help for ^omodel^                                           Statalist, 1Sep1997

Maximum-likelihood ordered logit and probit estimation - ------------------------------------------------------

^omodel logit^ depvar varlist [weight] [^if^ exp] [^in^ range]

^omodel probit^ depvar varlist [weight] [^if^ exp] [^in^ range]

^fweights^ are allowed; see help @weights@.

^omodel^ is not quite an estimation command; use @ologit@ or @oprobit@ to redisplay results.

To reset problem-size limits, see help @matsize@.

Description - -----------

^omodel^ is an alternative to @ologit@ and @oprobit@ for estimating ordered logit and probit models. It produces the same results but it also reports an approximate likelihood-ratio test of whether the coefficients are equal across categories (i.e. a test of the proportional-odds assumption if logit is the requested model).

Examples - --------

. use auto.dta, clear . ^omodel probit rep78 mpg weight^ . ^ologit^ /* to redisplay results */

. tab foreign rep78 . ^omodel logit rep78 foreign^ /* Put data into 2-way */ > . gen obs=1 /* table of counts to */ > . collapse (count) obs, by(rep78 foreign) /* demonstrate use of > */ . ^omodel logit rep78 foreign [fweight=obs]^ /* fweights */

Saved results - -------------

In addition to the results saved by ^ologit^ and ^oprobit^, ^omodel^ saves in the global ^S_^# macros

^S_1^ likelihood-ratio value ^S_2^ dof for likelihood-ratio test

Methods and formulas - --------------------

Let there be K outcomes of the dependent variable depvar and for convenience, let's call the outcomes 1, 2, ..., K, although ^omodel^ places no constraint on the labeling of the outcomes.

^omodel^ estimates the ordered logit or probit model using ^ologit^ or ^oprobit^ as requested.

An approximate version of the model is also fitted by using all K-1 binary variables obtained from dichotomisations of the ordered scale. From this an approximation to the log-likelihood obtained from the ^ologit^ or ^oprobit^ model is obtained. In most cases the approximation will be very good.

In a similar fashion, an approximation to the log-likelihood for a completely general model (in which there are different effects at each cut-point for every variable) is obtained. Note that this model cannot be fitted in Stata by maximum-likelihood. The difference between the two approximate log-likelihoods is the likelihood-ratio test reported by ^omodel^. The approximation to the log-likelihood value for the general model will usually be less reliable than the first approximation but both are underestimates of the respective true log-likelihoods. Hence in taking the difference between the two approximations we obtain a reasonable approximation to the true lieklihood-ratio test.

The ratio is tested on degrees of freedom that are the difference between the number of fitted parameters in the standard and general models. This will typically be (p)*(K-2), where p is the number of regressors specified, although under certain sparse data conditions there will be fewer degrees of freedom (see the second example above).

Finally, and very importantly, note that a significant p-value is evidence to reject the null hypothesis that the coefficients are equal across categories. A non-significant p-value does not justify the conclusion that we have an appropiate model for the data. This mistake is often made in the implementation of this test.

Authors - -------

Rory Wolfe <wolfer@@cryptic.rch.unimelb.edu.au>, Royal Children's Hospital, Melbourne. William Gould <wgould@@stata.com>, Stata Corp.

Also see - --------

On-line: help for @ologit@, @oprobit@