variance_othstr: Variance estimation for sample surveys by the new...
In vardpoor: Variance Estimation for Sample Surveys by the Ultimate Cluster Method

Description Usage Arguments Details Value References See Also Examples

Computes s2g and the variance estimation by the new stratification.

variance_othstr(
  Y,
  H,
  H2,
  w_final,
  N_h = NULL,
  N_h2,
  period = NULL,
  dataset = NULL,
  checking = TRUE
)

`Y`	Variables of interest. Object convertible to `data.table` or variable names as character, column numbers or logical vector with only one `TRUE` value (length of the vector has to be the same as the column count of `dataset`).
`H`	The unit stratum variable. One dimensional object convertible to one-column `data.table` or variable name as character, column number or logical vector with only one `TRUE` value (length of the vector has to be the same as the column count of `dataset`).
`H2`	The unit new stratum variable. One dimensional object convertible to one-column `data.table` or variable name as character, column number or logical vector with only one `TRUE` value (length of the vector has to be the same as the column count of `dataset`).
`w_final`	Weight variable. One dimensional object convertible to one-column `data.table` or variable name as character, column number or logical vector with only one `TRUE` value (length of the vector has to be the same as the column count of `dataset`).
`N_h`	optional; either a `data.frame` giving the first column - stratum, but the second column - the total of the population in each stratum.
`N_h2`	optional; either a `data.frame` giving the first column - new stratum, but the second column - the total of the population in each new stratum.
`period`	Optional variable for the survey periods. If supplied, the values for each period are computed independently. One dimensional object convertible to one-column `data.table` or variable name as character, column number or logical vector with only one `TRUE` value (length of the vector has to be the same as the column count of `dataset`).
`dataset`	Optional survey data object convertible to `data.table`.
`checking`	Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

It is possible to compute population size M_g from sampling frame. The standard deviation of g-th stratum is

S_g^2 =1/(M_g-1) ∑ k=1...M_g (y_gk - Ym_g)^2= 1/(M_g-1) ∑ k=1...M_g (y_gk)^2 - M_g/(M_g-1)*(Ym_g)^2

∑ k=1...M_g (y_gk)^2 and Ym_g^2 have to be estimated to estimate S_g^2. Estimate of ∑ k=1...M_g (y_gk)^2 is ∑ h=1...H N_h/n_h ∑ i=1...n_h (y_gi)^2*z_hi, where

z_hi=if(0, h_i notin θ_g; 1, h_i in θ_g) , θ_g is the index group of successfully surveyed units belonging to g-th stratum. #'Estimate of (Y_g)^2 is

Ym_g^2=(Ym_g)^2- Var(Ym)

Ym_g =Ym_g/M_g= 1/M_g ∑ h=1...H N_h/n_h ∑ i=1...n_h y_hi z_hi

So the estimate of S_g^2 is

s_g^2=\1/(M_g-1) ∑ h=1...H N_h/n_h ∑ i=1...n_h (y_hi)^2 * z_hi -

-M_g/(M_g-1) (1/M_g ∑ h=1...H N_h/n_h ∑ i=1...n_h y_hi z_hi)^2

Two conditions have to realize to estimate S_g^2: n_h>1, forall g and θ_g <> 0, forall g.

Variance of Y is

Var(Y) = ∑ g=1...G M_g^2 (1/m_g - 1/M_g)*(S_g)^2

Estimate of Var(Y) is

Var(Y)= ∑ g=1...G M_g^2 (1/m_g - 1/M_g)*(s_g)^2

A list with objects are returned by the function:

betas A numeric data.table containing the estimated coefficients of calibration.
s2g A data.table containing the s^2g value.
var_est A data.table containing the values of the variance estimation.

M. Liberts. (2004) Non-response Analysis and Bias Estimation in a Survey on Transportation of Goods by Road.

domain, lin.ratio, linarpr, linarpt, lingini, lingini2, lingpg, linpoormed, linqsr, linrmpg, residual_est, vardom, vardom_othstr, vardomh, varpoord

library("data.table")
Y <- data.table(matrix(runif(50) * 5, ncol = 5))
   
H <- data.table(H = as.integer(trunc(5 * runif(10))))
H2 <- data.table(H2 = as.integer(trunc(3 * runif(10))))
   
N_h <- data.table(matrix(0 : 4, 5, 1))
setnames(N_h, names(N_h), "H")
N_h[, sk:= 10]
   
N_h2 <- data.table(matrix(0 : 2, 3, 1))
setnames(N_h2, names(N_h2), "H2")
N_h2[, sk2:= 4]
   
w_final <- rep(2, 10)
   
vo <- variance_othstr(Y = Y, H = H, H2 = H2,
                      w_final = w_final,
                      N_h = N_h, N_h2 = N_h2,
                      period = NULL,
                      dataset = NULL)
vo