The regression estimator
Computes the regression estimator of the population total, using the design-based approach. The underling regression model is a model without intercept.
regest(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights)))
formula |
the 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 |
the matrix of joint inclusion probabilities for the sample. |
n |
the sample size. |
sigma |
vector of positive values accounting for heteroscedasticity. |
The function returns a list containing the following components:
regest |
the value of the regression estimator. |
coefficients |
a vector of beta coefficients. |
std_error |
the standard error of coefficients. |
t_value |
the t-values associated to the coefficients. |
p_value |
the p-values associated to the coefficients. |
cov_mat |
the covariance matrix of the coefficients. |
weights |
the specified weights. |
y |
the response variable. |
x |
the model matrix. |
# uses the MU284 population to draw a systematic sample data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85; sample size 40 pik=inclusionprobabilities(P85,40) # the joint inclusion probabilities for systematic sampling pikl=UPsystematicpi2(pik) # draws a systematic sample of size 40 s=UPsystematic(pik) # defines the variable of interest y=RMT85[s==1] # defines the auxiliary information x1=CS82[s==1] x2=SS82[s==1] # the joint inclusion probabilities for s pikls=pikl[s==1,s==1] # the first-order inclusion probabilities for s piks=pik[s==1] # computes the regression estimator with the model y~x1+x2-1 r=regest(formula=y~x1+x2-1,Tx=c(sum(CS82),sum(SS82)),weights=1/piks,pikl=pikls,n=40) # the regression estimator is r$regest # the beta coefficients are r$coefficients # regression estimator is the same as the calibration estimator 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)
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