st: Evaluating the importance of interaction effects in logistic regression

[Thomas Speidel <thomas@tmbx.com>]

A recent topic on interaction 
(http://www.stata.com/statalist/archive/2011-08/msg01455.html), made me 
wonder what is the correct way to identify important interactions in a 
logistic model.  Maarten in his Stata tip 87

Maarten L. Buis (2010) "Stata tip 87: Interpretation of interactions in 
non-linear models", The Stata Journal, 10(2), pp. 305-308.)

writes in the context of his first example that the interaction between 
the two dischotomies black and collgrad "is not significant" (the 
reported p-value is in fact 0.161).  However, another reference Maarten 
cited:

Edward Norton, Hua Wang, and Chunrong Ai (2004) "Computing interaction 
effects and standard errors in logit and probit models" The Stata 
Journal, 4(2): 154-167.

says that "The statistical significance cannot be determined from the 
z-statistic reported in the regression output" (p.1).
I am now confused on the appropriate way of identifying significant 
interactions.  This sentence has confused me.  Regardless of 
interpretation, how does one assess the importance of an interaction?

For example:
********************************************************************************
sysuse nlsw88, clear
gen byte high_occ = occupation < 3 if occupation < .
drop if race==3
logistic high_occ race##collgrad , nolog

Logistic regression                               Number of obs   =     
 2211
                                                  LR chi2(3)      =     
127.07
                                                  Prob > chi2     =     
0.0000
Log likelihood = -1199.4399                       Pseudo R2       =     
0.0503

-------------------------------------------------------------------------------
     high_occ | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
--------------+----------------------------------------------------------------
       2.race |   .4194072   .0655069    -5.56   0.000     .3088072    
.5696188
   1.collgrad |   2.465411    .293568     7.58   0.000     1.952238    
3.113478
              |
race#collgrad |
         2 1  |   1.479715   .4132536     1.40   0.161     .8559637    
2.558003
              |
        _cons |   .3220524   .0215596   -16.93   0.000     .2824512    
.3672059
-------------------------------------------------------------------------------
********************************************************************************

is it correct to say that the interaction race * collgrad is not 
important because its p-value is 1.161?
What if, for example, we had 3 levels to race:

********************************************************************************
sort idcode
replace race = 3 in 1/300
logistic high_occ race##collgrad, nolog

Logistic regression                               Number of obs   =     
 2211
                                                  LR chi2(5)      =     
133.72
                                                  Prob > chi2     =     
0.0000
Log likelihood =  -1196.114                       Pseudo R2       =     
0.0529

-------------------------------------------------------------------------------
     high_occ | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
--------------+----------------------------------------------------------------
         race |
           2  |   .3943154   .0652863    -5.62   0.000     .2850437    
.5454766
           3  |   .9770963   .1709298    -0.13   0.895     .6934755    
1.376713
              |
   1.collgrad |   2.325301   .3051036     6.43   0.000     1.798013    
3.007223
              |
race#collgrad |
         2 1  |   1.485761   .4431258     1.33   0.184      .828094    
2.665744
         3 1  |   1.466932   .4419418     1.27   0.203      .812772    
2.647591
              |
        _cons |   .3225389   .0235064   -15.53   0.000     .2796063    
.3720635
-------------------------------------------------------------------------------
********************************************************************************

and we want to evaluate the overall importance of the interaction 
between race and collgrad (i.e. jointly)?  Is it approriate to use the 
likelihood ratio test to compare the model without interaction to the 
model with interaction, and determine the importance of the interaction 
effect according based on the results of LR test?

--
Thomas Speidel


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