vargreg | R Documentation |
Compute the (approximated) design variance of the general regression estimator of the total of a study variable under different sampling designs.
vargreg(formula, design = NULL, n, stratum = NULL,
x_des = NULL, inc.p = NULL, ...)
formula |
an object of class |
design |
a character string giving the sampling design. It must be one of 'srs' (simple random sampling without replacement), 'poi' (Poisson sampling), 'stsi' (stratified simple random sampling), 'pips' (Pareto |
n |
either a positive number indicating the (expected) sample size (when |
stratum |
a vector indicating the stratum to which every unit belongs. Only used if |
x_des |
a positive numeric vector giving the values of the auxiliary variable that is used for defining the inclusion probabilities. Only used if |
inc.p |
a matrix giving the first and second order inclusion probabilities. Only used if |
... |
other arguments passed to |
The formula
should be of the form y~x
, where y
is the study variable and x
are the auxiliary variables used by the general regression (GREG) estimator, \hat{t}
,. See formula
for more details and ‘Examples’ for typical expressions for some well-known estimators (e.g. the Horvitz-Thompson, ratio, regression and poststratification estimators).
The variance of the GREG estimator is approximated by
AV\left(\hat{t}\right) = \sum_{k=1}^{N}\sum_{l=1}^{N}\pi_{kl}\frac{E_{k}}{\pi_{k}}\frac{E_{l}}{\pi_{l}} - \left(\sum_{k=1}^{N}E_{k}\right)^{2}
where
E_{k} = y_{k}-\hat{y}_{k} \textrm{ and } \hat{y}_{k} = x_{k}B \textrm{ with } B = \left(\sum_{k=1}^{N}w_{k}x_{k}^{'}x_{k}\right)\sum_{k=1}^{N}w_{k}x_{k}^{'}y_{k}
N
is the population size and \pi_{k}
and \pi_{kl}
are, respectively, the first and second order inclusion probabilities. w_{k}
is a weight associated to each element and it represents the inverse of the conditional variance (up to a scalar) of the underlying superpopulation model (see ‘Examples’).
If design=NULL
, the matrix of inclusion probabilities is obtained proportional to the matrix p.inc
. If design
is other than NULL
, the formula for the variance is simplified in such a way that the inclusion probabilities matrix is no longer necessary. In particular:
if design='srs'
, only the sample size n
is required;
if design='stsi'
, both the stratum ID stratum
and the sample size per stratum n
, are required;
if design
is either 'pips'
or 'poi'
, the inclusion probabilities are obtained proportional to the values of x_des
, corrected if necessary.
A numeric value giving the variance of the general regression estimator under the desired design.
Sarndal, C.E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling. Springer.
Rosen, B. (1997). On Sampling with Probability Proportional to Size. Journal of Statistical Planning and Inference 62, 159-191.
desvar
for the simultaneous calculation of the variance of six sampling strategies; expgreg
for the expected variance of the GREG estimator under a superpopulation model; expvar
for the simultaneous calculation of the expected variance of five sampling strategies under a superpopulation model; optimApp
for an interactive application of expgreg
.
f<- function(x,b0,b1,b2,...) {b0+b1*x^b2}
g<- function(x,b3,...) {x^b3}
x<- 1 + sort( rgamma(5000, shape=4/9, scale=108) )
y<- simulatey(x,f,g,dist="gamma",b0=10,b1=1,b2=1,b3=1,rho=0.95)
st1<- optiallo(n=100,x=x,H=6)
vargreg("y~0",design="srs",n=100) #SRS-HT
vargreg("y~0",design="poi",n=100,x_des=x) #Poi-HT
vargreg("y~0",design="stsi",n=st1$nh,stratum=st1$stratum) #STSI-HT
vargreg("y~0",design="pips",n=100,x_des=x) #PIPS-HT
vargreg("y~x-1",design="srs",n=100,weights=1/x) #SRS-ratio
vargreg("y~x-1",design="poi",n=100,x_des=x,weights=1/x) #Poi-ratio
vargreg("y~x-1",design="stsi",n=st1$nh,
stratum=st1$stratum,weights=1/x) #STSI-ratio
vargreg("y~x-1",design="pips",n=100,x_des=x,weights=1/x) #PIPS-ratio
vargreg("y~x",design="srs",n=100) #SRS-reg
vargreg("y~x",design="poi",n=100,x_des=x) #Poi-reg
vargreg("y~x",design="stsi",n=st1$nh,stratum=st1$stratum) #STSI-reg
vargreg("y~x",design="pips",n=100,x_des=x) #PIPS-reg
x2<- as.factor(st1$stratum)
vargreg("y~x2",design="srs",n=100) #SRS-pos
vargreg("y~x2",design="poi",n=100,x_des=x) #Poi-pos
vargreg("y~x2",design="stsi",n=st1$nh,stratum=st1$stratum) #STSI-pos
vargreg("y~x2",design="pips",n=100,x_des=x) #PIPS-pos
y2<- c(16,21,18)
x2<- y2
inc.probs<- matrix(c(8,5,4,5,7,3,4,3,6),3,3)
vargreg("y2~0",n=2.1,inc.p=inc.probs) #HT
vargreg("y2~x2-1",n=2.1,inc.p=inc.probs,weights=1/x2) #Ratio
vargreg("y2~x2",n=2.1,inc.p=inc.probs) #Regression
x3<- as.factor(c(1,2,2))
vargreg("y2~x3",n=2.1,inc.p=inc.probs) #Post.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.