I have some household surveys taken across three villages in West Africa. I want to look at relationships between different variables, and I want to account for village-level effects. The two ways I can think of to do this are to add the village of each record as a dummy variable, or to make a multilevel model with fixed or random effects for the villages. I'm trying to understand the difference between these to methods of partial pooling. Which approach is better at accounting for village-level effects?
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$\begingroup$ Are you sure that the dummy-variable approach results in a partial pooling? It's my impression that it would result in a non-pooling solution. (As opposed to no dummy variables which would be total pooling, and a multi-level model which would provide partial pooling.) $\endgroup$– WayneCommented Nov 3, 2015 at 23:15
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$\begingroup$ Thanks for the feedback @Wayne. I was under the impression that a dummy-variable approach was a type of partial pooling, because it is all in one model. If using dummy variables is a no-pooling approach, then how would such a model be different from running completely separate regressions for each village? $\endgroup$– Amadou KoneCommented Nov 3, 2015 at 23:24
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1$\begingroup$ In dummy-variable(=no pooling) approach, only the intercept is generally allowed to be separate for each village, the slope being the same. Running individual regression causes the intercept and slope vary for each village. The fixed models are generally "LSDV"=least squares dummy variable. So they just contain dummy for each village. So it is exactly the same as the dummy approach, if you use dummies for intercept only. $\endgroup$– DoleCommented Nov 4, 2015 at 0:33
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