Package 'sregsurvey'

Semiparametric Model-Assisted Estimation under a Bernoulli Sampling Design

Description

sreg_ber is used to estimate the total parameter of a finite population generated from a semi-parametric generalized gamma population under a Bernoulli sampling design.

Usage

sreg_ber(location_formula, scale_formula, data, pi, ...)

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.
pi	numeric, represents the first order probability. Default value is 0.5.
...	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 random 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 <[email protected]>

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

#This example use the data set 'apipop' of the survey package.
library(sregsurvey)
library(survey)
library(magrittr)
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)
fit <- sreg_ber(api00 ~  pb(grad.sch), scale_formula = ~ full - 1, data= Apipop, pi=0.2)
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

---

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 <[email protected]>

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

---

Semiparametric Model-Assisted Estimation under a Poisson Sampling Design

Description

sreg_poisson is used to estimate the total parameter of a finite population generated from a semi-parametric generalized gamma population under a Poisson sampling design.

Usage

sreg_poisson(location_formula, scale_formula, data, pis, ...)

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.
pis	numeric vector, first order inclusion probabilities. Default value 0.1 for each element.
...	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 random 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 <[email protected]>

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)
fit <- sreg_poisson(api00 ~  pb(grad.sch), scale_formula = ~ full - 1, data= Apipop)
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

---

Semiparametric Model-Assisted Estimation under a Simple Random Sampling Without Replace Sampling Design

Description

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

Usage

sreg_srswr(
  location_formula,
  scale_formula,
  data,
  fraction,
  format = "COMPLETE",
  ...
)

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.
fraction	numeric, represents a fraction of the size of the population. Default value is 0.2.
format	character, represents the type of summary of the methodology, 'SIMPLE' or 'COMPLETE'. Default value is 'COMPLETE'.
...	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 fixed 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 <[email protected]>

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)
fit <- sreg_srswr(api00 ~  pb(grad.sch), scale_formula = ~ full - 1, data= Apipop, fraction=0.25)
# 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

---

Semiparametric Model-Assisted Estimation under a Stratified Sampling with Simple Random Sampling Without Replace in each stratum.

Description

sreg_stsi is used to estimate the total parameter of a finite population generated from a semi-parametric generalized gamma population under a stratified sampling with simple random sampling without-replacement in each stratum.

Usage

sreg_stsi(
  location_formula,
  scale_formula,
  stratum,
  data,
  n,
  ss_sizes,
  allocation_type = "PA",
  aux_x,
  ...
)

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.
stratum	vector, represents the strata of each unit in the population
data	a data frame, list containing the variables in the model.
n	integer, represents a fixed sample size.
ss_sizes	vector, represents a vector with the sample size in each stratum.
allocation_type	character, there is two choices, proportional allocation, 'PA', and x-optimal allocation,'XOA'. By default is a 'PA', Sarndal et. al. (2003).
aux_x	vector, represents an auxiliary variable to help to calculate the sample sizes by the x-optimum allocation method, Sarndal et. al. (2003). This option is validated only when the argument allocation_type is equal to 'XOA'.
...	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.

H is the number of strata.

Ns is the population strata sizes.

allocation_type is the method used to calculate sample strata sizes.

global_n is the global 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 <[email protected]>

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(magrittr)
library(gamlss)
data(api)
attach(apipop)
Apipop <- filter(apipop,full!= 'NA')
Apipop <- Apipop %>% dplyr::select(api00,grad.sch,full,stype)
dim(Apipop)
fit <- sreg_stsi(api00~ pb(grad.sch), scale_formula =~ full-1, n=400, stratum='stype', data=Apipop)
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

---