Thanks for your answer, I would like to make clear my question: My data is like following and there is a response variable y:
Time Size Charge Density Replication
3 small + low 1
. . . . .
. . . . .
9 small + low 1
3 big + low .
. . . . .
. . . . .
9 big + low 1
3 small - low 1
. . . . .
. . . . .
9 small - low 1
3 big - low 1
. . . . .
. . . . .
9 big - low 1
3 small + high 1
. . . . .
. . . . .
9 small + high 1
3 big + high 1
. . . . .
. . . . .
9 big + high 1
3 small - high 1
. . . . .
. . . . 1
9 small - high 1
3 big - high 1
. . . . .
. . . . .
9 big - high 1
3 small + low 2
. . . . .
. . . . .
9 small + low 2
3 big + low 2
. . . . .
. . . . .
9 big + low 2
3 small - low 2
. . . . .
. . . . .
9 small - low 2
3 big - low 2
. . . . .
. . . . .
9 big - low 2
3 small + high 2
. . . . .
. . . . .
9 small + high 2
3 big + high 2
. . . . .
. . . . .
9 big + high 2
3 small - high 2
. . . . .
. . . . .
9 small - high 2
3 big - high 2
. . . . .
. . . . .
9 big - high 2
My code with comments:
##this function selects the knots
default.knots <- function(x,num.knots)
{
if (missing(num.knots))
num.knots <- max(5,min(floor(length(unique(x))/4),35))
return(quantile(unique(x),seq(0,1,length=
(num.knots+2))[-c(1,(num.knots+2))]))
}
knots <- default.knots(Time)
z <- outer(Time, knots, "-")
z <- z * (z > 0)
z<-z^2
i.size50 <- I(Size==small)
i.chargepos <- I(Charge=="+")
i.densitylow <- I(Density==low)
##Create X and Z matrices, I put interactions because I want intercept to
be zero at time 0.
X <- cbind( I(Time^2),Time*i.size50,Time*i.chargepos,Time*i.densitylow)
Z <- cbind( z, z*i.size50, z*i.chargepos,z*i.densitylow)
K <- length(knots)
## form blocked diagonal matrix Z to specify which columns of Z are used for
each group
block.ind <- list(1:K, (K+1):(2*K),(2*K+1):(3*K),(3*K+1):(4*K))
Z.block <- list()
for (i in 1:length(block.ind))
Z.block[[i]] <-
as.formula(paste("~Z[,c(",paste(block.ind[[i]],collapse=","),")]-1"))
##create dummy grouping variable since groupedData object is required for
lme
group <- rep(1, length(Time))
model.data <- groupedData(y~X|group, data=data.frame(X, y))
fit <- lme(y~-1+X, data=model.data, random=pdBlocked(list(
pdBlocked(Z.block,pdClass="pdIdent"), pdIdent(~-1+ Replication) ))
,control=list(maxIter=1000, msMaxIter=1000, niterEM=1000))
The experiment is repeated twice (Replication 1 and 2) , hence I think that
Replication should be random effect. As you said, my replications are
randomly chosen from a population and I should make inference about the
population. I don't have a chance to take more replications. Then, I am
planning to generate new data sets from the fitted model.
--
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