```..-
help for ^omodel^                                           Statalist, 1Sep1997
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Maximum-likelihood ordered logit and probit estimation
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^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
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^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
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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
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Rory Wolfe <wolfer@@cryptic.rch.unimelb.edu.au>, Royal Children's Hospital,
Melbourne.
William Gould <wgould@@stata.com>, Stata Corp.

Also see
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On-line:  help for @ologit@, @oprobit@
```