| Title: | Sample Size Determination for Accurate Predictive Linear Regression |
| Version: | 0.1.1 |
| Description: | Provides analytic and simulation tools to estimate the minimum sample size required for achieving a target prediction mean-squared error (PMSE) or a specified proportional PMSE reduction (pPMSEr) in linear regression models. Functions implement the criteria of Ma (2023) https://digital.wpi.edu/downloads/0g354j58c, support covariance-matrix handling, and include helpers for root-finding and diagnostic plotting. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | Matrix, stats, rootSolve |
| Suggests: | rmarkdown, testthat(≥ 3.0.0) |
| BugReports: | https://github.com/Chenaters/pmsesampling/issues |
| URL: | https://github.com/Chenaters/pmsesampling |
| NeedsCompilation: | no |
| Packaged: | 2025-09-04 04:29:42 UTC; 12245 |
| Author: | Louis Chen [aut, cre], Zheyang Wu [aut, ths] |
| Maintainer: | Louis Chen <chenaters@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-09-09 14:00:02 UTC |
pmsesampling: Sample Size Determination for Accurate Predictive Linear Regression
Description
Tools to estimate the minimum sample size required to achieve a target Prediction Mean-Squared Error (PMSE) or a specified proportional PMSE reduction (pPMSEr). Functions implement the analytic and simulation-based criteria described in Ma (2023) and include helpers for covariance-matrix handling, root-finding and diagnostic plotting.
Core functions
pmse_samplesize()Determines sample size from PMSE equation in basic and full models and the efficient sample size
Typical workflow
Obtain
\sigma_k^2and\sigma_p^2Or import or build a predictor covariance matrix.
Or obtain
Cohen's f^2and\R^2Call
pmse_samplesizewith available inputs to get sample size.
Author(s)
Maintainer: Louis Chen chenaters@gmail.com
Authors:
Zheyang Wu zheyangwu@wpi.edu [thesis advisor]
References
Ma Y. (2023) Predictive Power and Efficient Sample Size in Linear Regression Models. Worchester Polytechnic Institute
See Also
Useful links:
Report bugs at https://github.com/Chenaters/pmsesampling/issues
Compute efficient sample size under user-defined PMSE targets
Description
pmse_samplesize computes a sample size for a
prediction model. The function implements the formulas found in the thesis
"Predictive Power and Efficient Sample Size in Linear Regression Models" by Yifan Ma (2023).
Usage
pmse_samplesize(
k,
p,
PMSE_val_k = 1,
PMSE_val_p = 1,
efficiency_level = 0.9,
sigma_k2 = NULL,
sigma_p2 = NULL,
cov = NULL,
corr = NULL,
SD = 1,
f2 = NULL,
f2_2 = NULL,
R2_full = NULL,
R2_basic = NULL
)
Arguments
k |
Integer. Total number of predictors in the full model. |
p |
Integer. Number of basic predictors in the reduced model. |
PMSE_val_k |
Numeric. Target PMSE value for the full model. |
PMSE_val_p |
Numeric. Target PMSE value for the reduced model. |
efficiency_level |
Numeric. Target efficiency level. (default is 0.9, meaning 90% of asymptotic pPMSEr) |
sigma_k2 |
Numeric. Predictor error variance for full model. If 'NULL' it is derived. |
sigma_p2 |
Numeric. Predictor error variance for basic model. If 'NULL' it is derived. |
cov |
Optional covariance matrix. Must be |
corr |
Optional correlation matrix. (Same layout as |
SD |
Optional numeric vector of standard deviation for the predictors when
a correlation matrix is supplied. Default |
f2 |
Numeric. Cohen's f2 for effects of all predictors in full model. |
f2_2 |
Numeric. Cohen’s f2 for the effects of new predictors given the basic model. |
R2_full |
Numeric. Coefficient of determination for full model. |
R2_basic |
Numeric. Coefficient of determination for basic model. |
Details
pmse_samplesize
Sample Size Calculation for Prediction Models
pmse_samplesize The function calculates predictor error variance
for the full model, with all predictors, and the reduced model, with the basic
predictors using a provided covariance matrix or correlation matrix. It can
also calculate predictor error variance through Cohen's F^2 and R^2 values.
With the predictor error variance it determines a sample size from the
efficient sample size at a target efficiency level and a sample size from a
PMSE value of the full and reduced model. The final returned sample size is
the largest out of the outputs.
Value
Numeric representing the required sample size.
References
Ma, Y. (2023). Predictive Power and Efficient Sample Size in Linear Regression Models. Master’s Thesis, Worcester Polytechnic Institute.
Examples
## Example with a 5-predictor model (k = 5) and 2 basic predictors (p = 2)
pmse_samplesize(
k = 5, p = 2,
PMSE_val_k = 1,
PMSE_val_p = 1,
efficiency_level = 0.9,
sigma_k2 = 0.50,
sigma_p2 = 0.60
)