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st: Evaluating the importance of interaction effects in logistic regression


From   Thomas Speidel <thomas@tmbx.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Evaluating the importance of interaction effects in logistic regression
Date   Tue, 30 Aug 2011 15:31:33 -0600

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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