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

Gregor Gorjanc gregor.gorjanc at gmail.com
Tue May 9 23:43:54 CEST 2006

```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

## Is there any general way of constructing full design/model matrix
## without any constraints/reparametrizations?

Thanks!

--
Lep pozdrav / With regards,
Gregor Gorjanc

----------------------------------------------------------------------
University of Ljubljana     PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3                   mail: gregor.gorjanc <at> bfro.uni-lj.si

SI-1230 Domzale             tel: +386 (0)1 72 17 861
Slovenia, Europe            fax: +386 (0)1 72 17 888

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"One must learn by doing the thing; for though you think you know it,
you have no certainty until you try." Sophocles ~ 450 B.C.

```