Find target sample sizes for the accuracy in unstandardized conditions means estimation in CRD

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Description

Find target sample sizes (the number of clusters, cluster size, or both) for the accuracy in unstandardized conditions means estimation in CRD. If users wish to seek for both types of sample sizes simultaneously, an additional constraint is required, such as a desired width or a desired budget.

Usage

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ss.aipe.crd.nclus.fixedwidth(width, nindiv, prtreat, tauy=NULL, sigma2y=NULL, 
	totalvar=NULL, iccy=NULL, r2between = 0, r2within = 0, numpredictor = 0, 
	assurance=NULL, conf.level = 0.95, cluscost=NULL, indivcost=NULL, diffsize=NULL)
ss.aipe.crd.nindiv.fixedwidth(width, nclus, prtreat, tauy=NULL, sigma2y=NULL, 
	totalvar=NULL, iccy=NULL, r2between = 0, r2within = 0, numpredictor = 0, 
	assurance=NULL, conf.level = 0.95, cluscost=NULL, indivcost=NULL, diffsize=NULL)
ss.aipe.crd.nclus.fixedbudget(budget, nindiv, cluscost = 0, indivcost = 1, 
	prtreat = NULL, tauy=NULL, sigma2y=NULL, totalvar=NULL, iccy=NULL, r2between = 0, 
	r2within = 0, numpredictor = 0, assurance=NULL, conf.level = 0.95, diffsize=NULL)
ss.aipe.crd.nindiv.fixedbudget(budget, nclus, cluscost = 0, indivcost = 1, 
	prtreat = NULL, tauy=NULL, sigma2y=NULL, totalvar=NULL, iccy=NULL, r2between = 0, 
	r2within = 0, numpredictor = 0, assurance=NULL, conf.level = 0.95, diffsize=NULL)
ss.aipe.crd.both.fixedbudget(budget, cluscost=0, indivcost=1, prtreat, tauy=NULL, 
	sigma2y=NULL, totalvar=NULL, iccy=NULL, r2between = 0, r2within = 0, 
	numpredictor = 0, assurance=NULL, conf.level = 0.95, diffsize=NULL)
ss.aipe.crd.both.fixedwidth(width, cluscost=0, indivcost=1, prtreat, tauy=NULL, 
	sigma2y=NULL, totalvar=NULL, iccy=NULL, r2between = 0, r2within = 0, 
	numpredictor = 0, assurance=NULL, conf.level = 0.95, diffsize=NULL)

Arguments

width

The desired width of the confidence interval of the unstandardized means difference

budget

The desired amount of budget

nclus

The desired number of clusters

nindiv

The number of individuals in each cluster (cluster size)

prtreat

The proportion of treatment clusters

cluscost

The cost of collecting a new cluster regardless of the number of individuals collected in each cluster

indivcost

The cost of collecting a new individual

tauy

The residual variance in the between level before accounting for the covariate

sigma2y

The residual variance in the within level before accounting for the covariate

totalvar

The total resiudal variance before accounting for the covariate

iccy

The intraclass correlation of the dependent variable

r2within

The proportion of variance explained in the within level (used when covariate = TRUE)

r2between

The proportion of variance explained in the between level (used when covariate = TRUE)

numpredictor

The number of predictors used in the between level

assurance

The degree of assurance, which is the value with which confidence can be placed that describes the likelihood of obtaining a confidence interval less than the value specified (e.g, .80, .90, .95)

conf.level

The desired level of confidence for the confidence interval

diffsize

Difference cluster size specification. The difference in cluster sizes can be specified in two ways. First, users may specify cluster size as integers, which can be negative or positive. The resulting cluster sizes will be based on the estimated cluster size adding by the specified vectors. For example, if the cluster size is 25, the number of clusters is 10, and the specified different cluster size is c(-1, 0, 1), the cluster sizes will be 24, 25, 26, 24, 25, 26, 24, 25, 26, and 24. Second, users may specify cluster size as positive decimals. The resulting cluster size will be based on the estimated cluster size multiplied by the specified vectors. For example, if the cluster size is 25, the number of clusters is 10, and the specified different cluster size is c(-1, 0, 1), the cluster sizes will be 24, 25, 26, 24, 25, 26, 24, 25, 26, and 24. If NULL, the cluster size is equal across clusters.

Details

Here are the functions' descriptions:

  • ss.aipe.crd.nclus.fixedwidth Find the number of clusters given a specified width of the confidence interval and the cluster size

  • ss.aipe.crd.nindiv.fixedwidth Find the cluster size given a specified width of the confidence interval and the number of clusters

  • ss.aipe.crd.nclus.fixedbudget Find the number of clusters given a budget and the cluster size

  • ss.aipe.crd.nindiv.fixedbudget Find the cluster size given a budget and the number of clusters

  • ss.aipe.crd.both.fixedbudget Find the sample size combinations (the number of clusters and that cluster size) providing the narrowest confidence interval given the fixed budget

  • ss.aipe.crd.both.fixedwidth Find the sample size combinations (the number of clusters and that cluster size) providing the lowest cost given the specified width of the confidence interval

Value

The ss.aipe.crd.nclus.fixedwidth and ss.aipe.crd.nclus.fixedbudget functions provide the number of clusters. The ss.aipe.crd.nindiv.fixedwidth and ss.aipe.crd.nindiv.fixedbudget functions provide the cluster size. The ss.aipe.crd.both.fixedbudget and ss.aipe.crd.both.fixedwidth provide the number of clusters and the cluster size, respectively.

Author(s)

Sunthud Pornprasertmanit (psunthud@gmail.com)

References

Pornprasertmanic, S., & Schneider, W. J. (2014). Accuracy in parameter estimation in cluster randomized designs. Psychological Methods, 19, 356–379.

Examples

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## Not run: 
# Examples for each function
ss.aipe.crd.nclus.fixedwidth(width=0.3, nindiv=30, prtreat=0.5, tauy=0.25, sigma2y=0.75)

ss.aipe.crd.nindiv.fixedwidth(width=0.3, nclus=250, prtreat=0.5, tauy=0.25, sigma2y=0.75)

ss.aipe.crd.nclus.fixedbudget(budget=10000, nindiv=20, cluscost=20, indivcost=1)

ss.aipe.crd.nindiv.fixedbudget(budget=10000, nclus=30, cluscost=20, indivcost=1, 
prtreat=0.5, tauy=0.05, sigma2y=0.95, assurance=0.8)

ss.aipe.crd.both.fixedbudget(budget=10000, cluscost=30, indivcost=1, prtreat=0.5, tauy=0.25, 
	sigma2y=0.75)

ss.aipe.crd.both.fixedwidth(width=0.3, cluscost=0, indivcost=1, prtreat=0.5, tauy=0.25, 
	sigma2y=0.75)

# Examples for different cluster size
ss.aipe.crd.nclus.fixedwidth(width=0.3, nindiv=30, prtreat=0.5, tauy=0.25, sigma2y=0.75, 
diffsize = c(-2, 1, 0, 2, -1, 3, -3, 0, 0))

ss.aipe.crd.nclus.fixedwidth(width=0.3, nindiv=30, prtreat=0.5, tauy=0.25, sigma2y=0.75, 
diffsize = c(0.6, 1.2, 0.8, 1.4, 1, 1, 1.1, 0.9))

## End(Not run)

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