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I am reading an analysis which takes a model that regresses a response variable (= criminal activity) on a socio-economic independent variable (= parent salary during childhood). The parameters are highly significant, i.e., poor people do tend to commit more crime.

The analysis then claims (I don't have access to the actual analysis, only the final conclusions) that after adjusting the model for environmental, familial, and genetical factors, by using siblings and cousins as stratum, the significant affect of poverty on criminal activity became insignificant.

So basically they conclude that the model suggests it is not poverty which causes crime but environmental factors.

I have two questions.

  1. In a typical regression model, say $$\text{[criminal activity]} = \alpha + \beta \text{[poverty level]} + \epsilon$$ how exactly did they account for these environmental, familial, and genetical factors? Or, if there are different ways to do it, what is one way to do it? For example, looking at my simple linear regression model, how would you modify it to take into account familial factors, i.e., where you have data on a person's family, siblings, cousins, etc., and where you may want to account for whether you commit crime not because you are poor, but because you have been influenced to do so by your environment. How would we model that?

  2. My second question is, how would such a model avoid multicolinearity? As I stated above, the analysis I was reading concluded that the estimate of poverty-level on criminal activity became insignificant once they accounted for environmental factors. But it seems reasonable to hypothesize that those same environmental factors are colinear with poverty-levels. For example, it may be that a person commits crime because all their siblings are criminals, rather than because they are poor ... but perhaps all their siblings are criminals because they are poor? Therefore, one cannot conclude that poverty does not cause crime just because the estimate becomes insignificant, because one is just modelling the effect of poverty through the other independent variable that one has introduced, no?

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1) Using multiple linear regression, these additional factors are added as predictors. $$\text{[criminal activity]} = \alpha + \beta_1 \text{[poverty level]} + \beta_2 \text{[familial factor]} + ... + \epsilon$$ This can render the "poverty level" variable insignificant, i.e. given a certain family situation, your wealth does not explain your criminal behaviour anymore. Be wary of causal inference if your data do not come from an experimental research setup though.

2) Some degree of multicolinearity may be inevitable, which may inflate the variance. As long as it is not too excessive, the conclusions may still be valid, one should look at the variance-covariance matrix of the estimated coefficients indeed. I reiterate that the setup of this study does not seem to justify causal conclusions...

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