ODS (version 0.2.0)

se.spmle: standard error for MSELE estimator

Description

se.spmle calculates the standard error for MSELE estimator in Zhou et al. 2002

Usage

se.spmle(y, x, beta, sig, pis, a, N.edf, rhos, strat, size.nc)

Arguments

y

vector of the primary response

x

the design matrix with a column of 1's for the intercept

beta

final estimates of the regression coefficients obtained from odsmle

sig

final estimate of the error variance obtained from odsmle

pis

final estimates of the stratum probabilities obtained from odsmle

a

vector of cutpoints for the primary response (e.g., a = c(-2.5,2))

N.edf

should be the size of the SRS (simple random sample)

rhos

which is size/pis, where size is a vector representing the stratum sizes of supplemental samples. e.g. size = c(100, 0, 100), and pis are the final estimates obtained from odsmle.

strat

vector that indicates the stratum numbers of supplemental samples, except that you should only list stratum with size > 0. (e.g. if the supplemental size is c(100, 0, 100), then the strat vector should be c(1,3))

size.nc

total size of the validation sample (SRS plus supplemental samples)

Value

A list which contains the standard error estimates for betas in the model : $$Y=\beta_{0}+\beta_{1}X+\epsilon,$$ where epsilon has variance sig.

Examples

# NOT RUN {
library(ODS)
# take the example data from the ODS package
# please see the documentation for details about the data set ods_data

Y <- ods_data[,1]
X <- cbind(rep(1,length(Y)), ods_data[,2:5])

# use the simple random sample to get an initial estimate of beta, sig #
# perform an ordinary least squares #
SRS <- ods_data[1:200,]
OLS.srs <- lm(SRS[,1] ~ SRS[,2:5])
OLS.srs.summary <- summary(OLS.srs)

beta <- coefficients(OLS.srs)
sig <- OLS.srs.summary$sigma^2
pis <- c(0.1,0.8,0.1)

# the cut points for this data is Y < 0.162, Y > 2.59.
a <- c(0.162,2.59)
rs.size <- 200
size <- c(100,0,100)
strat <- c(1,2,3)

# obtain the parameter estimates
ODS.model = odsmle(Y,X,beta,sig,pis,a,rs.size,size,strat)

# calculate the standard error estimate
y <- Y
x <- X
beta <- ODS.model$beta
sig <- ODS.model$sig
pis <- ODS.model$pis
a <- c(0.162,2.59)
N.edf <- rs.size
rhos <- size/pis
strat <- c(1,3)
size.nc <- length(y)

se = se.spmle(y, x, beta, sig, pis, a, N.edf, rhos, strat, size.nc)

# summarize the result
ODS.tvalue <- ODS.model$beta / se
ODS.pvalue <- 2 * pt( - abs(ODS.tvalue), sum(rs.size, size)-2)

ODS.results <- cbind(ODS.model$beta, se, ODS.tvalue, ODS.pvalue)
dimnames(ODS.results)[[2]] <- c("Beta","SEbeta","tvalue","Pr(>|t|)")
row.names(ODS.results) <- c("(Intercept)","X","Z1","Z2","Z3")

ODS.results
# }