svrep (version 0.7.0)

rescale_replicates: Rescale replicate factors

Description

Rescale replicate factors. The main application of this rescaling is to ensure that all replicate weights are strictly positive.

Note that this rescaling has no impact on variance estimates for totals (or other linear statistics), but variance estimates for nonlinear statistics will be affected by the rescaling.

Usage

rescale_replicates(x, new_scale = NULL, min_wgt = 0.01, digits = 2)

Value

If the input is a numeric matrix, returns the rescaled matrix. If the input is a replicate survey design object, returns an updated replicate survey design object.

For a replicate survey design object, results depend on whether the object has a matrix of replicate factors rather than a matrix of replicate weights (which are the product of replicate factors and sampling weights). If the design object has combined.weights=FALSE, then the replication factors are adjusted. If the design object has combined.weights=TRUE, then the replicate weights are adjusted. It is strongly recommended to only use the rescaling method for replication factors rather than the weights.

For a replicate survey design object, the scale element of the design object will be updated appropriately.

Arguments

x

Either a replicate survey design object, or a numeric matrix of replicate weights. If x is a matrix, then it must have an attribute scale specifying the scale factor for variance estimation.

new_scale

Either a single positive number, or NULL. If supplied, new_scale will be the new scale factor used for estimating variances. For example, with B=10 bootstrap replicates, specifying new_scale=0.2 will change the scale factor for variance estimation from \(B^{-1}=0.1\) to \(0.2\).
If new_scale=NULL or is left unspecified, then the argument min_wgt should be used instead.

min_wgt

Should only be used if new_scale=NULL or new_scale is left unspecified. Specifies the minimum acceptable value for the rescaled weights, which will be used to automatically determine the new scale. Must be at least zero and must be less than one.

digits

Only used if the argument min_wgt is used. Specifies the number of decimal places to use for the scale adjustment factor, so that the ratio new_scale/orig_scale will be a number with at most digits decimal places. For example, let orig_scale denote the original scale and new_scale denote the new scale. Then if the user specifies digits=2, the ratio new_scale/orig_scale will be a number such as 0.25 or 0.10. This results in documentation that is easier to read.

Details

Let \(\mathbf{A} = \left[ \mathbf{a}^{(1)} \cdots \mathbf{a}^{(b)} \cdots \mathbf{a}^{(B)} \right]\) denote the \((n \times B)\) matrix of replicate adjustment factors. The overall scale factor \(C\) is used for estimating variances with the formula $$v(\hat{y}) = C \sum_{b=1}^{B} (\hat{y}_b - \hat{y})^2$$

The scale factor is changed from \(C\) to \(C^{\prime}\) by rescaling the replicate factor matrix \(\mathbf{A}\) using the transformation $$ 1 + \sqrt{\frac{C}{C^{\prime}}}(\mathbf{A}-1) $$

References

Rescaling was suggested by Fay (1989) for the specific application of creating replicate factors using his generalized replication method. This kind of rescaling is commony used in balanced repeated replication to implement Fay's method of balanced repeated replication. Beaumont and Patak (2012) provided an extended discussion of rescaling methods in the context of rescaling generalized bootstrap replication factors to avoid negative replicate weights.

- Beaumont, Jean-François, and Zdenek Patak. 2012. "On the Generalized Bootstrap for Sample Surveys with Special Attention to Poisson Sampling: Generalized Bootstrap for Sample Surveys." International Statistical Review 80 (1): 127–48. https://doi.org/10.1111/j.1751-5823.2011.00166.x.

- Fay, Robert. 1989. "Theory And Application Of Replicate Weighting For Variance Calculations." In, 495–500. Alexandria, VA: American Statistical Association. http://www.asasrms.org/Proceedings/papers/1989_033.pdf

Examples

# Example 1: Rescaling a matrix of replicate weights to avoid negative weights

 rep_wgts <- matrix(
   c(1.69742746694909, -0.230761178913411, 1.53333377634192,
     0.0495043413294782, 1.81820367441039, 1.13229198793703,
     1.62482013925955, 1.0866133494029, 0.28856654131668,
     0.581930729719006, 0.91827012312825, 1.49979905894482,
     1.26281337410693, 1.99327362761477, -0.25608700039304),
   nrow = 3, ncol = 5
 )
 attr(rep_wgts, 'scale') <- 1/5

 rescaled_wgts <- rescale_replicates(rep_wgts, min_wgt = 0.01)

 print(rep_wgts)
 print(rescaled_wgts)
 
 # Example 2: Rescaling replicate weights with a specified value of 'tau'
 
 rescaled_wgts <- rescale_replicates(rep_wgts, new_scale = 1/10)
 print(rescaled_wgts)

 # Example 3: Rescaling replicate weights of a survey design object
 set.seed(2023)
 library(survey)
 data('mu284', package = 'survey')

 ## First create a bootstrap design object
 svy_design_object <- svydesign(
   data = mu284,
   ids = ~ id1 + id2,
   fpc = ~  n1 +  n2
 )

 boot_design <- as_gen_boot_design(
   design = svy_design_object,
   variance_estimator = "Stratified Multistage SRS",
   replicates = 5
 )

 ## Rescale the weights
 rescaled_boot_design <- boot_design |>
   rescale_replicates(min_wgt = 0.01)

 boot_wgts <- weights(boot_design, "analysis")
 rescaled_boot_wgts <- weights(rescaled_boot_design, 'analysis')

 print(boot_wgts)
 print(rescaled_boot_wgts)