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I'm relatively new to statistical methods. I'm hoping to learn what kind of distribution I should use for some data I have.

My dependent variable is the results a candidate received by county. My independent variable is the labor participation rate of each county (a pct).

I am wondering what the best distribution to use is when constructing a GLM.

It seems to me like the gamma or normal distributions are ideal. Any further suggestions for where I can learn to build models for this kind of data are appreciated, either as books or papers or anything.

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  • $\begingroup$ 1. What does "results" mean, specifically? What does the variable consist of? 2. labor participation rate is a percentage? 3. Why are you predicting labor participation as a function of candidate results -- I imagine most people would expect the relationship to be formulated with results being predicted from labor participation rate $\endgroup$
    – Glen_b
    May 29, 2016 at 7:52
  • $\begingroup$ Ok so clearly have the two switched. Will amend. Thought the participation depended on the vote. And yes it's a pct. $\endgroup$
    – Learning stats by example
    May 29, 2016 at 12:44
  • $\begingroup$ If you think the vote causes participation, why would other peoples' expectation matter? (unless this is an exercise for a class or something?) $\endgroup$
    – Glen_b
    May 29, 2016 at 22:04
  • $\begingroup$ I'm just self-teaching. I suppose I had some other way of thinking about it, which in retrospect doesn't make much sense. $\endgroup$
    – Learning stats by example
    May 29, 2016 at 22:05
  • $\begingroup$ You still haven't clarified how "results" is measured, which is important if it is to be your DV. If participation were to be your response I'd be inclined to model something like labor participation as beta, but if the mean doesn't change a lot you might be able to treat it as normal, say. Another alternative that would at least deal with a beta-like mean-variance relation would be to teat it as quasibinomial. Beta regression is not likely to be included in GLM in most stats packages, but may offered separately $\endgroup$
    – Glen_b
    May 29, 2016 at 22:12

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Gaussian distributions are common, but not compulsory. They key is the rationale, which I cannot discern from your question.

To answer your question about where to find model-building information, Andrew Gelman and colleagues' book Bayesian Data Analysis 3rd edition is IMHO the gold standard. They outline the principles and analysis (using R and Stan) in Chapter 16, page 405. Gelman himself does the majority of his research in political analysis, he has a blog where these issues are discussed directly http://andrewgelman.com/, plus there is a Stan-users group available to refine your analysis.

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  • $\begingroup$ Thanks. Is Bayes definitely the best approach here? Seems like a glm without Bayes might do? $\endgroup$
    – Learning stats by example
    May 29, 2016 at 12:46
  • $\begingroup$ Of course, GLM with or without Bayesian approach; have a look at the Gelman et al. book though as I think it provides a very clear rationale and explanation for use of the method. Also, at some point look at the STAN code needed for a glm using R or Python; it is not as difficult as you might expect. :) $\endgroup$
    – Time Lord
    May 29, 2016 at 20:52
  • $\begingroup$ I do have the Gelman book -- it's quite hard for me. I will have to start from the beginning as by chapter 16, there's a lot of prior knowledge assumed. Stan and BUGS seem great. $\endgroup$
    – Learning stats by example
    May 29, 2016 at 20:52
  • $\begingroup$ Agree, it is a difficult read unless one is working through examples with guidance. I don't recall specifically, but does his other work on data analysis and hierarchical modelling have a more accessible approach? (stat.columbia.edu/~gelman/arm). I was wondering whether you can model your problem against his radon examples. $\endgroup$
    – Time Lord
    May 29, 2016 at 23:48
  • $\begingroup$ Another good author on the topic is Agresti. One could use a semi-parametric least squares model (dist=normal) with empirical sandwich standard errors. This would be valid for most any underlying distribution. Here is a related thread. $\endgroup$
    – Geoffrey Johnson
    Dec 16, 2021 at 12:22

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