Date:         Wed, 17 Dec 2008 15:49:07 -0800
Reply-To:     Richard <richard.hockey@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Richard <richard.hockey@GMAIL.COM>
Organization: http://groups.google.com
Subject:      Re: Regression: do you always need main effects with interactions?
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=ISO-8859-1

On Dec 18, 8:33 am, robe...@HEALTH.OK.GOV (Robert Feyerharm) wrote:
> I've found that when performing multivariate logistic regressions with
> categorical variables, including the main effect terms along with the
> interaction term is redundant when looking at the adjusted odds ratios
> (AORs). Both models produce the same Hosmer-Lemeshow Goodness-of-Fit
> values.
>
> For example, I recently ran the following model using categorical
> variables from public health survey data (PRAMS):
>
> log(odds LBW)= B0 + B1*mom_age + B2*postpartum_checkup + B3*PPC_BCtalk +
> B4*marital_status + B5*medicaid
>
> I found a significant interaction between the postpartum_checkup and
> PPC_BCtalk variables. If I include both main terms and the interaction
> term in the model, SAS produces the following AOR output:
>
> postpartum_checkup = Yes, AOR=1.00 (Reference)
> postpartum_checkup = No, AOR=1.55 (95% CI: 0.72, 3.36)
>
> PPC_BCtalk = Yes, AOR=1.00 (Reference)
> PPC_BCtalk = No, AOR=3,24 (95% CI: 1.44, 7.31)
>
> postpartum_checkup*PPC_BCtalk = Yes & Yes, AOR=1.00 (Reference)
> postpartum_checkup*PPC_BCtalk = Yes & No, AOR=1.00 (Reference)
> postpartum_checkup*PPC_BCtalk = No & Yes, AOR=1.00 (Reference)
> postpartum_checkup*PPC_BCtalk = No & No, AOR=2.32 (95% CI: 0.53, 10.18).
>
> Here the AOR=2.32 represents the interaction effect when both
> postpartum_checkup=No and PPC_BCtalk=No. Now, if I exclude the two main
> terms from the model and keep the interaction term, I get the following
> SAS output:
>
> postpartum_checkup*PPC_BCtalk = Yes & Yes, AOR=1.00 (Reference)
> postpartum_checkup*PPC_BCtalk = Yes & No, AOR=1.55 (95% CI: 0.72, 3.36)
> postpartum_checkup*PPC_BCtalk = No & Yes, AOR=3.24 (95% CI: 1.44, 7.31)
> postpartum_checkup*PPC_BCtalk = No & No, AOR=11.68 (95% CI: 3.91, 34.85).
>
> Notice that two of the interaction effect AORs are the same as the main
> effect AORs described in the first model. The interaction effect for
> postpartum_checkup=No and PPC_BCtalk=No is AOR=11.68, which is essentially
> the product of the main effect terms and the interaction effect term from
> the first model (11.68 = 3.24*1.55*2.32) after accounting for rounding
> errors.
>
> IMO the question over whether to include the main effects or not in this
> particular case hinges on how you want the regression results presented.
>
> Robert Feyerharm
> Maternal and Child Health Assessment
> Oklahoma State Health Department
> 1000 NE 10th St
> Oklahoma City, OK 73117
> (405) 271-6761

Categorical variables are definitely a separate case. My experience is
that including the main effects doesn't add anything and makes
interpretation very difficult.
R