# VGAM constraints-related puzzle

2 messages
 Hello R users, I have a puzzle with the VGAM package, on my first excursion into generalized additive models, in that this very nice package seems to want to do either more or less than what I want. Precisely, I have a 4-component 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 the following: vgam(formula = y ~ s(x), family = multinomial) fits the model \eta_j = \beta_{ (j) 0 } + \beta_{ (j) x } f_j (x) i.e. a different function f_j (x) is fit for each outcome. vgam(formula = y ~ s(x), family = multinomial, constraints = list((Intercept)= diag(1,3), 's(x)' = matrix(c(1,1,1),3,1)) ) fits the model \eta_j = \beta_{ (j) 0 } +  f (x) i.e. a single function f (x) is fit, but scaled the same for each outcome. I'd like one function, scaled differently. Of course, vgam(formula = y ~ x, family = multinomial) fits the model \eta_j = \beta_{ (j) 0 } + \beta_{ (j) x } x which has the scaling, but not the nonlinear function. Perhaps this is achievable using bs(), xij, and vglm, or even via the constraint matrix, but I did not succeed. Any help appreciated! Edward -- Edward Wallace, PhD Postdoctoral fellow, Drummond lab Harvard FAS center for Systems Biology [hidden email] 773-517-4009 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.