[R] Full or non constrained/reparametrized model.matrix

[Gabor Grothendieck]

On 5/9/06, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> On 5/9/06, Gregor Gorjanc <gregor.gorjanc at gmail.com> wrote:
> > Hello!
> >
> > Thank you very much for the response. Please read within the lines
> >
> > Gabor Grothendieck wrote:
> > > On 5/9/06, Gregor Gorjanc <gregor.gorjanc at gmail.com> wrote:
> > >
> > >> Hello!
> > >>
> > >> I have parameter estimates for a generalized linear model and would like
> > >> to produce fitted values i.e. fitted(). This can be easily done in R,
> > >> but my problem lies in fact that I have a vector of parameters from some
> > >> other software, that is is not constrained i.e. I have the following
> > >> estimates for model with one factor with 4 levels
> > >>
> > >> beta = c(intercept group1 group2 group3 group4)
> > >>
> > >> where group1:4 are estimated deviations from intercept i.e. sum to zero
> > >> contraint, but all parameter estimates are there! How can I create a
> > >> model matrix that will not contain any constraints since I would like to
> > >> compute
> > >>
> > >> model.matrix("some_formula") %*% beta
> > >>
> > >> I.e. I would like to have model.matrix of the form
> > >>
> > >> 1 1 0 0 0
> > >> 1 0 1 0 0
> > >> 1 0 0 1 0
> > >> 1 0 0 0 1
> > >>
> > >> and not of the following form with contr.treatment or any other
> > >> contraints
> > >>
> > >> 1 0 0 0
> > >> 1 1 0 0
> > >> 1 0 1 0
> > >> 1 0 0 1
> > >>
> > >> I could remove group4 from beta and use sum to zero contraint for
> > >> contrast in fomula, but I would like to overcome this, as my model can
> > >> be richer in number or parameters. The following example, will show what
> > >> I would like to do:
> > >>
> > >> ## --- Setup ---
> > >>
> > >> groupN <- 4
> > >> NPerGroup <- 5
> > >> min <- 1
> > >> max <- 5
> > >> g <- runif(n = groupN, min = min, max = max)
> > >>
> > >> ## --- Simulate ---
> > >>
> > >> group <- factor(rep(paste("G", 1:groupN, sep = ""), each = NPerGroup))
> > >> y <- vector(mode = "numeric", length = groupN * NPerGroup)
> > >> j <- 1
> > >> for (i in 1:groupN) {
> > >>  y[j:(i * NPerGroup)] <- rpois(n = NPerGroup, lambda = g[i])
> > >>  j <- (i * NPerGroup) + 1
> > >> }
> > >>
> > >> ## --- GLM ---
> > >>
> > >> contrasts(group) <- contr.sum(groupN)
> > >> fit <- glm(y ~ group, family = "poisson")
> > >> coef(fit)
> > >>
> > >> ## Now this goes nicely
> > >> model.matrix(y ~ group) %*% coef(fit)
> > >>
> > >> ## But pretend I have the following vector of estimated parameters
> > >> beta <- c(coef(fit), 0 - sum(coef(fit)[-1]))
> > >> names(beta) <- c(names(beta)[1:4], "group4")
> > >>
> > >> ## I can not apply this as model matrix does not conform to beta
> > >> model.matrix(y ~ group) %*% beta
> > >
> > >
> > > Try this:
> > >
> > > model.matrix(y ~ group-1) %*% beta[-1] + beta[1]
> >
> > This is a nice hack here, but does not work in general. Say I have
> > another factor
> >
> > sex <- factor(rep(paste("S", 1:2, sep = ""), times=10))
> >
> > model.matrix(y ~ group + sex - 1)
> >
> > produces a matrix of 5 columns and not 6 as I want to.
>
> Try this:
>
> cbind(1, model.matrix(~group-1), model.matrix(~sex-1))
>

In thinking about this a bit more, try this:

attr(group, "contrasts") <- diag(nlevels(group))
attr(sex, "contrasts") <- diag(nlevels(sex))
model.matrix(~ group + sex)