I fitted a Cox PH Model and upon examination of the Schoenfeld residuals it became apparent that the proportionality assumption was violated by several variables. Following Box-Steffensmeier & Jones (2004) I included interactions with time for these covariates. However I'm not sure how to interpret this. So its obvious that this indicates time-dependency of the covariate in the sense that the effect inflates/deflates over some function of time, but I work with sociological data and my theory indicates no time-dependency of the effects in whatever direction (Also it would not make sense in any way). So if I get that right I should therefore consider the time-dependency to come from some kind of unobserved heterogeneity? Due to the nature of the data I can also not implement frailty or fixed effects to account for this. So how do I interpret a coefficient that increases/decreases as time progresses given that the theory does not indicate this?