如何解决将lapply用于模拟研究列表列表中构造的数据
|| 关于lapply（）在模拟研究中的应用，我碰壁了。这些数据旨在帮助我们了解标准化公式如何影响提案评级活动的结果。 评估者需要满足以下三个条件：无偏差，统一偏差（各个评估者之间的偏差增加）和双向偏差（各个评估者之间的偏差为正负平衡）。 假定提案的真实价值是已知的。 我们希望在每个偏差条件下生成一组重复的数据集，以便这些数据集可以模拟一个提案评估期（一个小组）。然后，我们想复制面板以模拟具有许多投标评估期。 这是数据结构的示意图： The data structure looks like this:
p = number of proposals
r = number of raters
n.panels = number of replicate panels
t.reps = list of several replicate panels
three bias conditions: n.bias - no bias
u.bias - uniform bias (raters higher than previous rater)
b.bias - bidirectional bias (balanced up and down bias)
-|
t 1 |..| --> 10*(n.bias(p*r)) + 10*(u.bias(p*r)) + 10*(b.bias(p*r) {panel replication 1}
. 2 |..| --> 10*(n.bias(p*r)) + 10*(u.bias(p*r)) + 10*(b.bias(p*r) {panel replication 2}
r : : : : :
e : : : : :
p n.panels |..| --> 10*(n.bias(p*r)) + 10*(u.bias(p*r)) + 10*(b.bias(p*r) {n. panels replications}
s
_|
########## start of simulation parameters
set.seed(271828)
means <- matrix(c(rep(50,3),rep(60,rep(70,4) ),ncol = 1) # matrix of true proposal values
bias.u <- matrix(c(0,2,4,6,8),nrow=1) # unidirectional bias
bias.b <- matrix(c(0,3,-3,5,-5),nrow=1) # bidirectional bias
ones.u <- matrix(rep(1,ncol(bias.u)),nrow = 1) # number of raters is the number of columns (r)
ones.b <- matrix(rep(1,ncol(bias.b)),nrow = 1)
ones.2 <- matrix(rep(1,nrow(means)),ncol = 1) # number of proposals is the number of rows (p)
true.ratings <- means%*%ones.u # gives matrix of true proposal value for each rater (p*r)
uni.bias <- ones.2%*%bias.u
bid.bias <- ones.2%*%bias.b # gives matrix of true rater bias for each proposal (p*r)
n.val <- nrow(means)*ncol(ones.u)
# true.ratings
# uni.bias
# bid.bias
library(MASS)
#####
##### generating replicate data...
#####
##########-------------------- analyzing mse of adjusted scores across replications
##########-------------------- developing random replicates of panel data
##########----- This means that there are (reps) replications in each of the bias conditions
##########----- to represent a plausible set of ratings in a particular collection
##########----- of panels. So for one proposal cycle (panel),there are 3 * (reps) * nrow(means)
##########----- number of proposal ratings.
##########-----
##########----- There are (n.panels) replications of the total number of proposal ratings placed in a list
##########----- (t.reps).
n.panels <- 2 # put in the number of replicate panels that should be produced
reps <- 10 # put in the number of times each bias condition should be included in a panel
t.reps <- list()
n.bias <- list()
u.bias <- list()
b.bias <- list()
for (i in 1:n.panels)
{
{
for(j in 1:reps)
n.bias[[j]] <- true.ratings + matrix(round(rnorm(n.val,2),digits=0),nrow = nrow(means))
for(j in 1:reps)
u.bias[[j]] <- true.ratings + uni.bias + matrix(round(rnorm(n.val,nrow = nrow(means))
for(j in 1:reps)
b.bias[[j]] <- true.ratings + bid.bias + matrix(round(rnorm(n.val,nrow = nrow(means))
}
t.reps[[i]] <- list(n.bias,u.bias,b.bias)
}
# t.reps
adj.scores <- function(x,tot.dat)
{
t.sd <- sd(array(tot.dat))
t.mn <- mean(array(tot.dat))
ones.t.mn <- diag(1,ncol(x))
p <- nrow(x)
r <- ncol(x)
ones.total <- matrix(1,p,r)
r.sd <- diag(apply(x,sd))
r.mn <- diag(apply(x,mean))
den.r.sd <- ginv(r.sd)
b.shift <- x%*%den.r.sd
a <- t.mn*ones.t.mn - den.r.sd%*%r.mn
a.shift <- ones.total%*%a
l.x <- b.shift + a.shift
return(l.x)
}
########## I would like to do something like this...
########## apply the function to each element in the list t.reps
dat.1 <- matrix(unlist(t.reps[[1]]),ncol=5)
adj.rep.1 <- lapply(t.reps[[1]],adj.scores,tot.dat = dat.1)
解决方法
我不能说我完全理解了整个问题（我不是统计学家！），但您失败的行失败的原因是，当3期望矩阵时，3会通过4的列表。
由于您具有列表列表（列表！），所以
rapply
adj.rep.1 <- rapply(t.reps[[1]],adj.scores,how=\'replace\',tot.dat = dat.1)
# comparing the structures
str(t.reps[[1]])
str(adj.rep.1)
####################
########## proposal ratings project
########## 17 June 2011
########## original code by: jjb with help from es
##########------ functions to be read in and called when desired
########## applying this function to a single matrix will give detailed output
########## calculating generalizability theory components
########## not a very robust formulation,but a good place to start
########## for future,put panel facet on this design
g.pxr.long = function(x)
{
m.raters <<- colMeans(x)
n.raters <<- length(m.raters)
m.props <<- rowMeans(x)
n.props <<- length(m.props)
m.total <<- mean(x)
n.total <<- nrow(x)*ncol(x)
m.raters.2 <<- m.raters^2
m.props.2 <<- m.props^2
sum.m.raters.2 <<- sum(m.raters.2)
sum.m.props.2 <<- sum(m.props.2)
ss.props <<- n.raters*(sum.m.props.2) - n.total*(m.total^2)
ss.raters <<- n.props*(sum.m.raters.2) - n.total*(m.total^2)
ss.pr <<- sum(x^2) - n.raters*(sum.m.props.2) - n.props*(sum.m.raters.2) + n.total*(m.total^2)
df.props <- n.props - 1
df.raters <- n.raters - 1
df.pr <- df.props*df.raters
ms.props <- ss.props / df.props
ms.raters <- ss.raters / df.raters
ms.pr <- ss.pr / df.pr
var.p <- (ms.props - ms.pr) / n.raters
var.r <- (ms.raters - ms.pr) / n.props
var.pr <- ms.pr
out.1 <- as.data.frame( matrix(c( df.props,df.raters,df.pr,ss.props,ss.raters,ss.pr,ms.props,ms.raters,ms.pr,var.p,var.r,var.pr),ncol = 4))
out.2 <- as.data.frame(matrix(c(\"p\",\"r\",\"pr\" ),ncol = 1))
g.out.1 <- as.data.frame(cbind(out.2,out.1))
colnames(g.out.1) <- c(\" source\",\" df \",\" ss \",\" ms \",\" variance\")
var.abs <- (var.r / n.raters) + (var.pr / n.raters)
var.rel <- (var.pr / n.raters)
var.xbar <- (var.p / n.props) + (var.r / n.raters) + (var.pr / (n.raters*n.props) )
gen.coef <- var.p / (var.p + var.rel)
dep.coef <- var.p / (var.p + var.abs)
out.3 <- as.data.frame(matrix(c(var.rel,var.abs,var.xbar,gen.coef,dep.coef),ncol=1))
out.3 <- round(out.3,digits = 4)
out.4 <- as.data.frame(matrix(c(\"relative error variance\",\"absolute error variance\",\"xbar error variance\",\"E(rho^2)\",\"Phi\"),ncol=1))
g.out.2 <- as.data.frame(cbind(out.4,out.3))
colnames(g.out.2) <- c(\" estimate \",\" value\")
outs <- list(g.out.1,g.out.2)
names(outs) <- c(\"generalizability theory: G-study components\",\"G-study Indices\")
return(outs)
}
##########----- calculating confidence intervals using Chebychev,Cramer,and Normal
##########----- use this to find alpha for desired k
factor.choose = function(k)
{
alpha <- 1 / k^2
return(alpha)
}
conf.intervals = function(dat,alpha)
{
k <- sqrt( 1 / alpha ) # specifying what the k factor is...
x.bar <- mean(dat)
x.sd <- sd(dat)
n.obs <- length(dat)
sem <- x.sd / sqrt(n.obs)
ub.cheb <- x.bar + k*sem
lb.cheb <- x.bar - k*sem
ub.crem <- x.bar + (4/9)*k*sem
lb.crem <- x.bar - (4/9)*k*sem
ub.norm <- x.bar + qnorm(1-alpha/2)*sem
lb.norm <- x.bar - qnorm(1-alpha/2)*sem
out.lb <- matrix(c(lb.cheb,lb.crem,lb.norm),ncol=1)
out.ub <- matrix(c(ub.cheb,ub.crem,ub.norm),ncol=1)
dat <- as.data.frame(dat)
mean.raters <- as.matrix(rowMeans(dat))
dat$z.values <- matrix((mean.raters - x.bar) / x.sd)
select.cheb <- dat[ which(abs(dat$z.values) >= k ),]
select.crem <- dat[ which(abs(dat$z.values) >= (4/9)*k ),]
select.norm <- dat[ which(abs(dat$z.values) >= qnorm(1-alpha/2)),]
count.cheb <- nrow(select.cheb)
count.crem <- nrow(select.crem)
count.norm <- nrow(select.norm)
out.dat <- list()
out.dat <- list(select.cheb,select.crem,select.norm)
names(out.dat) <- c(\"Selected cases: Chebychev\",\"Selected cases: Cramer\'s\",\"Selected cases: Normal\")
out.sum <- matrix(c(x.bar,x.sd,n.obs),ncol=3)
colnames(out.sum) <- c(\"mean\",\"sd\",\"n\")
out.crit <- matrix(c(alpha,k,(4/9)*k,qnorm(1-alpha/2)),ncol=4 )
colnames(out.crit) <- c(\"alpha\",\"k\",\"(4/9)*k\",\"z\" )
out.count <- matrix(c(count.cheb,count.crem,count.norm),ncol=3 )
colnames(out.count) <- c(\"Chebychev\",\"Cramer\",\"Normal\")
rownames(out.count) <- c(\"count\")
outs <- list(out.sum,out.crit,out.count,out.dat)
names(outs) <- c(\"Summary of data\",\"Critical values\",\"Count of Selected Cases\",\"Selected Cases\")
return(outs)
}
rm(list = ls())
set.seed(271828)
means <- matrix(c( rep(50,19),rep(70,1) ),ncol = 1) # matrix of true proposal values
bias.u <- matrix(c(0,2,4),nrow=1) # unidirectional bias
bias.b <- matrix(c(0,5,-5),nrow=1) # bidirectional bias
ones.u <- matrix(rep(1,ncol(bias.u)),nrow = 1) # number of raters is the number of columns (r)
ones.b <- matrix(rep(1,ncol(bias.b)),nrow = 1)
ones.2 <- matrix(rep(1,nrow(means)),ncol = 1) # number of proposals is the number of rows (p)
true.ratings <- means%*%ones.u # gives matrix of true proposal value for each rater (p*r)
uni.bias <- ones.2%*%bias.u
bid.bias <- ones.2%*%bias.b # gives matrix of true rater bias for each proposal (p*r)
pan.bias.pos <- matrix(20,nrow=nrow(true.ratings),ncol=ncol(true.ratings)) # gives a matrix of bias for every member in a panel (p*r)
n.val <- nrow(true.ratings)*ncol(true.ratings)
# true.ratings
# uni.bias
# bid.bias
# pan.bias.pos
library(MASS)
#####
##### generating replicate data...
#####
n.panels <- 10 # put in the number of replicate panels that should be produced
reps <- 2 # put in the number of times each bias condition should be included in a panel
t.reps <- list()
n.bias <- list()
u.bias <- list()
b.bias <- list()
pan.bias <- list()
n.bias.out <- list()
u.bias.out <- list()
b.bias.out <- list()
pan.bias.out <- list()
for (i in 1:n.panels)
{
{
for(j in 1:reps)
n.bias[[j]] <- true.ratings + matrix(round(rnorm(n.val,4,2),digits=0),nrow = nrow(means))
for(j in 1:reps)
u.bias[[j]] <- true.ratings + uni.bias + matrix(round(rnorm(n.val,nrow = nrow(means))
for(j in 1:reps)
b.bias[[j]] <- true.ratings + bid.bias + matrix(round(rnorm(n.val,nrow = nrow(means))
}
pan.bias[[i]] <- true.ratings + pan.bias.pos + matrix(round(rnorm(n.val,nrow = nrow(means))
n.bias.out[[i]] <- n.bias
u.bias.out[[i]] <- u.bias
b.bias.out[[i]] <- b.bias
t.reps[[i]] <- c(n.bias,u.bias,b.bias,pan.bias[i])
}
# t.reps
# rm(list = ls())
##########----- this is the standardization formula to be applied to proposal ratings **WITHIN** a panel
adj.scores <- function(x,tot.dat)
{
t.sd <- sd(array(tot.dat))
t.mn <- mean(array(tot.dat))
ones.t.mn <- diag(1,ncol(x))
p <- nrow(x)
r <- ncol(x)
ones.total <- matrix(1,p,r)
r.sd <- diag(apply(x,sd))
r.mn <- diag(apply(x,mean))
den.r.sd <- ginv(r.sd)
b.shift <- x%*%den.r.sd
a <- t.mn*ones.t.mn - den.r.sd%*%r.mn
a.shift <- ones.total%*%a
l.x <- b.shift + a.shift
return(l.x)
}
##########----- applying standardization formula and getting
##########----- proposal means for adjusted and unadjusted ratings
adj.rep <- list()
m.adj <- list()
m.reg <- list()
for (i in 1:n.panels)
{
panel.data <- array(unlist(t.reps[[i]]))
adj.rep[[i]] <- lapply(t.reps[[i]],tot.dat = panel.data)
m.adj[[i]] <- lapply(adj.rep[[i]],rowMeans)
m.reg[[i]] <- lapply(t.reps[[i]],rowMeans)
}
##########-----
##########----- This function extracts the replicate proposal means for each set of reviews
##########----- across panels. So,if there are 8 sets of reviewers that are simulated 10 times,##########----- this extracts the first set of means across the 10 replications and puts them together,##########----- and then extracts the second set of means across replications and puts them together,etc..
##########----- The result will be 8 matrices made up of 10 columns with rows .
##########-----
##########----- first for unadjusted means
means.reg <- matrix(unlist(m.reg),nrow=nrow(means))
sets <- length(m.reg[[1]])
counter <- n.panels*length(m.reg[[1]])
m.reg.panels.set <- list()
for (j in 1:sets)
{
m.reg.panels.set[[j]] <- means.reg[,c(seq( j,counter,sets))]
}
##########----- now for adjusted means
means.adj <- matrix(unlist(m.adj),nrow=nrow(means))
sets <- length(m.adj[[1]])
counter <- n.panels*length(m.adj[[1]])
m.adj.panels.set <- list()
for (j in 1:sets)
{
m.adj.panels.set[[j]] <- means.adj[,sets))]
}
########## calculating msd as bias^2 and error^2
msd.calc <- function(x)
{
true.means <- means
calc.means <- as.matrix(rowMeans(x))
t.means.mat <- matrix(rep(true.means,n.panels),ncol=ncol(x))
c.means.mat <- matrix(rep(calc.means,ncol=ncol(x))
msd <- matrix( rowSums( (x - t.means.mat )^2) / ncol(c.means.mat) )
bias.2 <- (calc.means - true.means)^2
e.var <- matrix( rowSums( (x - c.means.mat )^2) / ncol(c.means.mat ) )
msd <- matrix(c(msd,bias.2,e.var),ncol = 3)
colnames(msd) <- c(\"msd\",\"bias^2\",\"e.var\")
return(msd)
}
########## checking work...
# msd.calc <- bias.2 + e.var
# all.equal(msd,msd.calc)
##########----- applying function to each set across panels
msd.reg.panels <- lapply(m.reg.panels.set,msd.calc)
msd.adj.panels <- lapply(m.adj.panels.set,msd.calc)
msd.reg.panels
msd.adj.panels
########## for the unadjusted scores,the msd is very large (as is expected)
########## for the adjusted scores,the msd is in line with the other panels
##########----- trying to evaluate impact of adjusting scores on proposal awards
reg.panel.1 <- matrix(unlist(m.reg[[1]]),nrow=nrow(means))
adj.panel.1 <- matrix(unlist(m.adj[[1]]),nrow=nrow(means))
reg <- matrix(array(reg.panel.1),ncol=1)
adj <- matrix(array(adj.panel.1),ncol=1)
panels.1 <- cbind(reg,adj)
colnames(panels.1) <- c(\"unadjusted\",\"adjusted\")
cor(panels.1,method=\"spearman\")
plot(panels.1)
######## identify(panels.1)
plot(panels.1,xlim = c(25,95),ylim = c(25,95) )
abline(0,1,col=\"red\")
########## the adjustment greatly reduces variances of ratings
########## compare the projection of the panel means onto the respective margins
##########----- examining the selection of the top 10% of the proposals
pro.names <- matrix(seq(1,nrow(reg),1))
df.reg <- as.data.frame(cbind(pro.names,reg))
colnames(df.reg) <- c(\"pro\",\"rating\")
df.reg$q.pro <- ecdf(df.reg$rating)(df.reg$rating)
df.adj <- as.data.frame(cbind(pro.names,adj))
colnames(df.adj) <- c(\"pro\",\"rating\")
df.adj$q.pro <- ecdf(df.adj$rating)(df.adj$rating)
awards.reg <- df.reg[ which(df.reg$q.pro >= .90),]
awards.adj <- df.adj[ which(df.adj$q.pro >= .90),]
awards.reg[order(-awards.reg$q.pro),]
awards.adj[order(-awards.adj$q.pro),]
awards.reg[order(-awards.reg$pro),]
awards.adj[order(-awards.adj$pro),]
##### using unadjusted scores,the top 10% of proposals come mostly from one (biased) panel,and the rest are made up of the
##### highest scoring proposal (from the biased rater) from the remaining panels.
##### using the adjusted scores,the top 10% of proposals are made up of the highest scoring proposal (the biased rater) from the
##### several panels,and a few proposals from other panels. Doesn\'t seem to be a systematic explanation as to why...
#########----- treating rating data in an ANOVA model
ratings <- do.call(\"rbind\",t.reps[[1]] )
panels <- factor(gl(7,20))
fit <- manova(ratings ~ panels)
summary(fit,test=\"Wilks\")
adj.ratings <- do.call(\"rbind\",adj.rep[[1]] )
adj.fit <- manova(adj.ratings ~ panels)
summary(adj.fit,test=\"Wilks\")
##########----- thinking... extra ideas for later
##########----- calculating Mahalanobis distance to identify biased panels
mah.dist = function(dat)
{md.dat <- as.matrix(mahalanobis(dat,center = colMeans(dat),cov = cov(dat) ))
md.pv <- as.matrix(pchisq(md.dat,df = ncol(dat),lower.tail = FALSE))
out <- cbind(md.dat,md.pv)
out.2 <- as.data.frame(out)
colnames(out.2) <- c(\"MD\",\"pMD\")
return(out.2)
}
mah.dist(ratings)
mah.dist(adj.ratings)
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