Type: | Package |
Title: | Bayes Linear Estimators for Finite Population |
Version: | 1.1.0 |
Date: | 2021-04-24 |
Maintainer: | Pedro Soares Figueiredo <pedrosfig@hotmail.com> |
Description: | Allows the user to apply the Bayes Linear approach to finite population with the Simple Random Sampling - BLE_SRS() - and the Stratified Simple Random Sampling design - BLE_SSRS() - (both without replacement), to the Ratio estimator (using auxiliary information) - BLE_Ratio() - and to categorical data - BLE_Categorical(). The Bayes linear estimation approach is applied to a general linear regression model for finite population prediction in BLE_Reg() and it is also possible to achieve the design based estimators using vague prior distributions. Based on Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014) https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886. |
URL: | https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886, https://github.com/pedrosfig/BayesSampling |
License: | GPL-3 |
Encoding: | UTF-8 |
LazyData: | true |
RoxygenNote: | 7.1.1 |
Depends: | R (≥ 3.5) |
Imports: | MASS, Matrix, stats, matrixcalc |
Suggests: | knitr, rmarkdown, TeachingSampling |
VignetteBuilder: | knitr |
Language: | en-US |
NeedsCompilation: | no |
Packaged: | 2021-05-01 18:31:42 UTC; pedro |
Author: | Pedro Soares Figueiredo
|
Repository: | CRAN |
Date/Publication: | 2021-05-01 19:00:02 UTC |
Bayes Linear Method for Categorical Data
Description
Creates the Bayes Linear Estimator for Categorical Data
Usage
BLE_Categorical(ys, n, N, m = NULL, rho = NULL)
Arguments
ys |
k-vector of sample proportion for each category. |
n |
sample size. |
N |
total size of the population. |
m |
k-vector with the prior proportion of each strata. If |
rho |
matrix with the prior correlation coefficients between two different units within categories. It must be a symmetric square matrix of dimension k (or k-1). If |
Value
A list containing the following components:
-
est.prop
- BLE for the sample proportion of each category -
Vest.prop
- Variance associated with the above -
Vs.Matrix
- Vs matrix, as defined by the BLE method (should be a positive-definite matrix) -
R.Matrix
- R matrix, as defined by the BLE method (should be a positive-definite matrix)
Source
https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886
References
Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.
Examples
# 2 categories
ys <- c(0.2614, 0.7386)
n <- 153
N <- 15288
m <- c(0.7, 0.3)
rho <- matrix(0.1, 1)
Estimator <- BLE_Categorical(ys,n,N,m,rho)
Estimator
ys <- c(0.2614, 0.7386)
n <- 153
N <- 15288
m <- c(0.7, 0.3)
rho <- matrix(0.5, 1)
Estimator <- BLE_Categorical(ys,n,N,m,rho)
Estimator
# 3 categories
ys <- c(0.2, 0.5, 0.3)
n <- 100
N <- 10000
m <- c(0.4, 0.1, 0.5)
mat <- c(0.4, 0.1, 0.1, 0.1, 0.2, 0.1, 0.1, 0.1, 0.6)
rho <- matrix(mat, 3, 3)
Ratio BLE
Description
Creates the Bayes Linear Estimator for the Ratio "estimator"
Usage
BLE_Ratio(ys, xs, x_nots, m = NULL, v = NULL, sigma = NULL, n = NULL)
Arguments
ys |
vector of sample observations or sample mean ( |
xs |
vector with values for the auxiliary variable of the elements in the sample or sample mean. |
x_nots |
vector with values for the auxiliary variable of the elements not in the sample. |
m |
prior mean for the ratio between Y and X. If |
v |
prior variance of the ratio between Y and X (bigger than |
sigma |
prior estimate of variability (standard deviation) of the ratio within the population. If |
n |
sample size. Necessary only if |
Value
A list containing the following components:
-
est.beta
- BLE of Beta -
Vest.beta
- Variance associated with the above -
est.mean
- BLE for each individual not in the sample -
Vest.mean
- Covariance matrix associated with the above -
est.tot
- BLE for the total -
Vest.tot
- Variance associated with the above
Source
https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886
References
Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.
Examples
ys <- c(10,8,6)
xs <- c(5,4,3.1)
x_nots <- c(1,20,13,15,-5)
m <- 2.5
v <- 10
sigma <- 2
Estimator <- BLE_Ratio(ys, xs, x_nots, m, v, sigma)
Estimator
# Same example but informing sample means and sample size instead of sample observations
ys <- mean(c(10,8,6))
xs <- mean(c(5,4,3.1))
n <- 3
x_nots <- c(1,20,13,15,-5)
m <- 2.5
v <- 10
sigma <- 2
Estimator <- BLE_Ratio(ys, xs, x_nots, m, v, sigma, n)
Estimator
General BLE case
Description
Calculates the Bayes Linear Estimator for Regression models (general case)
Usage
BLE_Reg(ys, xs, a, R, Vs, x_nots, V_nots)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
a |
vector of means from Beta |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
x_nots |
values of X for the individuals not in the sample |
V_nots |
covariance matrix of the individuals not in the sample |
Value
A list containing the following components:
-
est.beta
- BLE of Beta -
Vest.beta
- Variance associated with the above -
est.mean
- BLE of each individual not in the sample -
Vest.mean
- Covariance matrix associated with the above -
est.tot
- BLE for the total -
Vest.tot
- Variance associated with the above
Source
https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886
References
Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.
Examples
xs <- matrix(c(1,1,1,1,2,3,5,0),nrow=4,ncol=2)
ys <- c(12,17,28,2)
x_nots <- matrix(c(1,1,1,0,1,4),nrow=3,ncol=2)
a <- c(1.5,6)
R <- matrix(c(10,2,2,10),nrow=2,ncol=2)
Vs <- diag(c(1,1,1,1))
V_nots <- diag(c(1,1,1))
Estimator <- BLE_Reg(ys, xs, a, R, Vs, x_nots, V_nots)
Estimator
Simple Random Sample BLE
Description
Creates the Bayes Linear Estimator for the Simple Random Sampling design (without replacement)
Usage
BLE_SRS(ys, N, m = NULL, v = NULL, sigma = NULL, n = NULL)
Arguments
ys |
vector of sample observations or sample mean ( |
N |
total size of the population. |
m |
prior mean. If |
v |
prior variance of an element from the population (bigger than |
sigma |
prior estimate of variability (standard deviation) within the population. If |
n |
sample size. Necessary only if |
Value
A list containing the following components:
-
est.beta
- BLE of Beta (BLE for every individual) -
Vest.beta
- Variance associated with the above -
est.mean
- BLE for each individual not in the sample -
Vest.mean
- Covariance matrix associated with the above -
est.tot
- BLE for the total -
Vest.tot
- Variance associated with the above
Source
https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886
References
Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.
Examples
ys <- c(5,6,8)
N <- 5
m <- 6
v <- 5
sigma <- 1
Estimator <- BLE_SRS(ys, N, m, v, sigma)
Estimator
# Same example but informing sample mean and sample size instead of sample observations
ys <- mean(c(5,6,8))
N <- 5
n <- 3
m <- 6
v <- 5
sigma <- 1
Estimator <- BLE_SRS(ys, N, m, v, sigma, n)
Estimator
Stratified Simple Random Sample BLE
Description
Creates the Bayes Linear Estimator for the Stratified Simple Random Sampling design (without replacement)
Usage
BLE_SSRS(ys, h, N, m = NULL, v = NULL, sigma = NULL)
Arguments
ys |
vector of sample observations or sample mean for each strata ( |
h |
vector with number of observations in each strata. |
N |
vector with the total size of each strata. |
m |
vector with the prior mean of each strata. If |
v |
vector with the prior variance of an element from each strata (bigger than |
sigma |
vector with the prior estimate of variability (standard deviation) within each strata of the population. If |
Value
A list containing the following components:
-
est.beta
- BLE of Beta (BLE for the individuals in each strata) -
Vest.beta
- Variance associated with the above -
est.mean
- BLE for each individual not in the sample -
Vest.mean
- Covariance matrix associated with the above -
est.tot
- BLE for the total -
Vest.tot
- Variance associated with the above
Source
https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X201400111886
References
Gonçalves, K.C.M, Moura, F.A.S and Migon, H.S.(2014). Bayes Linear Estimation for Finite Population with emphasis on categorical data. Survey Methodology, 40, 15-28.
Examples
ys <- c(2,-1,1.5, 6,10, 8,8)
h <- c(3,2,2)
N <- c(5,5,3)
m <- c(0,9,8)
v <- c(3,8,1)
sigma <- c(1,2,0.5)
Estimator <- BLE_SSRS(ys, h, N, m, v, sigma)
Estimator
# Same example but informing sample means instead of sample observations
y1 <- mean(c(2,-1,1.5))
y2 <- mean(c(6,10))
y3 <- mean(c(8,8))
ys <- c(y1, y2, y3)
h <- c(3,2,2)
N <- c(5,5,3)
m <- c(0,9,8)
v <- c(3,8,1)
sigma <- c(1,2,0.5)
Estimator <- BLE_SSRS(ys, h, N, m, v, sigma)
Estimator
Full Person-level Population Database
Description
This data set corresponds to some socioeconomic variables from 150266 people of a city in a particular year.
Usage
data(BigCity)
Format
A data.frame with 150266 rows and 12 variables:
- HHID
The identifier of the household. It corresponds to an alphanumeric sequence (four letters and five digits).
- PersonID
The identifier of the person within the household. NOTE it is not a unique identifier of a person for the whole population. It corresponds to an alphanumeric sequence (five letters and two digits).
- Stratum
Households are located in geographic strata. There are 119 strata across the city.
- PSU
Households are clustered in cartographic segments defined as primary sampling units (PSU). There are 1664 PSU and they are nested within strata.
- Zone
Segments clustered within strata can be located within urban or rural areas along the city.
- Sex
Sex of the person.
- Income
Per capita monthly income.
- Expenditure
Per capita monthly expenditure.
- Employment
A person's employment status.
- Poverty
This variable indicates whether the person is poor or not. It depends on income.
Source
https://CRAN.R-project.org/package=TeachingSampling
References
Package ‘TeachingSampling’; see BigCity
calculates the C factor
Description
calculates the C factor
Usage
C(ys, xs, R, Vs)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
calculates the BLE for Beta
Description
calculates the BLE for Beta
Usage
E_beta(ys, xs, a, R, Vs)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
a |
vector of means from Beta |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
calculates the BLE for the individuals not in the sample
Description
calculates the BLE for the individuals not in the sample
Usage
E_theta_Reg(ys, xs, a, R, Vs, x_nots)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
a |
vector of means from Beta |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
x_nots |
values of X for the individuals not in the sample |
calculates BLE for the total T
Description
calculates BLE for the total T
Usage
T_Reg(ys, xs, a, R, Vs, x_nots)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
a |
vector of means from Beta |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
x_nots |
values of X for the individuals not in the sample |
calculates risk matrix associated with the BLE for for the total T
Description
calculates risk matrix associated with the BLE for for the total T
Usage
VT_Reg(ys, xs, a, R, Vs, x_nots, V_nots)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
a |
vector of means from Beta |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
x_nots |
values of X for the individuals not in the sample |
V_nots |
covariance matrix of the individuals not in the sample |
calculates the risk matrix associated with the BLE for Beta
Description
calculates the risk matrix associated with the BLE for Beta
Usage
V_beta(ys, xs, R, Vs)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
calculates the risk matrix associated with the BLE for the individuals not in the sample
Description
calculates the risk matrix associated with the BLE for the individuals not in the sample
Usage
V_theta_Reg(ys, xs, R, Vs, x_nots, V_nots)
Arguments
ys |
response variable of the sample |
xs |
explicative variable of the sample |
R |
covariance matrix of Beta |
Vs |
covariance of sample errors |
x_nots |
values of X for the individuals not in the sample |
V_nots |
covariance matrix of the individuals not in the sample |
creates vector of 1's to be used in the estimators
Description
creates vector of 1's to be used in the estimators
Usage
create1(y)
Arguments
y |
sample matrix |
Value
vector of 1's with size equal to the number of observations in the sample