Package 'NSAE' reference manual

Title:	Nonstationary Small Area Estimation
Description:	Executes nonstationary Fay-Herriot model and nonstationary generalized linear mixed model for small area estimation.The empirical best linear unbiased predictor (EBLUP) under stationary and nonstationary Fay-Herriot models and empirical best predictor (EBP) under nonstationary generalized linear mixed model along with the mean squared error estimation are included. EBLUP for prediction of non-sample area is also included under both stationary and nonstationary Fay-Herriot models. This extension to the Fay-Herriot model that accounts for the presence of spatial nonstationarity was developed by Hukum Chandra, Nicola Salvati and Ray Chambers (2015) <doi:10.1093/jssam/smu026> and nonstationary generalized linear mixed model was developed by Hukum Chandra, Nicola Salvati and Ray Chambers (2017) <doi:10.1016/j.spasta.2017.01.004>. This package is dedicated to the memory of Dr. Hukum Chandra who passed away while the package creation was in progress.
Authors:	Hukum Chandra [aut], Nicola Salvati [aut], Ray Chambers [aut], Saurav Guha [aut, cre]
Maintainer:	Saurav Guha <[email protected]>
License:	GPL-3
Version:	0.4.0
Built:	2024-11-20 06:33:05 UTC
Source:	CRAN

EBLUP under stationary Fay-Herriot model for sample area

Description

This function gives the EBLUP and the estimate of mean squared error (mse) based on a stationary Fay-Herriot model for sample area.

Usage

eblupFH1(formula, vardir, method = "REML", MAXITER, PRECISION, data)
eblupFH1(formula, vardir, method = "REML", MAXITER, PRECISION, data)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`method`	type of fitting method, default is "REML" method
`MAXITER`	number of iterations allowed in the algorithm. Default is 100 iterations
`PRECISION`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

eblup: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, eblup, mse, standard error (SE) and coefficient of variation (CV)
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
goodness : goodness of fit statistics
randomeffect : a data frame with the values of the random effect estimators

Examples

# Load data set
data(paddysample)
# Fit Fay-Herriot model using sample part of paddy data
result <- eblupFH1(y ~ x1+x2, var, "REML", 100, 1e-04,paddysample)
result
# Load data set
data(paddysample)
# Fit Fay-Herriot model using sample part of paddy data
result <- eblupFH1(y ~ x1+x2, var, "REML", 100, 1e-04,paddysample)
result

EBLUP under stationary Fay-Herriot model for sample and non-sample area

Description

This function gives the EBLUP and the estimate of mean squared error (mse) based on a stationary Fay-Herriot model for both sample and non-sample area.

Usage

eblupFH2(formula, vardir, indicator, method = "REML", MAXITER, PRECISION, data)
eblupFH2(formula, vardir, indicator, method = "REML", MAXITER, PRECISION, data)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`indicator`	a vector indicating the sample and non-sample area
`method`	type of fitting method, default is "REML" methods
`MAXITER`	number of iterations allowed in the algorithm. Default is 100 iterations
`PRECISION`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

eblup: a vector with the values of the estimators for each sample area
eblup.out: a vector with the values of the estimators for each non-sample area
mse: a vector of the mean squared error estimates for each sample area
mse.out: a vector of the mean squared error estimates for each non-sample area
sample: a matrix consist of area code, eblup, mse, SE and CV for sample area
nonsample: a matrix consist of area code, eblup, mse, SE and CV for non-sample area
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta),their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
goodness : goodness of fit statistics
randomeffect : a data frame with the values of the random effect estimators

Examples

# Load data set
data(paddy)
# Fit Fay-Herriot model using sample and non-sample part of paddy data
result <- eblupFH2(y ~ x1+x2, var, indicator ,"REML", 100, 1e-04,paddy)
result
# Load data set
data(paddy)
# Fit Fay-Herriot model using sample and non-sample part of paddy data
result <- eblupFH2(y ~ x1+x2, var, indicator ,"REML", 100, 1e-04,paddy)
result

EBLUP under nonstationary Fay-Herriot model for sample area

Description

This function gives the EBLUP and the estimate of mean squared error (mse) based on a nonstationary Fay-Herriot model for sample area.

Usage

eblupNSFH1(
  formula,
  vardir,
  lat,
  long,
  method = "REML",
  MAXITER,
  PRECISION,
  data
)
eblupNSFH1(
  formula,
  vardir,
  lat,
  long,
  method = "REML",
  MAXITER,
  PRECISION,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`lat`	a vector of latitude for each small area
`long`	a vector of longitude for each small area
`method`	type of fitting method, default is "REML" methods
`MAXITER`	number of iterations allowed in the algorithm. Default is 100 iterations
`PRECISION`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula, vardir, lat and long

Value

The function returns a list with the following objects:

eblup: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, eblup, mse, SE and CV
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta),their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
spatialcorr : spatial correlation parameter
randomeffect : a data frame with the values of the random effect estimators
goodness : goodness of fit statistics

Examples

# Load data set
data(paddysample)
# Fit nonstationary Fay-Herriot model using sample part of paddy data
result <- eblupNSFH1(y ~ x1+x2, var, latitude, longitude, "REML", 100, 1e-04,paddysample)
result
# Load data set
data(paddysample)
# Fit nonstationary Fay-Herriot model using sample part of paddy data
result <- eblupNSFH1(y ~ x1+x2, var, latitude, longitude, "REML", 100, 1e-04,paddysample)
result

EBLUP under nonstationary Fay-Herriot model for sample and non-sample area

Description

This function gives the EBLUP and the estimate of mean squared error (mse) based on a nonstationary Fay-Herriot model for both sample and non-sample area.

Usage

eblupNSFH2(
  formula,
  vardir,
  lat,
  long,
  indicator,
  method = "REML",
  MAXITER,
  PRECISION,
  data
)
eblupNSFH2(
  formula,
  vardir,
  lat,
  long,
  indicator,
  method = "REML",
  MAXITER,
  PRECISION,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`lat`	a vector of latitude for each small area
`long`	a vector of longitude for each small area
`indicator`	a vector indicating the sample and non-sample area
`method`	type of fitting method, default is "REML" methods
`MAXITER`	number of iterations allowed in the algorithm. Default is 100 iterations
`PRECISION`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula, vardir, lat and long

Value

The function returns a list with the following objects:

eblup: a vector with the values of the estimators for each sample area
eblup.out: a vector with the values of the estimators for each non-sample area
mse: a vector of the mean squared error estimates for each sample area
mse.out: a vector of the mean squared error estimates for each non-sample area
sample: a matrix consist of area code, eblup, mse, SE and CV for sample area
nonsample: a matrix consist of area code, eblup, mse, SE and CV for non-sample area
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta),their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
spatialcorr : estimated spatial correlation parameter
randomeffect : a data frame with the values of the random effect estimators
goodness : goodness of fit statistics

Examples

# Load data set
data(paddy)
# Fit nonstationary Fay-Herriot model using sample and non-sample part of paddy data
result <- eblupNSFH2(y ~ x1+x2, var, latitude, longitude, indicator , "REML", 100, 1e-04,paddy)
result
# Load data set
data(paddy)
# Fit nonstationary Fay-Herriot model using sample and non-sample part of paddy data
result <- eblupNSFH2(y ~ x1+x2, var, latitude, longitude, indicator , "REML", 100, 1e-04,paddy)
result

EBP for proportion under generalized linear mixed model

Description

This function gives the ebp and the estimate of mean squared error (mse) for proportion based on a generalized linear mixed model.

Usage

ebp(
  formula,
  vardir,
  Ni,
  ni,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)
ebp(
  formula,
  vardir,
  Ni,
  ni,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`Ni`	a vector of population size for each small area
`ni`	a vector of sample size for each small area
`method`	type of fitting method, default is "REML" method
`maxit`	number of iterations allowed in the algorithm. Default is 100 iterations
`precision`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

ebp: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, ebp, mse, standard error (SE) and coefficient of variation (CV)
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
randomeffect : a data frame with the values of the random effect estimators
loglike : value of the loglikelihood
deviance : value of the deviance
loglike1 : value of the restricted loglikelihood

Examples

# Load data set
data(headcount)
# Fit generalized linear mixed model using HCR data
result <- ebp(y~x1, var, N, n,"REML",100,1e-04, headcount)
result
# Load data set
data(headcount)
# Fit generalized linear mixed model using HCR data
result <- ebp(y~x1, var, N, n,"REML",100,1e-04, headcount)
result

Nonparametric ebp using spatial spline for proportion under generalized linear mixed model

Description

This function gives the nonparametric ebp and the estimate of mean squared error (mse) for proportion based on a nonstationary generalized linear mixed model.

Usage

ebpNP(
  formula,
  vardir,
  n.knot,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)
ebpNP(
  formula,
  vardir,
  n.knot,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`n.knot`	number of knot in spatial splines. Default is 25 knot
`Ni`	a vector of population size for each small area
`ni`	a vector of sample size for each small area
`lat`	a vector of latitude for each small area
`lon`	a vector of longitude for each small area
`method`	type of fitting method, default is "REML" method
`maxit`	number of iterations allowed in the algorithm. Default is 100 iterations
`precision`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

ebp: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, ebp, mse, standard error (SE) and coefficient of variation (CV)
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
lambda : estimated spatial intensity paprameter
randomeffect : a data frame with the values of the area specific random effect
gamma : a data frame with the values of the spatially correlated random effect
variance : a covariance matrix of estimated variance components

Examples

# Load data set
data(headcount)
# Fit a nonparametric generalized linear mixed model using headcount data
result <- ebpNP(y~x1, var,25, N, n,  lat, long, "REML", 100, 1e-04,headcount)
result
# Load data set
data(headcount)
# Fit a nonparametric generalized linear mixed model using headcount data
result <- ebpNP(y~x1, var,25, N, n,  lat, long, "REML", 100, 1e-04,headcount)
result

Nonstationary ebp for proportion under generalized linear mixed model

Description

This function gives the nonstationary ebp and the estimate of mean squared error (mse) for proportion based on a generalized linear mixed model.

Usage

ebpNS(
  formula,
  vardir,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)
ebpNS(
  formula,
  vardir,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`Ni`	a vector of population size for each small area
`ni`	a vector of sample size for each small area
`lat`	a vector of latitude for each small area
`lon`	a vector of longitude for each small area
`method`	type of fitting method, default is "REML" method
`maxit`	number of iterations allowed in the algorithm. Default is 100 iterations
`precision`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

ebp: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, ebp, mse, standard error (SE) and coefficient of variation (CV)
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
lambda : estimated spatial intensity parameter
randomeffect : a data frame with the values of the area specific random effect
gamma : a data frame with the values of the spatially correlated random effect
variance : a covariance matrix of estimated variance components
loglike : value of the loglikelihood
deviance : value of the deviance
loglike1 : value of the restricted loglikelihood

Examples

# Load data set
data(headcount)
# Fit a nonstationary generalized linear mixed model using headcount data
result <- ebpNS(y~x1, var, N, n, lat, long, "REML", 100, 1e-04, headcount)
result
# Load data set
data(headcount)
# Fit a nonstationary generalized linear mixed model using headcount data
result <- ebpNS(y~x1, var, N, n, lat, long, "REML", 100, 1e-04, headcount)
result

Spatial ebp for proportion under generalized linear mixed model

Description

This function gives the spatial ebp and the estimate of mean squared error (mse) for proportion based on a generalized linear mixed model.

Usage

ebpSP(
  formula,
  vardir,
  Ni,
  ni,
  proxmat,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)
ebpSP(
  formula,
  vardir,
  Ni,
  ni,
  proxmat,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`Ni`	a vector of population size for each small area
`ni`	a vector of sample size for each small area
`proxmat`	a D*D proximity matrix of D small areas. The matrix must be row-standardized.
`method`	type of fitting method, default is "REML" method
`maxit`	number of iterations allowed in the algorithm. Default is 100 iterations
`precision`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with the following objects:

ebp: a vector with the values of the estimators for each small area
mse: a vector of the mean squared error estimates for each small area
sample: a matrix consist of area code, ebp, mse, standard error (SE) and coefficient of variation (CV)
fit: a list containing the following objects:

estcoef : a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue)
refvar : estimated random effects variance
rho : estimated spatial correlation
randomeffect : a data frame with the values of the area specific random effect
variance : a covariance matrix of estimated variance components
loglike : value of the loglikelihood
deviance : value of the deviance

Examples

# Load data set
data(headcount)
# Fit a generalized linear mixed model with SAR spcification using headcount data
result <- ebpSP(ps~x1, var, N, n, Wmatrix, "REML", 100, 1e-04, headcount)
result
# Load data set
data(headcount)
# Fit a generalized linear mixed model with SAR spcification using headcount data
result <- ebpSP(ps~x1, var, N, n, Wmatrix, "REML", 100, 1e-04, headcount)
result

Head count data

Description

Dataset on head count used by Chandra et al. (2017).

Usage

data(headcount)
data(headcount)

Format

A data frame with 71 observations on the following 11 variables:

Area: Small area code
lat: Latitude of each small areas
long: Longitude of each small areas
N: Sample size of each small areas
n: Sample size of each small areas
y: Head count (direct estimates for the small areas)
ps: proportion of head count
var: Estimated variance
x1: First covariate used by Chandra et al. (2017)
x2: Second covariate used by Chandra et al. (2017)
x3: Second covariate used by Chandra et al. (2017)

Reference

Chandra, H., Salvati, N., & Chambers, R. (2017). Small area prediction of counts under a non-stationary spatial model. Spatial Statistics. 20. 30-56. DOI:10.1016/j.spasta.2017.01.004.

Examples

data(headcount)
y <- headcount$y
summary(y)
data(headcount)
y <- headcount$y
summary(y)

Parametric bootstrap-based spatial nonstationarity test for Fay-Herroit model

Description

This function performs a parametric bootstrap-based test procudure for testing spatial nonstationarity in the data.

Usage

NS.test(formula, vardir, lat, long, iter = 100, data)
NS.test(formula, vardir, lat, long, iter = 100, data)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`lat`	a vector of latitude for each small area
`long`	a vector of longitude for each small area
`iter`	number of iterations allowed in the algorithm. Default is 100 iterations
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with class "htest" containing the following components:

method: a character string indicating what type of test was performed.
p.value: the p-value for the test.
data.name: a character string giving the name of the data.

Examples

# Load data set
data(paddysample)
# Testing spatial nonstationarity of the data
result <- NS.test(y ~ x1+x2, var, latitude, longitude, iter=50, data = paddysample[1:10,])
result
# Load data set
data(paddysample)
# Testing spatial nonstationarity of the data
result <- NS.test(y ~ x1+x2, var, latitude, longitude, iter=50, data = paddysample[1:10,])
result

NSAE : Nonstationary Small Area Estimation

Description

Executes nonstationary Fay-Herriot model and nonstationary generalized linear mixed model for small area estimation. It produces empirical best linear unbiased predictor (EBLUP) and empirical best predictor (EBP) under stationary and nonstationary Fay-Herriot models. Functions give EBLUP and EBP estimators along with their mean squared error (MSE) estimator for each model. The nonstationary Fay-Herriot model was developed by Hukum Chandra, Nicola Salvati and Ray Chambers (2015) <doi:10.1093/jssam/smu026> and the nonstationary generalized linear mixed model was developed by Hukum Chandra, Nicola Salvati and Ray Chambers (2017) <doi:10.1016/j.spasta.2017.01.004>.

Author(s)

Hukum Chandra, Nicola Salvati, Ray Chambers, Saurav Guha

Maintainer: Saurav Guha [email protected]

Functions

eblupFH1: Provides the EBLUPs and MSE under stationary Fay-Herriot model for sample area
eblupFH2: Provides the EBLUPs and MSE under stationary Fay-Herriot model for sample and non-sample area
eblupNSFH1: Provides the EBLUPs and MSE under nonstationary Fay-Herriot model for sample area
eblupNSFH2: Provides the EBLUPs and MSE under nonstationary Fay-Herriot model for sample and non-sample area
NS.test: Provides a p-value for testing spatial nonstationarity in the data under Fay-Herriot model.
ebp: Provides the EBPs and MSE under stationary generalized linear mixed model.
ebpNS: Provides the EBPs and MSE under nonstationary generalized linear mixed model.
ebpSP: Provides the EBPs and MSE under a spatially correlated generalized linear mixed model.
ebpNP: Provides the EBPs and MSE under nonparametric generalized linear mixed model.
NSglm.test: Provides a p-value for testing spatial nonstationarity in the data under generalized linear mixed model.

Reference

Chandra, H., Salvati, N., & Chambers, R. (2015). A spatially nonstationary fay-herriot model for small area estimation. Journal of survey statistics and methodology. 3. 109-135. DOI:10.1093/jssam/smu026.
Chandra, H., Salvati, N., & Chambers, R. (2017). Small area prediction of counts under a non-stationary spatial model. Spatial Statistics. 20. 30-56. DOI:10.1016/j.spasta.2017.01.004.
Chandra, H., Salvati, N., & Chambers, R. (2018). Small area estimation under a spatially non-linear model. Computational Statistics and Data Analysis. 126. 19-38. DOI:10.1016/j.csda.2018.04.002.
Fay, R. E. & Herriot, R. A. (1979). Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data. Journal of the American Statistical Association. 74. 269-277. DOI:10.2307/2286322.
Rao, J.N.K & Molina. (2015). Small Area Estimation 2nd Edition. New York: John Wiley and Sons, Inc.

Parametric bootstrap-based spatial nonstationarity test for generalized linear mixed model

Description

This function performs a parametric bootstrap-based test procudure for testing spatial nonstationarity in the data.

Usage

NSglm.test(
  formula,
  vardir,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)
NSglm.test(
  formula,
  vardir,
  Ni,
  ni,
  lat,
  lon,
  method = "REML",
  maxit = 100,
  precision = 1e-04,
  data
)

Arguments

`formula`	an object of class list of formula, describe the model to be fitted
`vardir`	a vector of sampling variances of direct estimators for each small area
`Ni`	a vector of population size for each small area
`ni`	a vector of sample size for each small area
`lat`	a vector of latitude for each small area
`lon`	a vector of longitude for each small area
`method`	type of fitting method, default is "REML" method
`maxit`	number of iterations allowed in the algorithm. Default is 100 iterations
`precision`	convergence tolerance limit for the Fisher-scoring algorithm. Default value is 1e-04
`data`	a data frame comprising the variables named in formula and vardir

Value

The function returns a list with class "htest" containing the following components:

method: a character string indicating what type of test was performed.
p.value: the p-value for the test.
data.name: a character string giving the name of the data.

Examples

# Load data set
data(headcount)
# Testing spatial nonstationarity of the data
result <- NSglm.test(y~x1, var, N,n,lat,long, "REML", 10, 1e-04, headcount[1:10,])
result
# Load data set
data(headcount)
# Testing spatial nonstationarity of the data
result <- NSglm.test(y~x1, var, N,n,lat,long, "REML", 10, 1e-04, headcount[1:10,])
result

Yield data of paddy

Description

Dataset on paddy yield used by Chandra et al. (2016).

Usage

data(paddy)
data(paddy)

Format

A data frame with 70 observations on the following 9 variables:

D: Small area code
latitude: Latitude of each small areas
longitude: Longitude of each small areas
n: Sample size of each small areas
y: Average yield data of paddy crop for the year 2009-10 (direct estimates for the small areas)
var: Estimated variance of y
x1: First covariate (average household size) used by Chandra et al. (2016)
x2: Second covariate (female population of marginal household) used by Chandra et al. (2016)
indicator: Index for sample and non-sample area

Reference

Chandra, H., salvati, N., chambers, R. and Sud, U. C. (2016). A Spatially Nonstationary Fay-Herriot Model for Small Area Estimation - An Application to Crop Yield Estimation. Seventh International Conference on Agricultural Statistics. Rome. DOI:10.1481/icasVII.2016.f35.

Examples

data(paddy)
yield <- paddy$y
summary(yield)
data(paddy)
yield <- paddy$y
summary(yield)

Yield data of paddy for sample area

Description

Dataset on paddy yield for sample area used by Chandra et al. (2016).

Usage

data(paddysample)
data(paddysample)

Format

A data frame with 58 observations on the following 8 variables:

D: Small area code
latitude: Latitude of each small areas
longitude: Longitude of each small areas
n: Sample size of each small areas
y: Average yield data of paddy crop for the year 2009-10 (direct estimates for the small areas)
var: Estimated variance of y
x1: First covariate (average household size) used by Chandra et al. (2016)
x2: Second covariate (female population of marginal household) used by Chandra et al. (2016)

Reference

Examples

data(paddysample)
yield <- paddysample$y
summary(yield)
data(paddysample)
yield <- paddysample$y
summary(yield)

Proximity matrix

Description

Proximity matrix for the areas included in data set of Chandra et al. (2017)

Usage

data(Wmatrix)
data(Wmatrix)

Format

A 71*71 proximity matrix of the areas. It must be in row-standerdized form

Reference

Chandra, H., Salvati, N., & Chambers, R. (2017). Small area prediction of counts under a non-stationary spatial model. Spatial Statistics. 20. 30-56. DOI:10.1016/j.spasta.2017.01.004.

Examples

data(Wmatrix)
data(Wmatrix)

Package 'NSAE'

Help Index

EBLUP under stationary Fay-Herriot model for sample area

Description

Usage

Arguments

Value

Examples

EBLUP under stationary Fay-Herriot model for sample and non-sample area

Description

Usage

Arguments

Value

Examples

EBLUP under nonstationary Fay-Herriot model for sample area

Description

Usage

Arguments

Value

Examples

EBLUP under nonstationary Fay-Herriot model for sample and non-sample area

Description

Usage

Arguments

Value

Examples

EBP for proportion under generalized linear mixed model

Description

Usage

Arguments

Value

Examples

Nonparametric ebp using spatial spline for proportion under generalized linear mixed model

Description

Usage

Arguments

Value

Examples

Nonstationary ebp for proportion under generalized linear mixed model

Description

Usage

Arguments

Value

Examples

Spatial ebp for proportion under generalized linear mixed model

Description

Usage

Arguments

Value

Examples

Head count data

Description

Usage

Format

Reference

Examples

Parametric bootstrap-based spatial nonstationarity test for Fay-Herroit model

Description

Usage

Arguments

Value

Examples

NSAE : Nonstationary Small Area Estimation

Description

Author(s)

Functions

Reference

Parametric bootstrap-based spatial nonstationarity test for generalized linear mixed model

Description

Usage

Arguments

Value

Examples

Yield data of paddy

Description

Usage

Format

Reference

Examples

Yield data of paddy for sample area