Creates a Matrix of Appropriate Dimension
A support function for the argument xij, it generates a matrix
of an appropriate dimension.
fill(x, values = 0, ncolx = ncol(x))
x |
A vector or matrix which is used to determine the dimension of the
answer, in particular, the number of rows. After converting |
values |
Numeric.
The answer contains these values,
which are recycled columnwise if necessary, i.e.,
as |
ncolx |
The number of columns of the returned matrix.
The default is the number of columns of |
The xij argument for vglm allows the user to input
variables specific to each linear/additive predictor.
For example, consider
the bivariate logit model where the first/second linear/additive
predictor is the logistic regression of the first/second binary response
respectively. The third linear/additive predictor is log(OR) =
eta3, where OR is the odds ratio. If one has ocular pressure
as a covariate in this model then xij is required to handle the
ocular pressure for each eye, since these will be different in general.
[This contrasts with a variable such as age, the age of the
person, which has a common value for both eyes.] In order to input
these data into vglm one often finds that functions
fill, fill1, etc. are useful.
All terms in the xij
and formula arguments in vglm
must appear in the form2 argument too.
matrix(values, nrow=nrow(x), ncol=ncolx), i.e., a matrix
consisting of values values, with the number of rows matching
x, and the default number of columns is the number of columns
of x.
The effect of the xij argument is after other arguments such as
exchangeable and zero.
Hence xij does not affect constraint matrices.
Additionally, there are currently 3 other identical fill
functions, called fill1, fill2 and fill3;
if you need more then assign fill4 = fill5 = fill1 etc.
The reason for this is that if more than one fill function is
needed then they must be unique.
For example, if M=4 then
xij = op ~ lop + rop + fill(mop) + fill(mop) would reduce to
xij = op ~ lop + rop + fill(mop), whereas
xij = op ~ lop + rop + fill1(mop) + fill2(mop) would retain
all M terms, which is needed.
In Examples 1 to 3 below, the xij argument illustrates covariates
that are specific to a linear predictor. Here, lop/rop are
the ocular pressures of the left/right eye in an artificial dataset,
and mop is their mean. Variables leye and reye
might be the presence/absence of a particular disease on the LHS/RHS
eye respectively.
In Example 3,
the xij argument illustrates fitting the (exchangeable) model
where there
is a common smooth function of the ocular pressure. One should use
regression splines since s in vgam does not
handle the xij argument. However, regression splines such as
bs and ns need to have
the same basis functions here for both functions, and Example 3 illustrates
a trick involving a function BS to obtain this, e.g., same knots.
Although regression splines create more than a single column per term
in the model matrix, fill(BS(lop,rop)) creates the required
(same) number of columns.
T. W. Yee
fill(runif(5))
fill(runif(5), ncol = 3)
fill(runif(5), val = 1, ncol = 3)
# Generate eyes data for the examples below. Eyes are independent (OR=1).
nn <- 1000 # Number of people
eyesdata <- data.frame(lop = round(runif(nn), 2),
rop = round(runif(nn), 2),
age = round(rnorm(nn, 40, 10)))
eyesdata <- transform(eyesdata,
mop = (lop + rop) / 2, # Mean ocular pressure
op = (lop + rop) / 2, # Value unimportant unless plotting
# op = lop, # Choose this if plotting
eta1 = 0 - 2*lop + 0.04*age, # Linear predictor for left eye
eta2 = 0 - 2*rop + 0.04*age) # Linear predictor for right eye
eyesdata <- transform(eyesdata,
leye = rbinom(nn, size = 1, prob = logitlink(eta1, inverse = TRUE)),
reye = rbinom(nn, size = 1, prob = logitlink(eta2, inverse = TRUE)))
# Example 1. All effects are linear.
fit1 <- vglm(cbind(leye,reye) ~ op + age,
family = binom2.or(exchangeable = TRUE, zero = 3),
data = eyesdata, trace = TRUE,
xij = list(op ~ lop + rop + fill(lop)),
form2 = ~ op + lop + rop + fill(lop) + age)
head(model.matrix(fit1, type = "lm")) # LM model matrix
head(model.matrix(fit1, type = "vlm")) # Big VLM model matrix
coef(fit1)
coef(fit1, matrix = TRUE) # Unchanged with 'xij'
constraints(fit1)
max(abs(predict(fit1)-predict(fit1, new = eyesdata))) # Predicts correctly
summary(fit1)
## Not run:
plotvgam(fit1, se = TRUE) # Wrong, e.g., because it plots against op, not lop.
# So set op = lop in the above for a correct plot.
## End(Not run)
# Example 2. This model uses regression splines on ocular pressure.
# It uses a trick to ensure common basis functions.
BS <- function(x, ...)
sm.bs(c(x,...), df = 3)[1:length(x), , drop = FALSE] # trick
fit2 <- vglm(cbind(leye,reye) ~ BS(lop,rop) + age,
family = binom2.or(exchangeable = TRUE, zero = 3),
data = eyesdata, trace = TRUE,
xij = list(BS(lop,rop) ~ BS(lop,rop) +
BS(rop,lop) +
fill(BS(lop,rop))),
form2 = ~ BS(lop,rop) + BS(rop,lop) + fill(BS(lop,rop)) +
lop + rop + age)
head(model.matrix(fit2, type = "lm")) # LM model matrix
head(model.matrix(fit2, type = "vlm")) # Big VLM model matrix
coef(fit2)
coef(fit2, matrix = TRUE)
summary(fit2)
fit2@smart.prediction
max(abs(predict(fit2) - predict(fit2, new = eyesdata))) # Predicts correctly
predict(fit2, new = head(eyesdata)) # Note the 'scalar' OR, i.e., zero=3
max(abs(head(predict(fit2)) -
predict(fit2, new = head(eyesdata)))) # Should be 0
## Not run:
plotvgam(fit2, se = TRUE, xlab = "lop") # Correct
## End(Not run)
# Example 3. Capture-recapture model with ephemeral and enduring
# memory effects. Similar to Yang and Chao (2005), Biometrics.
deermice <- transform(deermice, Lag1 = y1)
M.tbh.lag1 <-
vglm(cbind(y1, y2, y3, y4, y5, y6) ~ sex + weight + Lag1,
posbernoulli.tb(parallel.t = FALSE ~ 0,
parallel.b = FALSE ~ 0,
drop.b = FALSE ~ 1),
xij = list(Lag1 ~ fill(y1) + fill(y2) + fill(y3) + fill(y4) +
fill(y5) + fill(y6) +
y1 + y2 + y3 + y4 + y5),
form2 = ~ sex + weight + Lag1 +
fill(y1) + fill(y2) + fill(y3) + fill(y4) +
fill(y5) + fill(y6) +
y1 + y2 + y3 + y4 + y5 + y6,
data = deermice, trace = TRUE)
coef(M.tbh.lag1)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.