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beta_j
2011 Jun 22
2
VGAM constraints-related puzzle
...nent outcome, y, and am fitting multinomial
logistic regression with one predictor x. What I would like to find
out is, is there a single nonlinear function f(x) which acts in place
of the linear predictor x. There is a mechanistic reason to believe
this is sensible. So I'd like to fit a model
\eta_j = \beta_{ (j) 0 } + \beta_{ (j) x } f(x)
where both the function f(x) and its scaling coefficients \beta_{ (j)
x } are fit simultaneously. Here \eta_j is the linear predictor, the
logodds of outcome j vs the reference outcome. I cannot see how to fit
exactly this. Instead I seem to be able to do t...