I have a treatment effects model (where on of the binary regressors is
endogenously subject to a set of predictors). This can be addressed by
2-step, MLE, or instrument variables.
The problem is that the dependent variable is skewed (censored at one
end). The errors are skewed, and a residual vs. fitted plot shows that the
error terms are limited in their range where the y variable is censored, not
surprising. The findings are erratic and press against the bounds of
defensibility.
In a simple model where the regressors are not subject to outside
causes, the nature of the y variable would call for using a model accounting
for its shape: treating it as binary, or "ordered" or mixed binary and
continuous (tobit).
However, I understand that models with an endogenous predictor are not
always logically consistent when the main the dependent variable is limited or
binary (cite below my name).
Clearly, it would be good if I can transform the dependent variable. It is
thin-tailed on the left, and "staircases" to the right until a high point
where it stops:
__________**
_______******
____*********
_************
It is an aggregation of generally 5 constituent parts, each one an indicator
of student behavior (e.g. disrupting class, fighting, cutting etc), each one
taking on any of 4 values, but with the mode generally lying near one end
(acquiescent good behavior).
I am not versed in transformations, but the answer may be there.
The study has a great number of models and sub-questions, and I should like
to avoid having to backtransform each coefficient across many models by hand.
My questions:
1) Is there a transformation which can make y normal, but which would also
be directly interpretable (to readers which are generalists). My dependent
variable has no theoretical zero, and is therefore amenable to transformation.
2) Same question, but note that some predictors are dichotomous.
3) Can someone suggest a good pedagogical treatment of transformations,
especially *applied* discussions aimed toward non-mathematical generalists?
(Would discussions of general linear models also be appropriate?)
4) Looking at the question from an entirely different angle, is there a way
to get around the usual prohibition of models with limited dependent variable
that have binary endogenous predictors?
Respond to me directly am I shall summarize upon request.
Andy
GWU
[log in to unmask]
See Joshua Angrist "Estimation of limited dependent variable models with
binary endogenous regressors: Simple strategies for empirical practice,"
Journal of Business and Economic Statistics, January 2001 for further insights
& references. [Relevant *might be: Madalla (83) chapter 5, or chapter 7, p
214.]
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