vardpoor (version 0.2.0.13)

variance_othstr: Variance estimation for sample surveys by the new stratification

Description

Computes the variance estimation by the new stratification.

Usage

variance_othstr(Y, H, H2, w_final, N_h=NULL, N_h2, s2g=FALSE, period=NULL, dataset=NULL)

Arguments

Y

Variables of interest. Object convertible to data.frame 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.frame 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

H2

The unit new stratum variable. One dimensional object convertible to one-column data.frame 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 co

w_final

Weight variable. One dimensional object convertible to one-column data.frame 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

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.

s2g

by default is FALSE; calculate variance, but if s2g is TRUE, then variance estimation is taken as S^2g value.

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.frame or variable name as character, column number or logical vector with only

dataset

Optional survey data object convertible to data.frame.

Value

• A data.table containing the values of the variance estimation.

Details

It is possible to compute population size $M_g$ from sampling frame. The standard deviation of $g$-th stratum is $$S_g^2 =\frac{1}{M_g-1} \sum\limits_{k=1}^{M_g} \left(y_{gk}-\bar{Y}_g \right)^2= \frac{1}{M_g-1} \sum\limits_{k=1}^{M_g} y_{gk}^2 - \frac{M_g}{M_g-1}\bar{Y}_g^2$$ $\sum\limits_{k=1}^{M_g} y_{gk} ^2$ and $\bar{Y}_g^2$ have to be estimeted to estimate $S_g^2$. Estimate of $\sum\limits_{k=1}^{M_g} y_{gk}^2$ is $\sum\limits_{h=1}^{H} \frac{N_h}{n_h} \sum\limits_{i=1}^{n_h} y_{gi}^2 z_{hi}$, where $z_{hi} = \left{ \begin{array}{ll} 0, & h_i \in \theta_g \ 1, & h_i \notin \theta_g \end{array} \right.$, $\theta_g$ is the index group of successfully surveyed units belonging to $g$-th stratum. Estimate of $\bar{Y}_g^2$ is $$\hat{\bar{Y}}_g^2=\left( \hat{\bar{Y}}_g \right)^2-\hat{Var} \left(\hat{\bar{Y}} \right)$$ $$\hat{\bar{Y}}_g =\frac{\hat{Y}_g}{M_g}= \frac{1}{M_g} \sum\limits_{h=1}^{H} \frac{N_h}{n_h} \sum\limits_{i=1}^{n_h} y_{hi} z_{hi}$$ $$\hat{Var} \left(\hat{\bar{Y}} \right) =\frac{1}{M_g^2} \sum\limits_{h=1}^{H} N_h^2 \left(\frac{1}{n_h} - \frac{1}{N_h}\right) \sigma_h^2$$ $$\sigma_h^2 =\frac{1}{n_h-1} \sum\limits_{i=1}^{n_h} \left(y_{hi} z_{hi} - \frac{1}{n_h} \sum\limits_{t=1}^{n_h} y_{ht} z_{ht} \right)^2$$ So the estimate of $S_g^2$ is $s_g^2=\frac{1}{M_g-1} \sum\limits_{h=1}^{H} \frac{N_h}{n_h} \sum\limits_{i=1}^{n_h} y_{hi}^2 z_{hi} -$ $-\frac{M_g}{M_g-1} \left( \left( \frac{1}{M_g} \sum\limits_{h=1}^{H} \frac{N_h}{n_h} \sum\limits_{i=1}^{n_h} y_{hi} z_{hi} \right)^2 - \frac{1}{M_g^2} \sum\limits_{h=1}^{H} N_h^2 \left(\frac{1}{n_h} - \frac{1}{N_h}\right) \frac{1}{n_h-1} \sum\limits_{i=1}^{n_h} \left(y_{hi} z_{hi} - \frac{1}{n_h} \sum\limits_{t=1}^{n_h} y_{ht} z_{ht} \right)^2 \right)$ Two conditions have to realize to estimate $S_g^2: n_h>1, \forall g$ and $\theta_g \ne , \forall g.$ Variance of $\hat{Y}$ is $$Var\left( \hat{Y} \right) = \sum\limits_{g=1}^{G} M_g^2 \left( \frac{1}{m_g} - \frac{1}{M_g} \right) S_g^2$$ Estimate of $\hat{Var}\left( \hat{Y} \right)$ is $$\hat{Var}\left( \hat{Y} \right) = \sum\limits_{g=1}^{G} M_g^2 \left( \frac{1}{m_g} - \frac{1}{M_g} \right)s_g^2$$

References

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

See Also

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

Examples

period=NULL
dataset=NULL
Y <- data.table(matrix(runif(50)*5, ncol=5))

H <- data.table(H=trunc(5*runif(10)))
H2 <- data.table(H2=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