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My aim is to carry out a GLM. I have 400 sites where I have count data of animals (response variable) and environmental characteristics (explanatory variables). At the moment I have around 40 explanatory variables.

  • The examples I have seen so far only have up to 10 explanatory variables so I guess I have to choose among the explanatory variables. How many explanatory variables normally are selected?

  • I read that no more than 10% of the number of responses should be chosen as the number of explanatory variables (which in my case is 40). Is that a general rule?

  • Are there any statistical tests which I can use to select the most appropriate explanatory variables? So far knowledge about the relationship of the explanatory variables and the animals is low and I can therefore not select my explanatory variables based on theory.

  • Moreover: How can I deal with multicollinearity and interactions of 40 explanatory variables?

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    $\begingroup$ In a nutshell, advice to use far fewer than 40 explanatory variables with 400 observations seems very sensible, both statistically and scientifically. When you say there is little or no theory, what was it that led you to measure explanatory variables in the first place? Your biological knowledge and your hypotheses should make some explanatory variables more interesting than others. Start with them. $\endgroup$
    – Nick Cox
    Mar 8 '15 at 9:00
  • $\begingroup$ What led me to measure explanatory variables was to understand which explanatory variables influence the animals abundance. I thought maybe there is an established statistical way to select appropriate explanatory variables before carrying out a regression analysis? I am not very familiar with the statistical possibilities and I do not know what the best method to start is. As I understand you suggest starting with biological knowledge and not statistics. I guess carrying Spearman rank correlation can help? is there any other test you would recommend?(thanks for correcting my post!) $\endgroup$
    – kalakaru
    Mar 8 '15 at 9:19
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How many variables you want to keep at least partly has to do with what exactly you want to do. Even if generally it would be nice to have as few variables as possible, if your goal is prediction, then having a greater number of variables is ok, as long as the prediction works well enough for you. You could look the the mean squared error of the prediction as a criterion for deciding on a certain number of variables. If on the other hand your goal is to develop a theory (or the extend an existing one) then you would probably want to go for fewer variables. The main reason here is that the model becomes less interpretable, the more predictors are included.

In any case, there are statistical methods for this task that fall under the rubric of "model selection". Some of the are Best Subset Selection, Stepwise (Forward of Backward) Selection, Lasso Regression. You might want to look into these methods.

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  • $\begingroup$ Model selection sounds like a very useful keyword. Many thanks! My goal is your 2nd suggestion: develop a theory. $\endgroup$
    – kalakaru
    Mar 8 '15 at 9:26
  • $\begingroup$ Starting with knowledge you already have as @NickCox suggested is certainly the way to go then. Finding appropriate statistical methods is of course important, but the first step should always be to get a very good understanding of the actual problem. Also, if my answer was helpful, please consider voting it up. $\endgroup$ Mar 8 '15 at 9:31
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Should you decide to reduce the number of explanatory variables and be willing to work with latent variables, consider performing an exploratory factor analysis (EFA), which usually is followed by a confirmatory factor analysis (CFA). Of course, this is not the only approach to consider.

For example, you can use principal component analysis (PCA) to perform factor analysis. PCA is a widely used method of dimensionality reduction, when one doesn't care much about latent structure of concepts, involved in a research study. Otherwise, I would recommend the EFA/CFA approach. This answer is not intended as a comprehensive one, but rather as one, illuminating some of the potential paths of further inquiry. Ultimately, it's a matter of your research problem and goals, time frame, resources and feasibility, considering all the above. I will let other, more knowledgeable, people to advise you on multicollinearity issues and interaction effects (or search this website).

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  • $\begingroup$ thanks, I will have a look at your different suggestions! $\endgroup$
    – kalakaru
    Mar 8 '15 at 9:33
  • $\begingroup$ @lara.faelivrin: My pleasure! $\endgroup$ Mar 8 '15 at 9:34

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