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I am doing an analysis on data from Tanzania, where one part of the analysis is looking into determinants of passing the primary school exam. This information is subtracted from two datasets for two years.

Firstly, in the newest year those who have taken the exam and were in primary school the year before are found. Then the ID's of these individuals are used to chose the sample from the survey from the year before, i.e. the year when the exam was taken. For this, my subset of the data comes down to 321 observations.

My question is now: given this, how "defendable" is it to make inference here? I am implementing Firth's Penalized ML method in a logit setup (since the outcome is pass or not) to alleviate bias problems.

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  • $\begingroup$ Good question! There are no quick, easy, magic bullet answers. One approach would be to treat the second, reduced sample as an issue of selection bias. James Heckman, U of Chicago Nobel Laureate, wrote several papers about estimating the extent of this bias back in the 70s and 80s (e.g., jstor.org/stable/1912352). Basically, his method involves estimating a new parameter that is to be included in the second, reduced model as a function of the full, original data. This new parameter is a kind of 'weight' applied to each observation that adjusts for bias in the reduced sample $\endgroup$
    – user78229
    Commented Mar 13, 2018 at 13:02
  • $\begingroup$ thanks for the answer :-) That may actually be a viable way forward, since the whole sample of those enrolled in primary school who are at the "end" of the age of primary school amounts to 1400 observations. Since I want to say something about the chances of passing the exam given various individual, household and community variables for this sample in general, this could work. On the other hand, not all of these observations are at the last stage of primary school - so it depends a bit on the definition of the larger sample. I think it may be OK when stating the assumptions. $\endgroup$
    – user469216
    Commented Mar 13, 2018 at 13:46

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