ss.aipe.crd.es: Find target sample sizes for the accuracy in standardized conditions means estimation in CRD

Description

Find target sample sizes (the number of clusters, cluster size, or both) for the accuracy in standardized 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. This function uses the likelihood-based confidence interval (Cheung, 2009) by the OpenMx package (Boker et al., 2011). See further details at Pornprasertmanit and Schneider (2010, submitted).

Usage

ss.aipe.crd.es.nclus.fixedwidth(width, nindiv, es, estype = 1, iccy, prtreat, 
	r2between = 0, r2within = 0, numpredictor = 0, assurance=NULL, 
	conf.level = 0.95, nrep = 1000, iccz = NULL, seed = 123321, multicore = FALSE, 
	numProc=NULL, cluscost=NULL, indivcost=NULL, diffsize=NULL)
ss.aipe.crd.es.nindiv.fixedwidth(width, nclus, es, estype = 1, iccy, prtreat, 
	r2between = 0, r2within = 0, numpredictor = 0, assurance=NULL, 
	conf.level = 0.95, nrep = 1000, iccz = NULL, seed = 123321, multicore = FALSE, 
	numProc=NULL, cluscost=NULL, indivcost=NULL, diffsize=NULL) 
ss.aipe.crd.es.nclus.fixedbudget(budget, nindiv, cluscost, indivcost, nrep=NULL, 
	prtreat=NULL, iccy=NULL, es=NULL, estype = 1, numpredictor = 0, 
	iccz=NULL, r2within=NULL, r2between=NULL, assurance=NULL, 
	seed=123321, multicore=FALSE, numProc=NULL, conf.level=0.95, diffsize=NULL)
ss.aipe.crd.es.nindiv.fixedbudget(budget, nclus, cluscost, indivcost, nrep=NULL, 
	prtreat=NULL, iccy=NULL, es=NULL, estype = 1, numpredictor = 0, 
	iccz=NULL, r2within=NULL, r2between=NULL, assurance=NULL, 
	seed=123321, multicore=FALSE, numProc=NULL, conf.level=0.95, diffsize=NULL) 
ss.aipe.crd.es.both.fixedbudget(budget, cluscost=0, indivcost=1, es, estype = 1, 
	iccy, prtreat, r2between = 0, r2within = 0, numpredictor = 0, assurance=NULL, 
	conf.level = 0.95, nrep = 1000, iccz = NULL, seed = 123321, multicore = FALSE, 
	numProc=NULL, diffsize=NULL)
ss.aipe.crd.es.both.fixedwidth(width, cluscost=0, indivcost=1, es, estype = 1, 
	iccy, prtreat, r2between = 0, r2within = 0, numpredictor = 0, assurance=NULL, 
	conf.level = 0.95, nrep = 1000, iccz = NULL, seed = 123321, multicore = FALSE, 
	numProc=NULL, 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

iccy

The intraclass correlation of the dependent variable

The amount of effect size

estype

The type of effect size. There are only three possible options: 0 = the effect size using total standard deviation, 1 = the effect size using the individual-level standard deviation (level 1), 2 = the effect size using the cluster-level standard deviation (level 2)

numpredictor

If 1, a single covariate is included into the model. If 0, the no-covariate model is used. This function cannot handle multiple covariates. Therefore, only the values of 0 and 1 are allowed.

iccz

The intraclass correlation of the covariate (used when covariate = TRUE). If iccz = 0, the within-level covariate will be only used. If iccz = 1, the between-level covariate will be only used.

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)

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)

nrep

The number of replications used in a priori Monte Carlo simulation

seed

A desired seed number

multicore

Use multiple processors within a computer. Specify as TRUE to use it.

numProc

The number of processors to be used when multicore=TRUE. If it is not specified, the package will use the maximum number of processors in a machine.

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.

Value

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

Details

Here are the functions' descriptions:

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

References

Boker, S., M., N., Maes, H., Wilde, M., Spiegel, M., Brick, T., et al. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76, 306-317.

Cheung, M. W.-L. (2009). Constructing approximate confidence intervals for parameters with structural constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling, 16, 267-294.

Pornprasertmanit, S., & Schneider, W. J. (2010). Efficient sample size for power and desired accuracy in Cohen's d estimation in two-group cluster randomized design (Master Thesis). Illinois State University, Normal, IL.

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

Examples

Run this code

## Not run: 
# # Examples for each function
# ss.aipe.crd.es.nclus.fixedwidth(width=0.3, nindiv=20, es=0.5, estype=1, iccy=0.25, prtreat=0.5, 
# 	nrep=20)
# 
# ss.aipe.crd.es.nindiv.fixedwidth(width=0.3, 250, es=0.5, estype=1, iccy=0.25, prtreat=0.5, 
# 	nrep=20)
# 
# ss.aipe.crd.es.nclus.fixedbudget(budget=1000, nindiv=20, cluscost=0, indivcost=1, nrep=20, 
# 	prtreat=0.5, iccy=0.25, es=0.5)
# 
# ss.aipe.crd.es.nindiv.fixedbudget(budget=1000, nclus=200, cluscost=0, indivcost=1, nrep=20, 
# 	prtreat=0.5, iccy=0.25, es=0.5)
# 
# ss.aipe.crd.es.both.fixedbudget(budget=1000, cluscost=5, indivcost=1, es=0.5, estype=1, 
# 	iccy=0.25, prtreat=0.5, nrep=20)
# 
# ss.aipe.crd.es.both.fixedwidth(width=0.5, cluscost=5, indivcost=1, es=0.5, estype=1, iccy=0.25, 
# 	prtreat=0.5, nrep=20)
# 
# # Examples for different cluster size
# ss.aipe.crd.es.nclus.fixedwidth(width=0.3, nindiv=20, es=0.5, estype=1, iccy=0.25, prtreat=0.5, 
# nrep=20, diffsize = c(-2, 1, 0, 2, -1, 3, -3, 0, 0))
# 
# ss.aipe.crd.es.nclus.fixedwidth(width=0.3, nindiv=20, es=0.5, estype=1, iccy=0.25, prtreat=0.5, 
# nrep=20, diffsize = c(0.6, 1.2, 0.8, 1.4, 1, 1, 1.1, 0.9))
# ## End(Not run)

Run the code above in your browser using DataLab