composite: Linear Composite Estimator from overlap and non overlapping...
In DanielBonnery/CompositeRegressionEstimation: X

Description Usage Arguments See Also Examples

Consider a sequence of monthly samples (S_m)_{m\in\{1,…,M\}}. For each individual k of the sample m, one observes the employment status Y_{k,m} (A binary variable) of individual k at time m, and the survey weight w_{k,m}. The following program allows to compute recursively for m=1,…,M the Census composite estimator of the total of Y_{.,m} with coefficients defined recursively as follows:

For m=1, \hat{t}_{Y_{.,1}}=∑_{k\in S_1}w_{k,m}Y_{k,m}.

For m≥q 2,

\hat{t}_{Y_{.,m}}= ≤ft[\begin{array}{c} \hat{t}_{Y_{.,m-1}}\\ ∑_{k\in S_{m}} w_{k,m} Y_{k,m}\\∑_{k\in S_{m-1}\cap S_{m}} w_{k,m-1} Y_{k,m-1}\\ ∑_{k\in S_{m-1}\cap S_{m}} w_{k,m} Y_{k,m}\\∑_{k\in S_{m}\setminus S_{m-1}} w_{k,m} Y_{k,m}\end{array}\right]^{\mathrm{T}}\times ≤ft[\begin{array}{c}α_{(-1)}\\α_{0}\\β_{(-1)}\\β_0\\γ_0\end{array}\right]

This function computes the estimators for given values of α,β,γ.

An example of use of such estimate is the Census Bureau AK estimator: it is a special case of this estimator, with the values of α,β,γ that are given as a function of two parameters A and K:

≤ft[\begin{array}{c}α_{(-1)}\\α_0\\β_{(-1)}\\β_0\\γ_0\end{array}\right]=≤ft[\begin{array}{c}K\\ 1-K\\ -4~K/3\\(4K-A)/3 \\A \end{array}\right]

for more references, please refer to the function CompositeRegressionEstimation::AK.

See “CPS Technical Paper (2006). Design and Methodology of the Current Population Survey. Technical Report 66, U.S. Census Bureau."

\begin{array}{clll}\hat{t}_{Y_{.,m}}=&& K&\times \hat{t}_{Y_{.,m-1}}\\&+&(1-K)&\times ∑_{k\in S_{m}} w_{k,m} Y_{k,m}\\&+&(-4K/3)&\times∑_{k\in S_{m-1}\cap S_{m}} w_{k,m-1} Y_{k,m-1}\\&+&(4K-A)/3 &\times∑_{k\in S_{m-1}\cap S_{m}} w_{k,m} Y_{k,m}\\&+&A&\times∑_{k\in S_{m}\setminus S_{m-1}} w_{k,m} Y_{k,m}\end{array}

Computing the estimators recursively is not very efficient. At the end, we get a linear combinaison of month in sample estimates The functions AK3, and WSrg computes the linear combination directly and more efficiently.

For the CPS, in month m the overlap S_{m-1}\cap S_{m} correspond to the individuals in the sample S_m with a value of month in sample equal to 2,3,4, 6,7 or 8. The overlap S_{m-1}\cap S_{m} correspond to the individuals in the sample S_m with a value of month in sample equal to 2,3,4, 6,7 or 8. as well as individuals in the sample S_{m-1} with a value of month in sample equal to 1,2,3, 5,6 or 7. When parametrising the function, the choice would be group_1=c(1:3,5:7) and group0=c(2:4,6:8).

composite(
  list.tables,
  w,
  list.y,
  id = NULL,
  groupvar = NULL,
  groups_1 = NULL,
  groups0 = NULL,
  Coef = c(alpha_1 = 0, alpha0 = 1, beta_1 = 0, beta0 = 0, gamma0 = 0),
  dft0.y = NULL
)

`list.tables`	a list of tables
`w`	a character string: name of the weights variable (should be the same in all tables)
`list.y`	a vector of variable names
`id`	a character string: name of the identifier variable (should be the same in all tables)
`groupvar`	a character string: name of the rotation group variable (should be the same in all tables)
`groups_1`	a character string:
`groups0`	if `groupvar` is not null, a vector of possible values for L[[groupvar]]

CompositeRegressionEstimation::AK

library(dataCPS)
data(cps200501,cps200502,cps200503,cps200504,
     cps200505,package="dataCPS") 
list.tables<-list(cps200501,cps200502,cps200503,cps200504,
                  cps200505)
w="pwsswgt";id=c("hrhhid","pulineno");groupvar=NULL;list.y="pemlr";dft0.y=NULL;
groups_1=NULL;groups0=NULL;Coef=c(alpha_1=0,alpha0=1,beta_1=0,beta0=0,gamma0=0)
composite(list.tables,w=w,list.y="pemlr",id=id,groupvar=groupvar)
##With the default choice of parameters for \code{Coef}, the composite is  equal to the direct estimator: we check
WS(list.tables = list.tables,weight = w,list.y = list.y)  
## Example of use of a group variable. 
w="pwsswgt";id=NULL;groupvar="hrmis";list.y="pemlr";dft0.y=NULL;
groups_1=c(1:3,5:7);groups0=c(2:4,6:8);Coef=c(alpha0=1,alpha_1=0,beta_1=0,beta0=0,gamma0=0)
composite(list.tables,w=w,list.y="pemlr",id=id,groupvar=groupvar)