ss.aipe.R2.sensitivity {MBESS}

Sensitivity analysis for sample size planning with the goal of Accuracy in Parameter Estimation (i.e., a narrow observed confidence interval)

Description

Given Estimated.R2 and True.R2, one can perform a sensitivity analysis to determine the effect of a misspecified population squared multiple correlation coefficient using the Accuracy in Parameter Estimation (AIPE) approach to sample size planning. The function evaluates the effect of a misspecified True.R2 on the width of obtained confidence intervals.

Usage

ss.aipe.R2.sensitivity(True.R2 = NULL, Estimated.R2 = NULL, w = NULL, 
p = NULL, Random.Predictors=TRUE, Selected.N=NULL, 
degree.of.certainty = NULL, assurance=NULL, certainty=NULL, 
conf.level = 0.95, Generate.Random.Predictors=TRUE, rho.yx = 0.3, 
rho.xx = 0.3,  G = 10000, print.iter = TRUE, ...)

Arguments

True.R2

value of the population squared multiple correlation coefficient

Estimated.R2

value of the estimated (for sample size planning) squared multiple correlation coefficient

w

full confidence interval width of interest

p

number of predictors

Random.Predictors

whether or not the sample size procedure and the simulation itself should be based on random (set to TRUE) or fixed predictors (set to FALSE)

Selected.N

selected sample size to use in order to determine distributional properties at a given value of sample size

degree.of.certainty

parameter to ensure confidence interval width with a specified degree of certainty

assurance

an alias for degree.of.certainty

certainty

an alias for degree.of.certainty

conf.level

confidence interval coverage (symmetric coverage)

Generate.Random.Predictors

specify whether the simulation should be based on random (default) or fixed regressors.

rho.yx

value of the correlation between y (dependent variable) and each of the x variables (independent variables)

rho.xx

value of the correlation among the x variables (independent variables)

G

number of generations (i.e., replications) of the simulation

print.iter

should the iteration number (between 1 and G) during the run of the function

...

for modifying parameters of functions this function calls upon

Details

When Estimated.R2=True.R2, the results are that of a simulation study when all assumptions are satisfied. Rather than specifying Estimated.R2, one can specify Selected.N to determine the results of a particular sample size (when doing this Estimated.R2 cannot be specified).

The sample size estimation procedure technically assumes multivariate normal variables (p+1) with fixed predictors (x/indepdent variables), yet the function assumes random multivariate normal predictors (having a p+1 multivariate distribution). As Gatsonis and Sampson (1989) note in the context of statistical power analysis (recall this function is used in the context of precision), there is little difference in the outcome.

In the behavioral, educational, and social sciences, predictor variables are almost always random, and thus Random.Predictors should generally be used. Random.Predictors=TRUE specifies how both the sample size planning procedure and the confidence intervals are calculated based on the random predictors/regressors. The internal simulation generates random or fixed predictors/regressors based on whether variables predictor variables are random or fixed. However, when Random.Predictors=FALSE, only the sample size planning procedure and the confidence intervals are calculated based on the parameter. The parameter Generate.Random.Predictors (where the default is TRUE so that random predictors/regressors are generated) allows random or fixed predictor variables to be generated. Because the sample size planning procedure and the internal simulation are both specified, for purposes of sensitivity analysis random/fixed can be crossed to examine the effects of specifying sample size based on one but using it on data based on the other.

Value

Results

a list containing vectors of the empirical results

Specifications

outputs the input specifications and required sample size

Summary

summary values for the results of the sensitivity analysis (simulation study)

Author(s)

Ken Kelley (University of Notre Dame; [e-mail])

References

Algina, J. & Olejnik, S. (2000). Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient. Multivariate Behavioral Research, 35, 119–136.

Gatsonis, C. & Sampson, A. R. (1989). Multiple Correlation: Exact power and sample size calculations. Psychological Bulletin, 106, 516–524.

Steiger, J. H. & Fouladi, R. T. (1992). R2: A computer program for interval estimation, power calculation, and hypothesis testing for the squared multiple correlation. Behavior research methods, instruments and computers, 4, 581–582.

Kelley, K. (2008). Sample size planning for the squared multiple correlation coefficient: Accuracy in parameter estimation via narrow confidence intervals, Multivariate Behavioral Research, 43, 524–555.

Kelley, K. & Maxwell, S. E. (2008). Sample Size Planning with applications to multiple regression: Power and accuracy for omnibus and targeted effects. In P. Alasuuta, J. Brannen, & L. Bickman (Eds.), The Sage handbook of social research methods (pp. 166–192). Newbury Park, CA: Sage.

See Also

ci.R2, conf.limits.nct, ss.aipe.R2

Examples

## Not run: 
# Change 'G' to some large number (e.g., G=10,000)
# ss.aipe.R2.sensitivity(True.R2=.5, Estimated.R2=.4, w=.10, p=5, conf.level=0.95,
# G=25)

## End(Not run)