I have a dataset of 10 years of a large-scale assessment of Brazil. The data set has students' characteristics and scores for each year. Moreover has several school characteristics.
I'm working at the school level, and I summarised all student characteristics for each school, including scores. The problem was modeled in a binary classification, then my target (average school score) is 1 for school in the upper quartile and 0 otherwise.
Taking advantage of the panel structure at the schools and Brazilian states levels, I am planning to control for the unobservables, that I assumed being present in two ways:
1) Student' ability, motivation, QI... (time-invariant on average in schools and I plan to eliminate)
2) State Policies (I plan to estimate its influence in school gains based on residual effect of each state relative to the reference state - left out dummy)
Then, to eliminate the bias of 1) I took out the school mean within each school for all features, including the target, which was binarized in the end. Now I have a vector of school demeaned features as dependent variables and a binary target which now means: 1 if the variation around the mean is in the upper quartile and 0 otherwise.
Now, I need to infer about 2) in a fixed fashion (for all periods). Therefore I just add a dummy variable for states. So, the time-variant effect relative to the reference state in the period will be estimated, while time-invariant biases will be eliminated.
Finally, I run this final model.
Is it my approach right under assumptions 1) and 2) in addition to those related to the logistic model?
how far am I from causal results?
I think you could better incorporate your unobservable variables if you would usw multilevel modelling. In these you could incorporate your unobservables in random terms.
Sven Greving , thanks. Actually, I have other approaches, including random effects and non-linear models. Anyway, fixed-effects could be important to reduce bias (maybe causal reasoning) under assumptions.
I thought that you wanted to control for unwanted influences of students on to the school level. This is were I would model student parameters as random factors.
You however write that you want to control for a bias, what exactly is that bias?
Sven Greving, The bias is related to unobservables from students (first level) and states (second level). To the best t of my knowledge, I could use Random effects to capture the residuals on the level of school. In this case, I would be inferring the unobservable school value-added l. But, for that, I don't need a panel data structure, only cross-sectional is enough. Actually, I did that in another model.
But, in this case, I am trying to take advantage of the panel data structure, to drop any time-invariant unobservables (and observables) and get different and realible results of the remaining time-variant features. The final model gives me a slope for school characteristics and others for each Brazilian States (dummies). Since, in this approach, every time-invariant feature, unobservable or observable is dropped.
I am not sure how would control students' unobservables, as you said, Could you send me some references about your thoughts?
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