# Odds Ratio for Interaction Terms in GenLin in SPSS

I have a generalized linear model using SPSS to determine the relationship between certain variables (sex, race/ethnicity, geographical area, etc.) and whether or not they use a computer. Also, we wanted to see how the relationship between those variables and computer use changed over time. So the outcome (computer use) is a dichotomous variable, and the inputs are nominal variables with various levels (2-4), and the interaction variable is follow-up year (2012-2018). Here is my SPSS code:

GENLIN BCompUse_Dichot (REFERENCE=FIRST) BY BIntvDt_year ASex RaceEthCond BMetro13_Cond2 BEducat2 BFmIncLv RecentTetraPara
RecentAIS CurrAge_Split (ORDER=DESCENDING) WITH CurrAge
/MODEL BIntvDt_year ASex RaceEthCond BMetro13_Cond2 BEducat2 BFmIncLv RecentTetraPara RecentAIS
CurrAge CurrAge_Split BIntvDt_year*ASex BIntvDt_year*RaceEthCond BIntvDt_year*BMetro13_Cond2 BIntvDt_year*BEducat2 BIntvDt_year*BFmIncLv
BIntvDt_year*RecentTetraPara BIntvDt_year*RecentAIS BIntvDt_year*RecentTetraPara*RaceEthCond BIntvDt_year*RecentAIS*RaceEthCond
BIntvDt_year*CurrAge BIntvDt_year*CurrAge_Split INTERCEPT=YES
/CRITERIA METHOD=FISHER(1) SCALE=1 COVB=MODEL MAXITERATIONS=100 MAXSTEPHALVING=5
PCONVERGE=1E-006(ABSOLUTE) SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 CITYPE=WALD
LIKELIHOOD=FULL
/MISSING CLASSMISSING=EXCLUDE
/PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION (EXPONENTIATED).


A portion of the SPSS Output is shown below:

Also, some information about the proportion of people of each race/ethnicity group, year, and computer use:

I would like advice on how to interpret the output for the interaction terms, mostly in terms of the odds ratio (exp(B)). I understand for the non-interaction terms how to interpret them (i.e. the odds of using a computer in 2018 are 2.505x the odds of using a computer in 2012), but I don't understand which term(s) are being used to compare for the interaction terms. For example, I can't see how the math matches up when calculating the odds ratio of 2018 Hispanic compared to 2018 White, 2012 Hispanic, or 2012 White and am not sure how the reference variable is determined. Thanks for the help!

EDIT 3/2/2020: The lower category is non-computer use (0) and the higher value is computer use (1). We used the cumulative logit model initially when some dependent variables had more than 2 categories, but we now have dichotomized all of them and using a binomial logistic regression results in the same parameter estimates, but makes the intercept easier to interpret as predicting computer use as David pointed out.

• Look at those confidence intervals--they all range by an order of magnitude and all include $1.$ You really can't say anything about any of the interaction terms, so why interpret them?
– whuber
Feb 25, 2020 at 20:54
• @whuber This was just of a portion of the model output with race/ethnicity as an example because it required less explanation to interpret and only had 3 categories. Many of the other variables had significant findings. This was only an example as I was looking more for a conceptual explanation than the exact interpretation for these variables. Mar 2, 2020 at 21:28

Note that with the command shown here, the use of the cumulative logit model renders the (REFERENCE=FIRST) specification irrelevant, and the default setting of (ORDER=ASCENDING) is applied, so the model is set up to predict the probability of the lower category (I'm assuming that's non-use). Thus the threshold (intercept) term is opposite in sign of what you'd want to predict the probability of the higher category (use?). The coefficients for the predictor variables enter into the cumulative response model by being subtracted from the threshold/intercept, and do have the same signs as they would have if you fitted this as a binary logistic model with the lower category as the reference category.

Assuming I'm right that non-use is the lower coded value of the response, if you ran the same command without the other predictors, with the same specifications for the type of model and the main effects and interaction of year and ethnicity, using the numbers in the data table you posted, you'd get a threshold parameter estimate (B) of -1.768, with an Exp(B) of .171. That represents the log odds and odds, respectively, of no use to use for Non-Hispanic Whites in 2012. The odds can be calculated from the data as 210/1230=.171.

If you're interested in predicting the odds of use, then you flip the sign of B or take the reciprocal of Exp(B), giving you 5.857.

The coefficient for the "main effect" of Year for 2018 would be .602, with an Exp(B) of 1.827. This is the ratio of the odds for 2018 to 2012 for Non-Hispanic Whites: (1455/136)/(1230/210)=1.827.

The interaction coefficient for [Year=2018]*[Ethnic=Hispanic/Other] would be .543, Exp(B) of 1.720. That Exp(B) represents the ratio of odds ratios of use among Hispanic/Others to Non-Hispanic Whites in 2018 vs. 2012:

[(299/47)/(1455/136)] / [(166/82)/(1230/210)] = 1.720