The case: I am investigating the impact of various predictors on the odds of migration using a discrete-time event history model within a multilevel framework. The outcome variable is dichotomous (0=not migrated; 1=migrated). The predictors are largely time varying covariates operating at the individual level (e.g., years of schooling, marital status) and community level (e.g., community wealth index, social networks). Individuals are observed during five years. As such, the multilevel-model structure is as follows: Level 1: years of observation; Level 2: individuals; Level 3: communities. I am estimating these models using multilevel logit models (lme4 package) on stacked data (person-year data file).

The problem: Does anyone know whether there is a limit to the number of time varying covariates that I can safely include in these models. Lets assume that I have 1000 individuals (level 2) that are observed up to 5 years leading to 4500 person year records at level 1 (e.g., about 4.5 records per individual). Those 1000 individuals are located in 25 communities (level 3) (e.g., 40 individuals per community). If I observe these individuals for only 5 years, would that mean that I can only include 5 time varying covariates? Do I run into issues of degrees of freedom if I include 10 time varying covariates? I have read the relevant literature on event history models (e.g., Allison, 1984) and did a thorough search on the internet but can't find any information on this topic. Any information or article/book recommendation on these questions would be highly appreciated! Thanks!

Best, Raphael

  • $\begingroup$ I am aware of the following related question Cross Validated 71511. However, my models are quite different (multi-level discrete event history) and unfortunately no one has provided an answer to the other question, so I am trying again here... Please help if anyone has an idea or opinion on this topic! $\endgroup$ – Raphael May 21 '14 at 2:59

Time-varying covariates vary at the lowest level of your hierarchy, so one consideration is that you have 4500-ish observations to work with. A second consideration is what is the variability in the covariates's values at each time period? If there's enough variation for each variable, I imagine your would be able to include quite a few more than five. Of course, all the usual caveats about confounding, colinearilty and the like still obtain.

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  • $\begingroup$ Thanks for the helpful answer, @Alexis. So, I assume that with my 4500 observations at level-1, I can include a large number of time-varying covariates. However, I don't think I quite understand the importance of the variability of my covariates. A few of my time-varying covariates are dummy variables (e.g., marital status) but the majority are continuous measures (e.g., years of working experience, number of children) and there is quite some variation for each time step across the individuals in my data set. So I guess I have the required variability? $\endgroup$ – Raphael May 21 '14 at 22:08
  • $\begingroup$ "there is quite some variation for each time step across the individuals in my data set." There is variability in what? The outcome? The time-varying predictors? Should be both. $\endgroup$ – Alexis May 21 '14 at 22:12
  • $\begingroup$ There is certainly a lot of variablity in the time-varying predictors and also some variability in the outcome (migration yes=1, no=0). However, I am investigating migration and this is in itself a more rare event and the majority of individuals did not migrate during any of the time windows. $\endgroup$ – Raphael May 21 '14 at 22:49

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