JackMLCSW {Frames2}

Confidence intervals for MLCSW estimator based on jackknife method

Description

Calculates confidence intervals for MLCSW estimator using jackknife procedure

Usage

JackMLCSW (ysA, ysB, pik_A, pik_B, pik_ab_B, pik_ba_A, domains_A, 
 domains_B, xsA, xsB, x, ind_sam, N_A, N_B, N_ab = NULL, met = "linear", 
 conf_level, sdA = "srs", sdB = "srs", strA = NULL, strB = NULL, clusA = NULL, 
 clusB = NULL, fcpA = FALSE, fcpB = FALSE)

Arguments

ysA

A data frame containing information about one or more factors, each one of dimension n_A, collected from s_A.

ysB

A data frame containing information about one or more factors, each one of dimension n_B, collected from s_B.

pik_A

A numeric vector of length n_A containing first order inclusion probabilities for units included in s_A.

pik_B

A numeric vector of length n_B containing first order inclusion probabilities for units included in s_B.

pik_ab_B

A numeric vector of size n_A containing first order inclusion probabilities according to sampling design in frame B for units belonging to overlap domain that have been selected in s_A.

pik_ba_A

A numeric vector of size n_B containing first order inclusion probabilities according to sampling design in frame A for units belonging to overlap domain that have been selected in s_B.

domains_A

A character vector of size n_A indicating the domain each unit from s_A belongs to. Possible values are "a" and "ab".

domains_B

A character vector of size n_B indicating the domain each unit from s_B belongs to. Possible values are "b" and "ba".

xsA

A numeric vector of length n_A or a numeric matrix or data frame of dimensions n_A x m, with m the number of auxiliary variables, containing auxiliary information in frame A for units included in s_A.

xsB

A numeric vector of length n_B or a numeric matrix or data frame of dimensions n_B x m, with m the number of auxiliary variables, containing auxiliary information in frame B for units included in s_B.

x

A numeric vector or length N or a numeric matrix or data frame of dimensions N x m, with m the number of auxiliary variables, containing auxiliary information for every unit in the population.

ind_sam

A numeric vector of length n = n_A + n_B containing the identificators of units of the population (from 1 to N) that belongs to s_A or s_B

N_A

A numeric value indicating the size of frame A

N_B

A numeric value indicating the size of frame B

N_ab

(Optional) A numeric value indicating the size of the overlap domain

met

(Optional) A character vector indicating the distance that must be used in calibration process. Possible values are "linear", "raking" and "logit". Default is "linear".

conf_level

A numeric value indicating the confidence level for the confidence intervals.

sdA

(Optional) A character vector indicating the sampling design considered in frame A. Possible values are "srs" (simple random sampling without replacement), "pps" (probabilities proportional to size sampling), "str" (stratified sampling), "clu" (cluster sampling) and "strclu" (stratified cluster sampling). Default is "srs".

sdB

(Optional) A character vector indicating the sampling design considered in frame B. Possible values are "srs" (simple random sampling without replacement), "pps" (probabilities proportional to size sampling), "str" (stratified sampling), "clu" (cluster sampling) and "strclu" (stratified cluster sampling). Default is "srs".

strA

(Optional) A numeric vector indicating the stratum each unit in frame A belongs to, if a stratified sampling or a stratified cluster sampling has been considered in frame A.

strB

(Optional) A numeric vector indicating the stratum each unit in frame B belongs to, if a stratified sampling or a stratified cluster sampling has been considered in frame B.

clusA

(Optional) A numeric vector indicating the cluster each unit in frame A belongs to, if a cluster sampling or a stratified cluster sampling has been considered in frame A.

clusB

(Optional) A numeric vector indicating the cluster each unit in frame B belongs to, if a cluster sampling or a stratified cluster sampling has been considered in frame B.

fcpA

(Optional) A logic value indicating if a finite population correction factor should be considered in frame A. Default is FALSE.

fcpB

(Optional) A logic value indicating if a finite population correction factor should be considered in frame B. Default is FALSE.

Details

Let suppose a non stratified sampling design in frame A and a stratified sampling design in frame B where frame has been divided into L strata and a sample of size n_{Bl} from the N_{Bl} composing the l-th stratum is selected In this context, jackknife variance estimator of an estimator \hat{Y}_c is given by

v_J(\hat{Y}_c) = \frac{n_{A}-1}{n_{A}}\sum_{i\in s_A} (\hat{Y}_{c}^{A}(i) -\overline{Y}_{c}^{A})^2 + \sum_{l=1}^{L}\frac{n_{Bl}-1}{n_{Bl}} \sum_{i\in s_{Bl}} (\hat{Y}_{c}^{B}(lj) -\overline{Y}_{c}^{Bl})^2

with \hat{Y}_c^A(i) the value of estimator \hat{Y}_c after dropping i-th unit from ysA and \overline{Y}_{c}^{A} the mean of values \hat{Y}_c^A(i). Similarly, \hat{Y}_c^B(lj) is the value taken by \hat{Y}_c after dropping j-th unit of l-th from sample ysB and \overline{Y}_{c}^{Bl} is the mean of values \hat{Y}_c^B(lj). If needed, a finite population correction factor can be included in frames by replacing \hat{Y}_{c}^{A}(i) or \hat{Y}_{c}^{B}(lj) with \hat{Y}_{c}^{A*}(i)= \hat{Y}_{c}+\sqrt{1-\overline{\pi}_A} (\hat{Y}_{c}^{A}(i) -\hat{Y}_{c}) or \hat{Y}_{c}^{B*}(lj)= \hat{Y}_{c}+\sqrt{1-\overline{\pi}_B} (\hat{Y}_{c}^{B}(lj) -\hat{Y}_{c}), where \overline{\pi}_A = \sum_{i \in s_A}\pi_{iA}/nA and \overline{\pi}_B = \sum_{j \in s_B}\pi_{jB}/nB A confidence interval for any parameter of interest, Y can be calculated, then, using the pivotal method.

Value

A numeric matrix containing estimations of population total and population mean and their corresponding confidence intervals obtained through jackknife method.

References

Molina, D., Rueda, M., Arcos, A. and Ranalli, M. G. (2015) Multinomial logistic estimation in dual frame surveys Statistics and Operations Research Transactions (SORT). To be printed.

Wolter, K. M. (2007) Introduction to Variance Estimation. 2nd Edition. Springer, Inc., New York.

See Also

MLCSW

Examples

data(DatMA)
data(DatMB)
data(DatPopM)

IndSample <- c(DatMA$Id_Pop, DatMB$Id_Pop)
N_FrameA <- nrow(DatPopM[DatPopM$Domain == "a" | DatPopM$Domain == "ab",])
N_FrameB <- nrow(DatPopM[DatPopM$Domain == "b" | DatPopM$Domain == "ab",])


#Let obtain a 95% jackknife confidence interval for variable Feeding,
#supposing a pps sampling in frame A and a simple random sampling
#without replacement in frame B with no finite population correction
#factor in any frame.
JackMLCSW(DatMA$Prog, DatMB$Prog, DatMA$ProbA, DatMB$ProbB, DatMA$ProbB, 
DatMB$ProbA, DatMA$Domain, DatMB$Domain, DatMA$Read, DatMB$Read, DatPopM$Read, 
IndSample, N_FrameA, N_FrameB, conf_level = 0.95, sdA = "pps", sdB = "srs")