appe.lm {APPEstimation}

L_1 and L_2 errors adjusted for predictor distributions

Description

Calculates adjusted L_1 and L_2 errors by predictor distributions for a linear model.

Usage

appe.lm(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 lm object describing a prediction model to be evaluated.

dat.train

same as in appe.glm.

dat.test

same as in appe.glm.

method

same as in appe.glm.

sigma

same as in appe.glm.

lambda

same as in appe.glm.

kernel_num

same as in appe.glm.

fold

same as in appe.glm.

stabilize

same as in appe.glm.

qstb

same as in appe.glm.

reps

same as in appe.glm.

conf.level

same as in appe.glm.

Value

Adjusted and non-adjusted estimates of L_1 and L_2 errors are provided as matrix form. "L1" and "L2" indicate non-adjusted versions, "L1 adjusted by score" and "L2 adjusted by score" indicate adjusted versions by linear predictors distribution, "L1 adjusted by predictors" and "L2 adjusted by predictors" indicate adjusted versions 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 development data
n0  = 100
Z   = cbind(rbeta(n0, 3, 3), rbeta(n0, 3, 3))
Y   = apply(Z, 1, function(xx) { rlnorm(1, sum(c(1, 1) * xx), 0.3) })
dat = data.frame(Za=Z[,1], Zb=Z[,2], Y=Y)

# the model to be evaluated
mdl = lm(Y~ Za + Zb, data=dat)

# generating validation dataset 
n1   = 100
Z1   = cbind(rbeta(n0, 3.5, 2.5), rbeta(n0, 3.5, 2.5))
Y1   = apply(Z1, 1, function(xx) { rlnorm(1, sum(c(1, 1) * xx), 0.3) })
dat1 = data.frame(Za=Z1[,1], Zb=Z1[,2], Y=Y1)

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