Help with interpreting time by categorical interaction term in a logistic regression model to see the effect of change over time.

[Jodie Luker]

Hi,

I am looking for some help regarding interpretation of some tables and graph I have attached. Particularly, what the co-efficients are in the first table and margins. Are these log odds or predictive probabilities?

each wave is a different year
wave 1 = 1996
wave 2 = 2006
wave 3 = 2016
city coded as 0 city 1 non city

The final table, is it correct to infer that this means that the wave variable is significant alone while the city variable is not, but when they interact it is significant and explains 10.57% of the variance in the model?

if anyone could give me an example of interpretation it would be greatly appreciated!

Kind Regards, Jodie.

[Clyde Schechter]

First, let's talk about the regression output. You have run an interaction model here. By using an interaction model, you are stipulating that there is no such thing as "the effect of city," nor "the effect of wave." Rather you are saying that there are multiple different effects of city, one for each wave, and vice versa. Consequently, the coefficient of city only reflects the effect of city when wave = 1 (the base category for wave). Similarly, the coefficients of 2.wave and 3.wave reflect the effects of those waves only when city = 0. The numbers shown in the regression output table are logistic regression coefficients, which can also be understood as the logarithms of odds ratios.

In your -margins- command you specified that you wanted -xb-, so, the numbers of the Margin column represent logarithms of the odds of samesex.

Your -contrast- output I can't really help you with: you specified orthogonal polynomial contrasts, and I don't have a clear sense of how those work here. Nevertheless, I can tell you that the 10.57 in the chi square column for wave#city has nothing at all to do with a percentage of variance. Indeed, while there are various pseudo-R² statistics that are used in association with logistic regression, none of them is a true proportion of variance. In fact, the very concept of proportion of variance isn't really applicable in logistic regression.

If you made a clear statement of your research hypothesis, it should be possible to advise you whether these outputs tend to support or refute that hypothesis, or whether some additional calculations need to be done to answer the question.

Finally, do read the Forum FAQ, with special reference to #12. The use of screenshots to post Stata output works poorly. Often they are completely unreadable. Yours was readable, but just barely so. The useful way to show Stata output is to paste it directly from your Results window or log file into the Forum editor, between code delimiters. FAQ #12 explains how to do that. Please follow the advice there going forward.