{smcl}
{* 13oct2004}{...}
{hline}
help for {hi:mcross}{right:(SJ4-4: sqv10_1; STB-23: sqv10)}
{hline}

{title:Expanded multinomial comparisons}

{p 8 17 2}
{cmd:mcross}
[{cmd:,}
    {cmdab:l:evel(#)}
    {cmdab:r:rr}
]


{title:Description}

{p 4 4 2}
{cmd:mcross} follows an {cmd:mlogit} or {cmd:svymlogit} command and displays
the contrasts of coefficients for every possible pair of outcomes, except for
the pairs that have already been displayed by {cmd:mlogit} or {cmd:svymlogit}.


{title:Options}

{p 4 8 2}
{cmdab:l:evel(#)} specifies the level of the confidence intervals.

{p 4 8 2}
{cmdab:r:rr} displays relative risk ratios instead of coefficients.


{title:Remarks} 

{p 4 4 2}
Multinomial regression results are normalized so one category{c -}one level or
outcome of the response or dependent variable{c -}is the base category: that
is, one category is compared with all the other categories.  You can specify
the base category with the {cmd:basecategory()} option of {help mlogit} or
{help svymlogit}, or you can let the program pick a default, which is the
category with the largest sample.

{p 4 4 2}
As an example, consider using the {cmd:mlogit} command to estimate the
relationship between {cmd:headroom} and repair record {cmd:rep78} in the auto
data set supplied with Stata.  The category {cmd:rep78 == 3} is chosen as the
base category.  The contrasts of non-base categories can be calculated from
these results, but the process is tedious.  To test the contrast for the effect
of {cmd:headroom} between categories 5 and 2, we could resort to the
specialized syntax Stata uses for multi-equation models:

{p 4 8 2}{cmd:. display [5]hdroom - [2]hdroom}{p_end}
{p 4 8 2}{cmd:. test [5]hdroom = [2]hdroom} 

{p 4 4 2}
and so forth, or we could rerun {cmd:mlogit} and explicitly specify a
different base category.  Depending on the size of the dataset, the number of
explanatory variables, and the number of categories, this process can quickly
become unwieldy.

{p 4 4 2} 
{cmd:mcross} simplifies this process by calculating and displaying the
contrasts for each pair of categories.  Note that {cmd:mcross} works just as
easily when there are multiple predictors.

{p 4 4 2} 
Consider two categories with coefficient vectors beta_1 and beta_2
and estimates b_1 and b_2, normalized against a third category.
The contrast of b_1 and b_2 has variance

	var(b_1 - b_2) = var(b_1) + var(b_2) 
	        - E[(b_1 - beta_1)(b_2 - beta_2)' - (b_2 - beta_2)(b_1 - beta_1)']

{p 4 8 2} 
Note that the covariance matrix is not symmetric; thus, its transpose
must also be considered.


{title:Examples}

{p 4 8 2}{cmd:. mlogit insure age male nonwhite site2 site3}{p_end}
{p 4 8 2}{cmd:. mcross}

{p 4 8 2}{cmd:. svymlogit insure age male nonwhite site2 site3}{p_end}
{p 4 8 2}{cmd:. mcross}


{title:Author}

{p 4 4 2}Dan Blanchette, Carolina Population Center UNC-CH{break} 
	 dan_blanchette@unc.edu


{title:Acknowledgements} 

{p 4 4 2}This program is an update of a previous version by
William H. Rogers, who at the time of writing was employed
by Stata Corporation. The present version modernises the 
program to Stata 8 and thus extends the program to apply also to 
{cmd:svymlogit}. Thanks to Nicholas J. Cox, University of Durham, 
for help. 


{title:Also see}

{p 4 13 2}manual:  [R] mlogit; [SVY] svy estimators{p_end}
{p 4 13 2}STB:  sqv10 (STB-23){p_end}
{p 4 13 2}Online:  help for {help mlogit}, {help svymlogit}, {help logit}