amer.R
#######################################################
## Functions from amer ##
#######################################################
# I changed the original expand.call in amer to remove the use of .Internal
expand.call <-
function(call = sys.call(sys.parent(1)))
{
#given args:
ans <- as.list(call)
# ans1 <- ans[[1]]
# ans <- lapply(ans[-1], eval, envir = sys.frame(sys.parent(2)))
# ans <- c(ans1, ans)
#possible args:
frmls <- formals(safeDeparse(ans[[1]]))
#remove formal args with no presets:
frmls <- frmls[!sapply(frmls, is.symbol)]
add <- which(!(names(frmls) %in% names(ans)))
return(as.call(c(ans, frmls[add])))
}
indsF <-
function(m, fct, fctterm){
# add assign-like info to fctterm:
# which penalization/ranef groups and coefficients (fixed/random) belong to which function
# also include info on global intercept and by-level intercepts
ranefinds <- lme4:::reinds(m@Gp)
indIntercept <- ifelse("(Intercept)" %in% names(fixef(m)), 1, 0)
for(i in 1:length(fctterm)){
if(length(fct[[i]]$Z) == 1){
attr(fctterm[[i]], "indGrp") <- match(names(fct)[i], colnames(m@flist))
if(eval(attr(fct[[i]], "call")$allPen)) {
#add pen. group(s) with grouping factor u.x.by
indUGrp <- match(sub("f.", "u.", names(fct)[i]), colnames(m@flist))
attr(fctterm[[i]], "indGrp") <- c(attr(fctterm[[i]], "indGrp"), which(attr(m@flist, "assign")==indUGrp))
}
attr(fctterm[[i]], "indPen") <- unlist(ranefinds[attr(fctterm[[i]], "indGrp")])
if(!(eval(attr(fct[[i]], "call")$allPen)||ncol(fct[[i]]$X[[1]])==0)){
attr(fctterm[[i]], "indUnpen") <- sapply(paste("^",colnames(fct[[i]]$X[[1]]),"$",sep=""),
grep, x=names(m@fixef))
names(attr(fctterm[[i]], "indUnpen")) <- colnames(fct[[i]]$X[[1]])
} else attr(fctterm[[i]], "indUnpen") <- 0
attr(fctterm[[i]], "indConst") <- indIntercept
attr(fctterm[[i]], "indGrp") <- list(attr(fctterm[[i]], "indGrp"))
attr(fctterm[[i]], "indPen") <- list(attr(fctterm[[i]], "indPen"))
attr(fctterm[[i]], "indUnpen") <- list(attr(fctterm[[i]], "indUnpen"))
attr(fctterm[[i]], "indConst") <- list(attr(fctterm[[i]], "indConst"))
} else {
by <- eval(attr(fct[[i]],"call")$by, m@frame)
attr(fctterm[[i]], "indGrp") <- vector(mode="list", length=nlevels(by))
attr(fctterm[[i]], "indPen") <- vector(mode="list", length=nlevels(by))
attr(fctterm[[i]], "indUnpen") <- vector(mode="list", length=nlevels(by))
attr(fctterm[[i]], "indConst") <- vector(mode="list", length=nlevels(by))
for(j in 1:nlevels(by)){
attr(fctterm[[i]], "indGrp")[[j]] <- grep(paste("^",paste(names(fct)[i],".",names(fct[[i]]$Z)[j],sep=""), "$", sep=""), colnames(m@flist))
attr(fctterm[[i]], "indPen")[[j]] <- ranefinds[[attr(fctterm[[i]], "indGrp")[[j]]]]
if( ncol(fct[[i]]$X[[j]]) == 0){
attr(fctterm[[i]], "indUnpen")[[j]] <- 0
} else {
attr(fctterm[[i]], "indUnpen")[[j]] <- sapply(
paste("^",colnames(fct[[i]]$X[[j]]),"$",sep=""), grep, x=names(m@fixef))
names(attr(fctterm[[i]], "indUnpen")[[j]]) <- colnames(fct[[i]]$X[[j]])
}
#add by-level intercept:
indBy <- grep(paste("^",safeDeparse(attr(fct[[i]],"call")$by), levels(by)[j],"$", sep=""), names(m@fixef))
indBy <- indBy[!(indBy %in% attr(fctterm[[i]], "indUnpen")[[j]])]
attr(fctterm[[i]], "indConst")[[j]] <- c(indIntercept, indBy)
}
}
}
return(fctterm)
}
safeDeparse <- function(expr){
ret <- paste(deparse(expr), collapse="")
#rm whitespace
gsub("[[:space:]][[:space:]]+", " ", ret)
}
expandBasis <-
function(basis, by, varying, bySetToZero = T){
#multiply X, Z with varying
#set up lists of design matrices if by-variable and/or allPen are given:
allPen <- eval(attr(basis, "call")$allPen, parent.frame())
X <- basis$X
Z <- basis$Z
xName <- safeDeparse(attr(basis, "call")$x)
if(!is.null(varying)){
xName <- paste(xName, "X", safeDeparse(attr(basis, "call")$varying), sep="")
X <- cbind(varying, X * varying)
Z <- Z * varying
}
if(!is.null(by)){
X.o <- X
Z.o <- Z
byName <- safeDeparse(attr(basis, "call")$by)
if(!allPen){
basis$X <- basis$Z <- vector(mode="list", nlevels(by))
for(i in 1:nlevels(by)){
if(bySetToZero){
keep <- 1*(by == levels(by)[i])
} else keep <- rep(1, length(by))
#set X,Z partially to zero for each level of by-variable
if(NCOL(X.o)){
basis$X[[i]] <- X.o * keep
#naming scheme: x.fx.bylevel1.fx1, x.fx.bylevel1.fx2, ...,x.fx.bylevel2.fx1, or xXvarying.fx.bylevel1.fx1
colnames(basis$X[[i]]) <- paste(xName,".",byName,levels(by)[i],
paste(".fx",1:NCOL(basis$X[[i]]),sep=""), sep="")
}
basis$Z[[i]] <- Z.o * keep
}
#naming scheme: bylevel1, bylevel2, ...
names(basis$X) <- names(basis$Z) <- paste(byName, levels(by), sep="")
} else {
basis$X <- basis$Z <- vector(mode="list", 1)
by <- C(by[, drop=TRUE], contr.treatment) #make sure treatment contrasts are used, unused levels dropped
#basis$Z[[1]] <- Matrix(model.matrix(~ 0 + Z.o:by)) #TODO: can this be done without intermediate dense matrix?
basis$Z[[1]] <- model.matrix(~ 0 + Z.o:by) #FIXME: ?constructing directly as sparse breaks transposing Z in subAZ?
#cbind Z set partially to zero for each level of by-variable:
## for(i in 1:nlevels(by[, drop=TRUE])) {
## if(bySetToZero){
## keep <- (by == levels(by[, drop=TRUE])[i])
## } else keep <- 1
## basis$Z[[1]] <- cBind(basis$Z[[1]], Z.o * keep)
## #basis$Z[[1]] <- Matrix(model.matrix(~ 0 + Z.o:by[, drop=TRUE]))
## }
basis$X[[1]] <- X.o
if(NCOL(X.o)) colnames(basis$X[[1]]) <- paste(xName,".",byName,paste(".fx",1:NCOL(X),sep=""), sep="")
#naming scheme: u.x.by (also: name of duplicated by-variable in expandMf, subFcts)
names(basis$X) <- paste("u", xName, byName, sep=".")
}
} else {
if(NCOL(X)) colnames(X) <- paste(xName,paste(".fx",1:NCOL(X),sep=""), sep="")
basis$X <- list(X)
basis$Z <- list(Z)
}
return(basis)
}
subFcts <-
function(rhs, fctterm, fct, fr)
# replace formula parts for smooth functions with xi + (xi^2+ )... + xi^dimUnpen + (1|fcti) or
# by*(xi + xi^2+ ... + xi^dimUnpen) + (1|fcti.1) + ... + (1|fcti.N) for by-variable with N levels
{
for(i in 1:length(fct)){
by <- eval(attr(fct[[i]],"call")$by, fr)
allPen <- eval(attr(fct[[i]],"call")$allPen)
diag <- eval(attr(fct[[i]],"call")$diag)
replacement <-
if(is.null(by)){
# 1 + x.fx1 + x.fx2+ ... + (1|f.x)
paste(ifelse(ncol(fct[[i]]$X[[1]])!=0,
paste(as.vector(sapply(fct[[i]]$X,colnames)),collapse=" + "),
"1"),
" + (1|",names(fct)[i],")",sep="")
} else {
if(allPen){
if(!diag){
# add correlated random effects for normally unpenalized part of basis grouped according to by and fake random intercept
# (1 + x.fx1 + x.fx2+ ...|u.x.by) + (1|f.x.by)
paste(
paste(paste("(1",
paste(as.vector(sapply(fct[[i]]$X,colnames)), collapse="+"),
sep="+"),
"|",
names(fct[[i]]$X),")",
sep=""),
paste("(1|",names(fct)[i],")",sep="", collapse=" + "),
sep =" + ")
} else {
# add independent random effects for normally unpenalized part of basis grouped according to by and fake random intercept
# (1|u.x.by) + x.fx1|u.x.by) + x.fx2|u.x.by) + ... + (1|f.x.by)
paste(
paste(c("(1", paste("(0+", as.vector(sapply(fct[[i]]$X,colnames)),sep="")),"|", names(fct[[i]]$X),")",sep="",collapse=" + "),
paste("(1|",names(fct)[i],")",sep="", collapse=" + "),
sep =" + ")
}
} else {
# add fixed effect for unpenalized part of basis + fake random intercept for each by-level
# by + x.fx1.BYlevel1 + x.fx2.BYlevel1 +...+ (1|f.x.BYlevel1) + ... + x.fx1.BYlevelD + x.fx2.BYlevelD +... + (1|f.x.BYlevelD)
paste(#deparse(attr(fct[[i]],"call")$by),
ifelse(ncol(fct[[i]]$X[[1]])!=0,
paste(as.vector(sapply(fct[[i]]$X,colnames)),collapse=" + "),
"1"),
paste("(1|",names(fct)[i],".",names(fct[[i]]$Z),")",sep="", collapse=" + "),
sep =" + ")
}
}
rhs <- sub(safeDeparse(fctterm[[i]]), replacement, rhs, fixed=T)
}
return(rhs)
}
expandMf <-
function(fr, fct)
# cbind model frame with design matrices for unpenalized&penalized parts of the smooth fcts.
{
for(i in 1:length(fct)){
#matrix with all unpenalized terms for fct
newX <- do.call(cBind, fct[[i]]$X)
#factor variables with no. of levels = no. of penalized basis fcts
#newFact <- replicate(length(fct[[i]]$Z), rep(1:ncol(fct[[i]]$Z[[1]]), length=nrow(fct[[i]]$Z[[1]])))
newFact <- data.frame(factor(rep(1:ncol(fct[[i]]$Z[[1]]), length=nrow(fct[[i]]$Z[[1]]))))
if(length(fct[[i]]$Z) > 1){
for(j in 2:length(fct[[i]]$Z)){
newFact <- cbind(newFact, factor(rep(1:ncol(fct[[i]]$Z[[1]]), length=nrow(fct[[i]]$Z[[1]]))))
}
}
colnames(newFact) <- if(length(fct[[i]]$Z) == 1){
names(fct)[i]
} else {
paste(names(fct)[i],".",names(fct[[i]]$Z),sep="")
}
if(eval(attr(fct[[i]],"call")$allPen)){
# duplicate grouping factor for allPen-function groups so that assignment (which entries in ranef belong to which penalization
# group) can be reconstructed from the fitted model object m if there is another random effect associated with the by-variable.
# will need this for predict etc.. since attr(m@flist,"assign") only works the other way around....
newFact <- cBind(newFact, eval(attr(fct[[i]],"call")$by, fr))
colnames(newFact)[ncol(newFact)] <- names(fct[[i]]$X)
}
fr <- cBind(cBind(fr, newX),newFact)
}
return(fr)
}
subAZ <-
function(m, fct)
# replace design matrices for fake factors with designs for penalized spline basis
{
for(i in 1:length(fct)){
if(length(fct[[i]]$Z) == 1){
ind <- which(names(m$FL$fl)[attr(m$FL$fl, "assign")]==names(fct[i]))
Zt <- as(t(fct[[i]]$Z[[1]]), "sparseMatrix")
m$FL$trms[[ind]]$A <- m$FL$trms[[ind]]$Zt <- Zt
dimnames(m$FL$trms[[ind]]$ST) <- list(safeDeparse(attr(fct[[i]], "call")[[1]]), safeDeparse(attr(fct[[i]], "call")[[1]]))
} else {
for(j in 1:length(fct[[i]]$Z)){
ind <- grep(paste("^",paste(names(fct[i]),names(fct[[i]]$Z)[j],sep='.'), "$", sep=""), names(m$FL$fl)[attr(m$FL$fl, "assign")])
Zt <- as(t(fct[[i]]$Z[[j]]), "sparseMatrix")
m$FL$trms[[ind]]$A <- m$FL$trms[[ind]]$Zt <- Zt
dimnames(m$FL$trms[[ind]]$ST) <- list(safeDeparse(attr(fct[[i]], "call")[[1]]), safeDeparse(attr(fct[[i]], "call")[[1]]))
}
}
}
return(m)
}
set.mfrow <-
function (Nchains = 1, Nparms = 1, nplots = 1, sepplot = FALSE)
# taken from coda
{
mfrow <- if (sepplot && Nchains > 1 && nplots == 1) {
if (Nchains == 2) {
switch(min(Nparms, 5), c(1, 2), c(2, 2), c(3, 2),
c(4, 2), c(3, 2))
}
else if (Nchains == 3) {
switch(min(Nparms, 5), c(2, 2), c(2, 3), c(3, 3),
c(2, 3), c(3, 3))
}
else if (Nchains == 4) {
if (Nparms == 1)
c(2, 2)
else c(4, 2)
}
else if (any(Nchains == c(5, 6, 10, 11, 12)))
c(3, 2)
else if (any(Nchains == c(7, 8, 9)) || Nchains >= 13)
c(3, 3)
}
else {
if (nplots == 1) {
mfrow <- switch(min(Nparms, 13), c(1, 1), c(1, 2),
c(2, 2), c(2, 2), c(3, 2), c(3, 2), c(3, 3),
c(3, 3), c(3, 3), c(3, 2), c(3, 2), c(3, 2),
c(3, 3))
}
else {
mfrow <- switch(min(Nparms, 13), c(1, 2), c(2, 2),
c(3, 2), c(4, 2), c(3, 2), c(3, 2), c(4, 2),
c(4, 2), c(4, 2), c(3, 2), c(3, 2), c(3, 2),
c(4, 2))
}
}
return(mfrow)
}
tp <-
function(x, degree=1, k = 15, by=NULL, allPen = FALSE, varying = NULL, diag=FALSE,
knots= quantile(x, probs = (1:(k - degree))/(k - degree + 1)), centerscale=NULL, scaledknots=FALSE)
{
call <- as.list(expand.call(match.call()))
stopifnot(is.numeric(x), is.factor(by)||is.null(by), is.numeric(varying)||is.null(varying), degree >= 0)
degree <- as.integer(degree); call$degree <- degree
knots <- eval(knots)
if(is.null(centerscale)){
x <- scale(x)
#make sure prediction data uses the same center/scale as the data used to fit the model:
call$centerscale <- c(attr(x, "scaled:center"),attr(x, "scaled:scale"))
x <- as.vector(x)
} else x <- (x - centerscale[1])/centerscale[2]
if(!scaledknots){
knots <- (knots - call$centerscale[1])/call$centerscale[2]
call$scaledknots <- TRUE
}
if(length(unique(knots))!=length(knots)) warning("duplicate knots detected and removed.")
knots <- sort(unique(knots))
call$knots <- knots
if(k != length(knots)+ degree){
k <- length(knots) + degree; call$k <- k
warning("set k to ", k," to conform with given knots and degree.")
}
if((knots[1]<min(x)||(knots[k-degree]>max(x)))) warning("knots outside range of variable.")
if(is.null(by) && allPen) stop("allPen = TRUE only makes sense for smooths with a by-variable.")
#design for unpenalised part: global polynomial trends (no intercept)
if(degree>0){
X <- outer(x, 1:degree, "^")#poly(x, degree)
#colnames(X) <- paste(as.character(call$x),".fx",1:NCOL(X),sep="")
} else{
X <- matrix(nrow=length(x), ncol=0)
}
#design for penalised part:
Z <- outer(x,knots,"-")^degree*outer(x,knots,">")
res <- list(X=X, Z=Z, knots=knots)
attr(res, "call") <- as.call(call)
return(res)
}
bsp <- function(x, k=15, spline.degree = 3, diff.ord = 2,
knots=NULL, by=NULL, allPen = FALSE, varying = NULL, diag=FALSE)
{
require(splines)
call <- as.list(expand.call(match.call()))
stopifnot(diff.ord>=0, spline.degree>=0, is.numeric(x), k > spline.degree)
if(is.null(call$knots)){
knots.no <- k - spline.degree + 1
#generate a B-Spline-Matrix with equidistant knots (adapted from code by Thomas Kneib):
n<-length(x)
xl<-min(x)
xr<-max(x)
xmin<-xl-(xr-xl)/100
xmax<-xr+(xr-xl)/100
dx<-(xmax-xmin)/(knots.no-1)
knots<-seq(xmin-spline.degree*dx,xmax+spline.degree*dx,by=dx)
call$knots <- knots
}
B<-spline.des(knots,x,spline.degree+1)$design
#generate Penalization-Matrix
D<-diag(k)
if((d<-min(diff.ord,spline.degree))<diff.ord) warning(paste("order of differences > degree of splines:\n new order of differences=",d,"\n"))
if(d > 0) for(i in 1:d) D<-diff(D)
call$diff.ord <- d
#reparametrization: X = unpenalized part, Z =penalized part
X <-rep(1,k)
if(diff.ord>1) {for(i in 2:diff.ord) X <-cbind(X, knots[1:k]^(i-1)) }
X <- (B%*%X)[,-1, drop=FALSE]
Z <- B%*%t(D)%*%solve(tcrossprod(D))
res <- list(X=unname(X), Z=unname(Z))
attr(res, "call") <- as.call(call)
return(res)
}
