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#' Adaptive Fence model selection
#'
#' Adaptive Fence model selection
#'
#' @param mf function for fitting the model
#' @param f formula of full model
#' @param ms list of formula of candidates models
#' @param d data
#' @param lf measure lack of fit (to minimize)
#' @param pf model selection criteria, e.g., model dimension
#' @param bs bootstrap samples
#' @param grid grid for c
#' @param bandwidth bandwidth for kernel smooth function
#' @return
#' \item{models}{list all model candidates in the model space}
#' \item{B}{list the number of bootstrap samples that have been used}
#' \item{lack_of_fit_matrix}{list a matrix of Qs for all model candidates (in columns). Each row is for each bootstrap sample}
#' \item{Qd_matrix}{list a matrix of QM - QM.tilde for all model candidates. Each row is for each bootrap sample}
#' \item{bandwidth}{list the value of bandwidth}
#' \item{model_mat}{list a matrix of selected models at each c values in grid (in columns). Each row is for each bootstrap sample}
#' \item{freq_mat}{list a matrix of coverage probabilities (frequency/smooth_frequency) of each selected models for a given c value (index)}
#' \item{c}{list the adaptive choice of c value from which the parsimonious model is selected}
#' \item{sel_model}{list the selected (parsimonious) model given the adaptive c value}
#' @author Jiming Jiang Jianyang Zhao J. Sunil Rao Thuan Nguyen
#' @references
#' \itemize{
#' \item{Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692}
#' \item{Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629}
#' \item{Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662}
#' }
#' @examples
#' \dontrun{
#' require(fence)
#'
#' #### Example 1 #####
#' data(iris)
#' full = Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + (1|Species)
#' test_af = fence.lmer(full, iris)
#' plot(test_af)
#' test_af$sel_model
#'
#' #### Example 2 #####
#' r =1234; set.seed(r)
#' p=8; n=150; rho = 0.6
#' id = rep(1:50,each=3)
#' R = diag(p)
#' for(i in 1:p){
#' for(j in 1:p){
#' R[i,j] = rho^(abs(i-j))
#' }
#' }
#' R = 1*R
#' x=mvrnorm(n, rep(0, p), R) # all x's are time-varying dependence #
#' colnames(x)=paste('x',1:p, sep='')
#' tbetas = c(0,0.5,1,0,0.5,1,0,0.5) # non-zero beta 2,3,5,6,8
#' epsilon = rnorm(150)
#' y = x%*%tbetas + epsilon
#' colnames(y) = 'y'
#' data = data.frame(cbind(x,y,id))
#' full = y ~ x1+x2+x3+x4+x5+x6+x7+x8+(1|id)
#' #X = paste('x',1:p, sep='', collapse='+')
#' #full = as.formula(paste('y~',X,'+(1|id)', sep="")) #same as previous one
#' fence_obj = fence.lmer(full,data) # it takes 3-5 min #
#' plot(fence_obj)
#' fence_obj$sel_model
#' }
#' @export
adaptivefence = function(
# model and lack of fit related
mf, f, ms, d, lf, pf,
# bootstrap sample
bs,
# fence related
grid = 101, bandwidth) {
ans = list(full = f, models = ms, pickfunc = pf)
mf = cmpfun(mf)
if (missing(ms)) {
stop("No candidate models specified!")
}
if (missing(bs)) {
stop("No bootstrap sample specified!")
}
eval_models = sfClusterApplyLB(ms, function(m) {
lapply(bs, function(b) {
try(mf(m, b), silent = TRUE)
})
})
sfStop()
em = sapply(eval_models, function(eval_model) sapply(eval_model, class))
eb = rowSums(em == "try-error") == 0
if (sum(eb) != length(bs)) {
warning(paste0("Some bootstrap sample are not avaiable, new bootstrap size is ", sum(eb)))
}
B = sum(eb)
ans$B = sum(eb)
for (i in 1:length(ms)) {
eval_models[[i]] = eval_models[[i]][eb]
}
mi = 0
bi = 0
lack_of_fit_matrix = replicate(length(ms), {
mi <<- mi + 1
bi <<- 0
replicate(B, {
bi <<- bi + 1
lf(eval_models[[mi]][[bi]])
})
})
ans$lack_of_fit_matrix = lack_of_fit_matrix
mi = 0
bi = 0
pick_matrix = replicate(length(ms), {
mi <<- mi + 1
bi <<- 0
replicate(B, {
bi <<- bi + 1
pf(eval_models[[mi]][[bi]])
})
})
ans$pick_matrix = pick_matrix
rm(mi, bi)
Q_m = sweep(lack_of_fit_matrix, 1, apply(lack_of_fit_matrix, 1, min), '-')
ans$Qd_matrix = Q_m
lof_lower = 0
lof_upper = max(Q_m)
cs = seq(lof_lower, lof_upper, length.out = grid)
if (is.na(bandwidth)) {
bandwidth = (cs[2] - cs[1]) * 3
}
ans$bandwidth = bandwidth * 1
model_mat = matrix(NA, nrow = B, ncol = grid)
for (i in 1:length(cs)) {
infence_matrix = Q_m <= cs[i]
for (bi in 1:B) {
b_infence = infence_matrix[bi,]
b_lack = lack_of_fit_matrix[bi,]
b_pick = pick_matrix[bi,]
b_pick[!b_infence] = Inf
b_pick = which(b_pick == min(b_pick))
model_mat[bi, i] = b_pick[which.min(b_lack[b_pick])]
}
}
ans$model_mat = model_mat
# if two models have same frequency, this frequency must
# be lower than 0.5, so maybe we don't have to worry about
# this case too much?
freq_mat = apply(model_mat, 2, function(l) {
tab = sort(table(l), decreasing = TRUE)
c(as.numeric(names(tab)[1]), tab[1])
})
freq_mat[2,] = freq_mat[2,] / B
freq_mat = rbind(freq_mat, ksmooth(cs, freq_mat[2,], kernel = "normal", bandwidth = bandwidth, x.points = cs)$y)
colnames(freq_mat) = cs
rownames(freq_mat) = c("index", "frequency", "smooth_frequency")
ans$freq_mat = freq_mat
cindex = peakw(cs, freq_mat[3,], 2)
ans$c = cs[cindex]
if (!is.na(cindex)) {
ans$formula = ms[[freq_mat[1,cindex]]]
ans$sel_model = mf(ans$formula, d)
}
else {
ans$formula = NA
ans$sel_model = NA
}
class(ans) = "AF"
return(ans)
}
#' Plot Adaptive Fence model selection
#'
#' @param x Object to be plotted
#' @param ... Additional arguments. CNot currently used.
#'
#' @export
plot.AF = function(x = res, ...) {
res <- m <- sp <- NULL
rm(res,m,sp)
tmp = data.frame(c = as.numeric(colnames(x$freq_mat)),
p = x$freq_mat[2, ],
sp = x$freq_mat[3, ],
m = as.factor(x$freq_mat[1, ]))
p = ggplot(tmp) +
geom_point(aes(x = c, y = p, colour = m)) +
geom_line(aes(x = c, y = sp), linetype="dashed") +
geom_line(aes(x = c, y = sp, colour = m)) +
ylim(0, 1)
p
}
#' Summary Adaptive Fence model selection
#'
#' @param object Object to be summarized
#' @param ... addition arguments. Not currently used
#'
#' @export
summary.AF = function(object = res, ...) {
res <- m <- sp <- NULL
rm(res,m,sp)
print(object$sel_model)
}
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