I am trying to demonstrate or model reciprocal effects between self reported substance abuse and crime among a sample of criminal justice appointed clients to residential drug treatment. Two techniques keep coming up in the literature: LISREL and two-stage least squares. LISREL is totally unfeasible because training is not readily available and very expensive. It is also not the type of progam one can learn on their own.
I've been examining two stage least squares regression and I have some questions. Specifically, I'm not sure about the apporpriateness of the first stage for my data. At the first stage I am supposed to "predict the predictor" that is theoretically related to the dependent variable. It appears that once this is done I do a few OLS regressions to find a reciprocal relationship: one with the dependent and predictor variables in their proper places, and another in which they are reversed (regress the predictor on the dependent variable).
In my case, I'm not sure why I should bother with the first stage. I have approximately 25 variables measuring various forms of drug use (pot, coke snorted, coke injected, crack, etc.). I also have approximately 25 variables measuring various forms of criminal behavior (dui, burglary, robbery, simple assault, etc.). I also have several "control" or exogenous variables that could be related to both drug use and criminal behavior (age, history of physical and verbal abuse, co-occuring disorders, family history of drug use, etc).
My contention is that for the population under study (cj clients in residential drug tx) drug use and crime are reciprocally related regardless of the inclusion of the control or exogenous variables. I don't see why I need the first stage to examine a reciprocal effect. To reduce the amount of variables, I have done a factor analysis and found seven or so crime factors and as little as three drug factors depending on how I do the factor analysis. Could the variables that compose each of the factors serve in the first stage of a 2 stage least squares regression?
As it stands I don't see an advantage of two stage least squares over just using my factors and running several least squares regressions swapping places of the dependent variables and the predictors to find a reciprocal relationship. Additionally, one expert who has a few articles out there in which he used 2 stage least squares to show reciprocal effects, suggested simple OLS for each of the reciprocal paths I want to test.
What do you think?
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