.-
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
-------------------------------------------------------

        ^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 gro
> ups
    (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 esti
> mates
    for unstratified cluster-sampled data.  Specifying ^cluster()^ implies ^rob
> ust^.

^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 <vfu@@ucla.edu>, 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@