Simulation Method
For each of 400 simulations generate a training sample of 500 observations with p predictors (p=15, 30, 60, 90) and a binary reponse. The predictors are independently U(-0.5,0.5). The response is sampled so as to follow a logistic model where the intercept is zero and the regression coefficients have each of two patterns. First, all coefficients are set to 0.0 so that the true predictive model has no predictive discrimination ability (\(D_{xy}=0, c=\) AUROC \(=0.5\)). Then regression coefficients were uniformly spaced between -1 and 1, multiplied by a scaling factor that is < 1 when the number of predictors p is 30 and > 1 when p > 30. The “gold standard” is the predictive ability of the fitted model on a test sample containing 50,000 observations generated from the same population model. The task of a validation method is to recover this gold standard.
Validation Methods
For each of the 400 training and validation samples, several validation methods were employed to estimate how the training sample model predicts responses in the 50,000 observations. These validation methods involve fitting 40 or 200 models per training sample.
g-fold cross-validation was done using the command validate(f, method='cross', B=4 or B=10)
in the R rms
package. This was repeated 4, 10, 20, or 50 times and averaged.
For bootstrap methods validate(f, method=‘boot’ or ‘632’, B=40 or B=200) was used. method=‘632’ does Efron’s “.632” method, labeled “632a” in the output. An ad-hoc modification of the .632 method, “632b” was also done. Here a “bias-corrected” index of accuracy is simply the index evaluated in the observation omitted from the bootstrap re-sample.
The “gold standard” external validations were done using the val.prob
function in the rms
package.
I didn’t run all combinations of validation methods and number of predictors, and I only used one sample size (500).
Indexes of Predictive Accuracy
\(D_{xy}\): Somers’ rank correlation between predicted probability that Y=1 vs. the binary Y values. This equals 2(c - 0.5) where the c-index is the “ROC Area” or concordance probability.
Q: Logarithmic accuracy score - a scaled version of the log-likelihood achieved by the predictive model
Slope: calibration slope (slope of predicted log odds vs. true log odds)
Measure of Accuracy of Validation Estimates
Three measures of accuracy of estimates of validated model performance are computed, in descending order of robustness and statistical efficiency.
- Root mean squared error of estimates (e.g., of \(D_{xy}\) from the bootstrap on the 500 observations) against the “gold standard” (e.g., \(D_{xy}\) for the fitted 500-observation model achieved in the 50,000 observations).
- Mean absolute error
- Median absolute error
Code for the Simulations
require(rms)
options(prType='html')
knitrSet(lang='markdown')
mdchunk <- markupSpecs$html$mdchunk # in Hmisc
dosims <- FALSE
set.seed(1) # so can reproduce results
P <- c(15, 30, 60, 90)
n <- 500 # Size of training sample
reps <- 400 # Simulations
npop <- 50000 # Size of validation gold standard sample
methods <- c('Boot 40','Boot 200','632a 40','632a 200',
'632b 40','632b 200','10-fold x 4','4-fold x 10',
'10-fold x 20','4-fold x 50')
R <- expand.grid(sim = 1:reps,
p = P,
method = methods,
sbeta = 1:2)
R$Dxy <- R$Intercept <- R$Slope <- R$D <- R$U <- R$Q <- R$repmeth <- R$B <- NA
R$n <- n
Rpop <- R
## Function to do r overall reps of B resamples, averaging to get
## estimates similar to as if r*B resamples were done
val <- function(fit, method, B, r) {
contains <- function(m) length(grep(m, method)) > 0
meth <- if(contains('Boot')) 'boot' else
if(contains('fold')) 'crossvalidation' else
if(contains('632')) '.632'
z <- 0
for(i in 1:r) z <- z + validate(fit, method=meth, B=B)[
c("Dxy","Intercept","Slope","D","U","Q"),'index.corrected']
z/r
}
for(sbeta in 1 : 2) {
for(p in P) {
## For each p create the true betas, the design matrix,
## and realizations of binary y in the gold standard large sample
Beta <- if(sbeta == 1) rep(0, p) else seq(-1, 1, length=p) * 30 / p
X <- matrix(runif(npop*p), nrow=npop) - 0.5
LX <- matxv(X, Beta)
Y <- ifelse(runif(npop) <= plogis(LX), 1, 0)
## For each simulation create the data matrix and realizations of y
for(j in 1:reps) {
# cat(j, file='/tmp/z.txt')
## Make training sample
x <- matrix(runif(n*p), nrow=n) - 0.5
L <- matxv(x, Beta)
y <- ifelse(runif(n) <= plogis(L), 1, 0)
f <- lrm(y ~ x, x=TRUE, y=TRUE)
beta <- f$coef
forecast <- matxv(X, beta)
## Validate in population
v <- val.prob(logit=forecast, y=Y, pl=FALSE)[
c("Dxy","Intercept","Slope","D","U","Q")]
for(method in methods) {
repmeth <- 1
if(method %in% c('Boot 40','632a 40','632b 40')) B <- 40
if(method %in% c('Boot 200','632a 200','632b 200')) B <- 200
if(method == '10-fold x 4') {
B <- 10
repmeth <- 4
}
if(method == '4-fold x 10') {
B <- 4
repmeth <- 10
}
if(method == '10-fold x 20') {
B <- 10
repmeth <- 20
}
if(method == '4-fold x 50') {
B <- 4
repmeth <- 50
}
z <- val(f, method, B, repmeth)
k <- which(R$sim == j & R$p == p & R$method == method & R$sbeta == sbeta)
if(length(k) != 1) stop('program logic error')
R[k, names(z)] <- z - v
R[k, c('B','repmeth','sbeta')] <- c(B=B, repmeth=repmeth, sbeta=sbeta)
Rpop[k, names(z)] <- v
Rpop[k, c('B', 'repmeth','sbeta')] <- c(B=B, repmeth=repmeth, sbeta=sbeta)
Save(R) ## temporary until simulations are finished -
## can examine preliminary results
Save(Rpop)
} # end over methods
} # end over reps
} # end over p
} # end over sbeta
valSimresult <- R
Save(valSimresult)
valSimTrue <- Rpop
save(valSimTrue)
Population Indexes
Let’s examine the “population” (true) values of \(D_{xy}\) that were achieved. For the null model simulations the true values are exactly zero.
Distribution of Values for Null Models
A separate histogram is made for each number of predictors p.
Load(valSimresult)
Load(valSimTrue)
v <- valSimTrue
v$p <- paste0('p=', v$p)
r <- subset(v, sbeta == 1)
require(ggplot2)
ggplot(r, aes(Dxy)) + facet_wrap(~ p) + geom_histogram(bins=50)
![](data:image/png;base64,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)
Distribution of Values for Non-Null Models
r <- subset(v, sbeta == 2)
ggplot(r, aes(Dxy)) + facet_wrap(~ p) + geom_histogram(bins=50)
![](data:image/png;base64,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)
Main Results
The three types of accuracies of the various estimators of forecast accuracy are summarized with multi-way dot charts. A trio of charts is produced first for the null models then for the non-null models.
Load(valSimresult)
dop <- function(sb) {
R <- subset(valSimresult, sbeta == sb)
statnames <- names(R)[7:12]
w <- reshape(R, direction='long', varying=list(statnames),
v.names='x', timevar='stat', times=statnames)
w$p <- paste('p', w$p, sep='=')
s <- with(w, summarize(x^2, llist(p, method, stat), smean.cl.boot,
stat.name='mse'))
P <- vector('list', 3)
P[[1]] <-
ggplot(s, aes(x=sqrt(mse), y=method)) + geom_point() +
facet_grid(stat ~ p) +
geom_errorbarh(aes(xmin=sqrt(Lower), xmax=sqrt(Upper), y=method), height=0) +
xlab(expression(sqrt(MSE)))
s <- with(w, summarize(abs(x), llist(p, method, stat), smean.cl.boot,
stat.name='mae'))
P[[2]] <-
ggplot(s, aes(x=mae, y=method)) + geom_point() +
facet_grid(stat ~ p) +
geom_errorbarh(aes(xmin=Lower, xmax=Upper, y=method), height=0) +
xlab('Mean |error|')
s <- with(w, summarize(abs(x), llist(p, method, stat), median,
stat.name='medae'))
P[[3]] <-
ggplot(s, aes(x=medae, y=method)) + geom_point() +
facet_grid(stat ~ p) +
xlab('Median |error|')
mdchunk(robj=P, h=8, w=8,
cnames=paste0(c('rmse', 'mae', 'medae'), sb))
}
Event Proportions Studied
for(sbeta in 1 : 2) {
for(p in P) {
Beta <- if(sbeta == 1) rep(0, p) else seq(-1, 1, length=p) * 30 / p
X <- matrix(runif(npop*p), nrow=npop) - 0.5
LX <- matxv(X, Beta)
Y <- ifelse(runif(npop) <= plogis(LX), 1, 0)
cat('sbeta=', sbeta, ' p=', p, ' Event probability=', round(mean(Y), 3),
'\n', sep='')
}
}
sbeta=1 p=15 Event probability=0.498
sbeta=1 p=30 Event probability=0.505
sbeta=1 p=60 Event probability=0.501
sbeta=1 p=90 Event probability=0.501
sbeta=2 p=15 Event probability=0.501
sbeta=2 p=30 Event probability=0.499
sbeta=2 p=60 Event probability=0.504
sbeta=2 p=90 Event probability=0.504
Conclusions
Some general conclusions from this limited simulation experiment when p=15 or 30 are as follows.
- 40 bootstrap samples was almost as good as 200.
- The ordinary bootstrap is better than the 0.632 bootstraps (except for slope when p=15)
- Ordinary bootstrap is better than or equal to all cross-validation strategies tried
- 10-fold cross-validation repeated 4 times was better then 4-fold cv repeated 10 times except for estimating calibration slope
- 10-fold x 20 times was better than 4-fold x 50 except for slope
- 10 fold x 20 is not much better than 10 fold x 4
- 4-fold x 50 is not much better than 4-fold x 10
- Except for slope, 10-fold is better than 4-fold cv
- Apparently, to estimate the calibration slope (shrinkage factor) larger validation (hold-out) samples are needed.
- The relative comparison of validation methods depends in general on which index you are validating
- Calibration slope estimates appear to be volatile and require more simulations to precisely estimate performance of the various resampling estimators.
For the cases with larger number of predictors, i.e., p=60 or 90, the bootstrap has higher expected absolute errors than cross-validation with regard to some of the indexes, in particular \(D_{xy}\).