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.
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, ...)TRUE) or fixed predictors (set to FALSE)degree.of.certainty degree.of.certaintyG) during the run of the functionEstimated.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.
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.
ci.R2, conf.limits.nct, ss.aipe.R2## 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)
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