# How to use cross-section country samples of different years in multiple regression analysis?

I want to run a multiple regression analysis measuring the effect of various independent variables on a continuous dependent variable measuring the strength of a political institution. The problem is that the data is measured in different years. Thus I might have data for countries A and B only for the year 2009 and for countries C and D only for the year 2010. In order to increase my sample, I would like to use all countries. How can I do that, ie which statistical method is most adequate? Thank you sooo much!

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Is this a homework question? There's a deep, lengthy academic literature on this topic. I suggest you look at what others have done. –  Keith May 20 '11 at 14:01
@Keith Which topic in particular? Regression? Time series? Adjusting data? Model selection? Political statistics? It would be good to have some place to start in following your suggestion! –  whuber May 20 '11 at 14:20
I was referring to the literature which empirically studies "institutions" Big names among economists include Acemoglu, Easterly, Kaufmann, Levin, North, Rodrik. But there's TONS more. Put "corruption" or something like that into Google Scholar :) –  Keith May 20 '11 at 14:32
I don't know, but my gess is that you have to extrapolate or estimate the data, treating it as missing data. You do that using a bayesian approch, in which you could estimate both the effect of the covariates on the dependente variable and estimate the missing data. –  Manoel Galdino May 20 '11 at 18:18

## migrated from stackoverflow.comMay 20 '11 at 13:45

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You originally asked this in reference to R (on stackoverflow), so I'll answer with reference to R.

I'm not sure exactly what your goal is, but I'd guess that you want to estimate a panel data model. In that context, you have an "unbalanced panel" and if you want to stick with R, I'd recommend the package plm. The package documentation describes how it deals with unbalanced panels.

You will need to sort out how to model panel data and interpret the results--I'd suggest looking at an econometrics textbook (whichever one is at the appropriate level for you; these models are covered in almost all econometrics texts). The book "Applied Econometrics with R" also gives some examples and a short, fairly accessible (if terse) introduction to these and other models.

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I think that a Bayesian approach may solve your problem. But it depends on how many data you have.

I ned did it, but I guesst's possible to estimate a hierarchical model, in which data are nested by country or time. For example, assume you have $i = 1, 2, ..., n$ countries and $t = 1, 2, ..., T$ years. For country $j$ you don't have information for year $l$ and for country $k$ you don't have information for year $m$. So, you would have a model like this:

$y_{it} \sim N(a + b_{t}*x_{it})$

$b_{t} \sim N(0, sigma^{2})$

$sigma^{2} \sim Unif(0, 100)$

$x_{jk} \sim N(0, 100)$

$x_{lm} \sim N(0, 100)$

The details of the priors will depend of your theory and your data. It is fairly simple to estimate this model using WinBugs or Jags (so you don't have to worry about the MCMC machinery).

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