regest {sampling}

Regression estimator

Description

Computes the regression estimator of the population total, using the design-based approach. The underling regression model is a model without intercept.

Usage

regest(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights)))

Arguments

formula

regression model formula (y~x).

Tx

population total of x, the auxiliary variable.

weights

vector of the weights; its length is equal to n, the sample size.

pikl

matrix of joint inclusion probabilities for the sample.

n

the sample size.

sigma

vector of positive values accounting for heteroscedasticity.

Value

The function returns a list with following components:

regest

value of the regression estimator.

coefficients

vector of estimated beta coefficients.

std_error

estimated standard error of the estimated coefficients.

t_value

t-values associated to the coefficients.

p_value

p-values associated to the coefficients.

cov_mat

covariance matrix of the estimated coefficients.

weights

specified weights.

y

response variable.

x

model matrix.

See Also

ratioest,regest_strata

Examples

# uses the MU284 population to draw a systematic sample
data(MU284)
# there are 3 outliers which are deleted from the population
MU281=MU284[MU284$RMT85<=3000,]
attach(MU281)
# computes the inclusion probabilities using the variable P85; sample size 40
pik=inclusionprobabilities(P85,40)
# joint inclusion probabilities for systematic sampling
pikl=UPsystematicpi2(pik)
# draws a systematic sample of size 40
s=UPsystematic(pik)
# defines the variable of interest for the selected sample
y=RMT85[s==1]
# defines the auxiliary information for the selected sample
x1=CS82[s==1]
x2=SS82[s==1]
# joint inclusion probabilities for the selected sample
pikls=pikl[s==1,s==1]
# first-order inclusion probabilities for the selected sample
piks=pik[s==1]
# computes the regression estimator with the model y~x1+x2-1 
r=regest(formula=y~x1+x2-1,Tx=c(sum(CS82),sum(SS82)),weights=1/piks,pikl=pikls,n=40)
# the regression estimator
r$regest
# the estimated beta coefficients 
r$coefficients
# the regression estimator is the same as the calibration estimator (method="linear") 
Xs=cbind(x1,x2)
total=c(sum(CS82),sum(SS82))
g1=calib(Xs,d=1/piks,total,method="linear")
checkcalibration(Xs,d=1/piks,total,g1)
calibev(y,Xs,total,pikls,d=1/piks,g1,with=TRUE,EPS=1e-6)
detach(MU281)