Usefulness and estimation of proportionality constraints
Maarten L. Buis
Stata has for a long time the capability of imposing the constraint that parameters are a linear function of one another. It does not have the capability to impose the constraint that if a set of parameters change (due to interaction terms) they will maintain the relative differences among them. Such a proportionality constraint has a nice interpretation: the constrained variables together measure some latent concept. For instance if a proportionality constraint is imposed on the variables father’s education, mother’s education, father’s occupational status, and mother’s occupational status, than together they might be thought to measure the latent variable family socioeconomic status. With the proportionality constraint one can estimate the effect of the latent variable and how strong each observed variable loads on the latent variable (i.e. does the mother, the father, or the highest status parent matter most). Such a model is a special case of a so called MIMIC model. In principle these models can be estimated using standard ml algorithms, however as the parameters are rather strongly correlated ml has a hard time finding the maximum. An EM algorithm is proposed that will find the maximum. This maximum is than fed into ml to get the right standard errors.
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