedasticity, and can also be used when the variance of responses is itself of substantive interest (rather than just a "nuisance" parameter). A more complete description of oglm follows:

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, labeling of links, and the variables that are allowed when modeling heteroskedasticity.

------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 FAX: (574)288-4373 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW (personal): http://www.nd.edu/~rwilliam WWW (department): http://www.nd.edu/~soc

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Tag: statalist