Design effect of unequal weighting and clustering

Formula: DEFF = Var_complex / Var_SRS

Usage

Desigeff(y, weights = NULL, cluster = NULL)

Arguments

y

Survey variable, length n.

weights

Sampling weights, or NULL for equal weights.

cluster

Cluster (PSU) identifier per unit, or NULL.

Value

List with estimate (DEFF), deff_w, deff_c, rho, m0, n_eff, n, method.

Details

Decomposed the way Kish does it, into the unequal-weighting effect DEFF_w = n sum w_i^2 / (sum w_i)^2 and the clustering effect DEFF_c = 1 + (m0 - 1) rho, where rho is the one-way ANOVA intraclass correlation and m0 the Kish average cluster size. The reported DEFF is their product. Equal weights give DEFF_w = 1 exactly, and singleton clusters give DEFF_c = 1 exactly.

References

Kish (1965), Survey Sampling, Wiley, sections 8.2 and 5.4.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Desigeff(V)
#> $estimate
#> [1] 1
#> 
#> $deff_w
#> [1] 1
#> 
#> $deff_c
#> [1] 1
#> 
#> $rho
#> [1] 0
#> 
#> $m0
#> [1] 1
#> 
#> $n_eff
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Kish design effect: unequal weighting x clustering"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"