[R] Combining estimates from multiple regressions

[James Shaw]

I am interested in using quantile regression to fit the following model at
different quantiles of a response variable:

(1)  y = b0 + b1*g1 + b2*g2 + B*Z

where b0 is an intercept, g1 and g2 are dummy variables for 2 of 3
independent groups, and Z is a matrix of covariates to be adjusted for in
the estimation (e.g., age, gender).  The problem is that estimates for g2
and g1 are not estimable at all quantiles.  To overcome this, one option is
to fit a separate model for each group (i.e., group 0, which is reflected
by intercept above, group 1, and group 2):

(2)  y = b11 + B1*Z (model for group 0)
(3)  y = b12 + B2*Z (model for group 1)
(4)  y = b13 + B3*Z (model for group 2)

This would correspond to fitting a single model in which group membership
was interacted with all covariates, albeit some of the interaction terms
would not be estimable for the reason noted above.  However, I ultimately
would like to base inferences on a single set of estimates.

Can anyone suggest an approach to combine estimates from models (2)-(4),
perhaps through weighted averaging, to generate estimates for the model
presented in (1) above?  An approach is not immediately clear to me since
the group effects are subsumed in the intercepts in (2)-(4), whereas (1)
includes separate estimates of group effects instead of a single weighted
average.

Regards,

Jim

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