st: Updates to oglm, gologit2

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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
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WWW (department):    http://www.nd.edu/~soc 
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