.-
help for ^gologit^ Statalist, 3 December 1997
revised 7 December 1997
revised 16 January 1998
revised 24 June 1998
revised 3 April 2000
.-
Maximum-likelihood generalized ordered logit estimation
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^gologit^ depv varlist [weight] [^if^ exp] [^in^ range]
[^,^ ^c^luster^(^varname^) l^evel^(^#^) or^ ^r^obust]
This command should share the features of all estimation commands; see help
@est@.
This command typed without arguments redisplays previous results. The
following options may be given when redisplaying results
^l^evel^(^#^) or^
^aweight^s, ^fweight^s, and ^pweight^s are allowed. See help @weights@.
Using ^pweight^s implies the ^robust^ option.
Coefficients are estimated using Stata's @ml@ interface.
Stata's @ologit@ command is used to produce starting values.
Description
-----------
This command estimates regression models for ordinal dependent variables.
The actual values taken on by the dependent variable are irrelevant except
that larger values are assumed to correspond to "higher" outcomes.
The @ologit@ command included with Stata imposes what is called the
proportional odds assumption on the data. This model relaxes the
proportional odds assumption and allows the effects of the explanatory
variables to vary with the point at which the categories of the dependent
variable are dichotomized.
Options
-------
^cluster(^varname^)^ specifies that the observations are independent across groups
(clusters) but not necessarily within groups. varname specifies to which
group each observation belongs; e.g., ^cluster(personid)^ in data with
repeated observations on individuals. See ^[U] 26.10 Obtaining robust^
^variance estimates^. ^cluster()^ can used with @pweight@s to produce estimates
for unstratified cluster-sampled data. Specifying ^cluster()^ implies ^robust^.
^level(^#^)^ specifies the confidence level, in percent, for calculation of
confidence intervals of the odds ratios.
^or^ reports the estimated coefficients transformed to odds ratios, i.e., exp(b)
rather than b. Standard errors and confidence intervals are similarly
transformed. This option affects how results are displayed, not how they
are estimated. ^or^ may be specified at estimation or when redisplaying
previously estimated results.
^robust^ specifies that the Huber/White/sandwich estimator of variance is to be
used in place of the traditional calculation; see ^[U] 26.10 Obtaining^
^robust variance estimates^. ^robust^ combined with ^cluster()^ allows
observations which are not independent within cluster (although they may
be independent between clusters).
Remarks
-------
More formally, suppose we have an ordinal dependent variable Y which takes
on the values 0, 1, 2, ..., m. The generalized ordered logit model estimates
a set of coefficients (including one for the constant) for each of the m - 1
points at which the dependent variable can be dichotomized. These sets of
coefficients B_k to a set of cumulative distribution functions:
P( Y < k ) = F( -XB_k ) k = 1, ..., m
From this set of cumulative distribution functions, it is straightforward to
derive formulas for the probabilities that Y will take on each of the
values 0, 1, ..., m:
P( Y = 0 ) = F( -XB_1 )
P( Y = j ) = F( -XB_(j+1) ) - F( -XB_j ) j = 1, ..., m - 1
P( Y = m ) = 1 - F( -XB_m )
The generalized ordered logit model uses the logistic distribution as the
cumulative distribution, although other distributions may also be used.
The logistic distribution allows researchers to interpret this model in terms
of logits:
log[ P( Y >= k ) / P( Y < k ) ] = XB_k k = 1, ..., m
The proportional odds property of Stata's ologit command restricts the
B_k coefficients to be the same for every dividing point k = 1, ..., m.
Note that unlike models such as OLS regression and binary logit, the
generalized ordered logit model imposes explicit restrictions on the range
of the X variables. Since probabilities are by definition constrained to be
in the range [0,1], valid combinations the X variables must satisfy the
following inequalities:
XB_2 <= XB_1
XB_3 <= XB_2
...
XB_m <= XB_(m-1)
Examples
--------
. gologit meduc mwhite fhsd fcoll fba if(mwhite | mmexican) [pw=fpwgt1]
. gologit rep78 price mpg, robust
. gologit, level(99)
Author
------
Vincent Kang Fu , UCLA Department of Sociology
Acknowledgement
---------------
Portions of this help file were taken from help files produced by Stata Corp.
Jeremy Freese suggested the changes for making -gologit- compatible with
-fitstat-.
Also see
--------
Manual: ^[U] 26 Estimation and post-estimation commands^
^[U] 35 Overview of model estimation^
^[R] ml^
^[R] ologit^
^[R] _robust^
On-line: help for @_robust@, @svyolog@, @ologit@, @ml@, @est@