appe.glm {APPEstimation}

C-statistics adjusted for predictor distributions

Description

Calculates adjusted C statistics by predictor distributions for a generalized linear model with binary outcome.

Usage

appe.glm(mdl, dat.train, dat.test, method = "uLSIF", sigma = NULL,
         lambda = NULL, kernel_num = NULL, fold = 5, stabilize = TRUE, 
         qstb = 0.025, reps = 2000, conf.level = 0.95)

Arguments

mdl

a glm object describing a prediction model to be evaluated.

dat.train

a dataframe used to construct a prediction model (specified in mdl), corresponding to a training data. Need to include outcome and all predictors.

dat.test

a dataframe corresponding to a validation (testing) data. Need to include outcome and all predictors.

method

uLSIF or KLIEP. Same as the argument in densratio function from densratio package.

sigma

a positive numeric vector corresponding to candidate values of a bandwidth for Gaussian kernel. Same as the argument in densratio function from densratio package.

lambda

a positive numeric vector corresponding to candidate values of a regularization parameter. Same as the argument in densratio function from densratio package.

kernel_num

a positive integer corresponding to number of kernels. Same as the argument in densratio function from densratio package.

fold

a positive integer corresponding to a number of the folds of cross-validation in the KLIEP method. Same as the argument in densratio function from densratio package.

stabilize

a logical value as to whether tail weight stabilization is performed or not. If TRUE, both tails of the estimated density ratio distribution are replaced by the constant value which is specified at qstb option.

qstb

a positive numerical value less than 1 to control the degree of weight stabilization. Default value is 0.025, indicating estimated density ratio values less than the 2.5 percentile and more than the 97.5 percentile are set to 2.5 percentile and 97.5 percentile, respectively.

reps

a positive integer to specify bootstrap repetitions. If 0, bootstrap calculations are not performed.

conf.level

a numerical value indicating a confidence level of interval.

Value

Adjusted and non-adjusted estimates of C-statistics are provided as matrix form. "Cstat" indicates non-adjusted version, "C adjusted by score" indicates adjusted version by linear predictors distribution, and "C adjusted by predictors" indicates adjusted version by predictor distributions (multi-dimensionally). For confidence intervals, "Percentile" indicates a confidence interval by percentile method and "Approx" indicates approximated versions by Normal distribution.

Examples

set.seed(100)

# generating learning data
n0  = 100
Z   = cbind(rbeta(n0, 5, 5), rbeta(n0, 5, 5))
Y   = apply(Z, 1, function (xx) {
        rbinom(1, 1, (1/(1+exp(-(sum(c(-2,2,2) * c(1,xx)))))))})
dat = data.frame(Y=Y, Za=Z[,1], Zb=Z[,2])

# the model to be evaluated
mdl = glm(Y~., binomial, data=dat)

# validation dataset, with different centers on predictors
n1   = 100
Z1   = cbind(rbeta(n1, 6, 4), rbeta(n1, 6, 4))
Y1   = apply(Z1, 1, function (xx) {
         rbinom(1, 1, (1/(1+exp(-(sum(c(-2,2,2) * c(1,xx)))))))})
dat1 = data.frame(Y=Y1, Za=Z1[,1], Zb=Z1[,2])

# calculation of L1 and L2 for this model
appe.glm(mdl, dat, dat1, reps=0)