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I have fitted a model with 7-8 covariates.

Here's what I do to reduce it:

I first look at the p-values. I select all covariates with p-values > 0.05. Then I remove them one by one, get the AIC, and then see what had the lowest values. I pick that model.

Then I repeat: again, look at p-values, pick candidates, do AIC.

Is this how it's usually done?

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    $\begingroup$ What are your reasons for removing the covariates in the first place? Removing them just because they are not significant is generally a bad idea, especially if they are warranted by the theory. I think that similar questions have already been asked; have a look at this and this $\endgroup$ – Michael R Jun 2 '17 at 22:04
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I really would like to say that Michael R is spot on. The covariates in your model are included for a reason, e.g. their inclusion aligns with theory. For example, if I study school performance, I am going to include socioeconomic status in my model. Maybe socioeconomic status doesn't matter, but you can be certain that if it was not in my model, a reader would wonder why not and also wonder if that were the true cause of the effect. Parsimony is important, but so is creating a model that is firmly grounded in theory. In short, to answer your question, the only reason I would see to remove covariates is if there were issues of covariance between them, in which case, there is probably theory behind that as well (e.g. in the prior example a model that includes socioeconomic status and free/reduced lunch status would probably have a lot of covariance between the two covariates)

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