How would you interpret coefficients when using time-varying covariates (dummies / categorical) in a regression model?

[Andrea Berni]

Hello.

Sorry for the very basic question, but I have one big doubt. How are to be interpreted the coefficients of time-varying variables when using discrete categories? For example, using time-ratios, what if the coefficient of someone who is employed in an atypical job is 0.71 compared to the reference that is a typical job (which is 1.00 of course, being multiplicative)? Overall, I would say that being employed in an atypical job speeds up the transition to the outcome by 29% with respect to being in a typical one. However, is this correct? By the way, I am using individuals as "id", not episodes, also because I have more time-varying covariates with different start and end points in time for each individual. I guess the interpretation would be correct if that was a constant covariate, but they are not, since one might jump from atypical to typical employment and vice versa.

Thanks in advance.

[Matt Warkentin]

Hi Andrea,

Just to ensure that I am understanding your question, and to ensure we agree on terminology, it sounds like you are using an accelerated failure time model for your outcome with a predictor whose value can vary over time, and you have collected repeat measures for it. So you have an indicator variable for having an 'atypical job' where 0=typical and 1=atypical, and it changes over time for individuals in your sample.

You are correct that in settings with fixed covariates (e.g. sex, race, etc.) a one-unit change is more easily viewed as making simple group comparisons because values cannot change within an individual. However, the interpretation for time-varying covariates is still the on-average effect on the outcome for a 1-unit change in the predictor. In your case, since people can go from typical to atypical jobs, and vice versa, I would say that this contrast and interpretation is very natural, more so than thinking about switching values for fixed covariates.

So in your wording, being employed in an atypical job, on average, leads to a 29% faster transition to the outcome, compared to a typical job.

[Andrea Berni]

You assumed very well what I meant, sorry for not providing more specific information. So, you are basically telling me there is no difference in interpretation. I have noted that you wrote about "being" employed under one or another type of contract. Thus the focus is on "being" in the condition instead of comparing between different groups (something you can do when you have covariates with constant values, or non-time-varying, I guess), am I correct? That was my main concern here.

[Matt Warkentin]

Yes, the practical interpretation of the coefficient is the same. As you've said, when the covariate we are interested in can change values within an individual then it is more natural to think of it this way (i.e. the same individual going from one type of job to another). However, the coefficient for a fixed covariate like sex could be interpreted the same, as it represents the same type of estimate, it is you as the end-user that knows the practical meaning of the estimate.

[Andrea Berni]

Thanks a lot, I appreciate much your help. Sorry for the late reply