sreg_pips {sregsurvey}

Semiparametric Model-Assisted Estimation under a Proportional to Size Sampling Design

Description

sreg_pips is used to estimate the total parameter of a finite population generated from a semi-parametric generalized gamma population under a proportional to size without-replacement sampling design.

Usage

sreg_pips(location_formula, scale_formula, data, x, n, ...)

Arguments

location_formula

a symbolic description of the systematic component of the location model to be fitted.

scale_formula

a symbolic description of the systematic component of the scale model to be fitted.

data

a data frame, list containing the variables in the model.

x

vector, an auxiliary variable to calculate the inclusion probabilities of each unit.

n

numeric, sample size.

...

further parameters accepted by caret and survey functions.

Value

sampling_design is the name of the sampling design used in the estimation process.

N is the population size.

n is the sample size used in the estimation process.

first_order_probabilities vector of the first order probabilities used in the estimation process.

sample is the random sample used in the estimation process.

estimated_total_y_sreg is the SREG estimate of the total parameter of the finite population.

Author(s)

Carlos Alberto Cardozo Delgado <[e-mail]>

References

Cardozo C.A, Alonso C. (2021) Semi-parametric model assisted estimation in finite populations. In preparation.

Cardozo C.A., Paula G., and Vanegas L. (2022). Generalized log-gamma additive partial linear models with P-spline smoothing. Statistical Papers.

Sarndal C.E., Swensson B., and Wretman J. (2003). Model Assisted Survey Sampling. Springer-Verlag.

Examples

library(sregsurvey)
library(survey)
library(dplyr)
library(gamlss)
data(api)
attach(apipop)
Apipop <- filter(apipop,full!= 'NA')
Apipop <- filter(Apipop, stype == 'H')
Apipop <- Apipop %>% dplyr::select(api00,grad.sch,full,api99)
n=ceiling(0.2*dim(Apipop)[1])
aux_var <- Apipop %>% dplyr::select(api99)
fit <- sreg_pips(api00 ~  pb(grad.sch), scale_formula = ~ full - 1, data= Apipop, x= aux_var, n=n)
fit
# The total population value is
true_total <- sum(Apipop$api00)
# The estimated relative bias in percentage is
round(abs((fit$estimated_total_y_sreg - true_total)/true_total),3)*100