Sample Size Necessary for the Accuracy in Parameter Estimation Approach for an Unstandardized Regression Coefficient of Interest

A function used to plan sample size from the accuracy in parameter estimation perspective for an unstandardized regression coefficient of interest given the input specification.

Usage

ss_aipe_rc(
  rho2_Y_X = NULL,
  Rho2_j_X_without_j = NULL,
  p = NULL,
  b_j = NULL,
  width,
  which_width = "Full",
  sigma_Y = 1,
  sigma_X_j = 1,
  rho_XX = NULL,
  rho_YX = NULL,
  which_predictor = NULL,
  alpha_lower = NULL,
  alpha_upper = NULL,
  conf_level = 0.95,
  assurance = NULL
)

Arguments

rho2_Y_X: Population value of the squared multiple correlation coefficient
Rho2_j_X_without_j: Population value of the squared multiple correlation coefficient predicting the jth predictor variable from the remaining p-1 predictor variables
p: The number of predictor variables
b_j: The regression coefficient for the jth predictor variable (i.e., the predictor of interest)
width: The desired width of the confidence interval
which_width: Which Width ("Full", "Lower", or "Upper") the width refers to (at present, only "Full" can be specified)
sigma_Y: The population standard deviation of Y (i.e., the dependent variables)
sigma_X_j: The population standard deviation of the jth X variable (i.e., the predictor variable of interest)
rho_XX: Population correlation matrix for the p predictor variables
rho_YX: Population p length vector of correlation between the dependent variable (Y) and the p independent variables
which_predictor: Identifies which of the p predictors is of interest
alpha_lower: Type I error rate for the lower confidence interval limit
alpha_upper: Type I error rate for the upper confidence interval limit
conf_level: Desired level of confidence for the computed interval (i.e., 1 - the Type I error rate)
assurance: Degree of certainty that the obtained confidence interval will be sufficiently narrow

Value

Returns the necessary sample size in order for the goals of accuracy in parameter estimation to be satisfied for the confidence interval for a particular regression coefficient given the input specifications.

Details

Not all of the arguments need to be specified, only those that provide all of the necessary information so that the sample size can be determined for the conditions specified.

Note

This function calls upon ss_aipe_reg_coef in DMAR but has a different naming scheme. See ss_aipe_reg_coef for more details.

References

Kelley, K., & Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8(3), 305–321. doi:10.1037/1082-989X.8.3.305

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons of means and Chapter 6 on trend analysis.)

Author

Ken Kelley kkelley@nd.edu

Examples

# Exchangeable correlation structure
rho_YX <- c(.3, .3, .3, .3, .3)
rho_XX <- rbind(c(1, .5, .5, .5, .5), c(.5, 1, .5, .5, .5), c(.5, .5, 1, .5, .5),
c(.5, .5, .5, 1, .5), c(.5, .5, .5, .5, 1))

ss_aipe_rc(width = .1, which_width = "Full", sigma_Y = 1, sigma_X = 1, rho_XX = rho_XX,
           rho_YX = rho_YX, which_predictor = 1, conf_level = 1 - .05)
#>  term        value
#>  necessary_N 2185 
#> 
#> Confidence level: 95%

ss_aipe_rc(width = .1, which_width = "Full", sigma_Y = 1, sigma_X = 1, rho_XX = rho_XX,
           rho_YX = rho_YX, which_predictor = 1, conf_level = 1 - .05, assurance = .85)
#>  term        value
#>  necessary_N 2259 
#> 
#> Confidence level: 95%