Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models

  title={Exact Analysis of Squared Cross-Validity Coefficient in Predictive Regression Models},
  author={Gwowen Shieh},
  journal={Multivariate Behavioral Research},
  pages={105 - 82}
  • G. Shieh
  • Published 10 February 2009
  • Business
  • Multivariate Behavioral Research
In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference procedures of the squared multiple correlation coefficient have been extensively developed. In contrast, a full range of statistical methods for the… 
Sample size calculations for model validation in linear regression analysis
The results show that the exact approach has a distinct advantage over the current method with greater accuracy and high robustness.


Improved Shrinkage Estimation of Squared Multiple Correlation Coefficient and Squared Cross-Validity Coefficient
The sample squared multiple correlation coefficient is widely used for describing the usefulness of a multiple linear regression model in many areas of science. In this article, the author considers
Methodology Review: Estimation of Population Validity and Cross-Validity, and the Use of Equal Weights in Prediction
In multiple regression, optimal linear weights are obtained using an ordinary least squares (OLS) procedure. However, these linear weighted combinations of predictors may not optimally predict the
Estimating R 2 Shrinkage in Multiple Regression: A Comparison of Different Analytical Methods
Abstract The effectiveness of various analytical formulas for estimating R 2 shrinkage in multiple regression analysis was investigated. Two categories of formulas were identified: estimators of the
Cross-Validation Sample Sizes
The squared cross-validity coefficient is a measure of the predictive validity of a sample linear prediction equation. It provides a more realistic assessment of the usefulness of the equation than
The squared correlation coefficient, w2, between an empirically chosen linear function of predictors, B0 + B′x, and a criterion, y, is employed as a measure of predictive precision. This coefficient
Accuracy of Population Validity and Cross-Validity Estimation: An Empirical Comparison of Formula-Based, Traditional Empirical, and Equal Weights Procedures
An empirical monte carlo study was performed using predictor and criterion data from 84,808 U.S. Air Force enlistees. 501 samples were drawn for each of seven sample size conditions: 25, 40, 60, 80,
Confidence Intervals, Power Calculation, and Sample Size Estimation for the Squared Multiple Correlation Coefficient under the Fixed and Random Regression Models: A Computer Program and Useful Standard Tables
In this article, the authors introduce a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple
Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis
This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed
Sample Size Tables for Correlation Analysis with Applications in Partial Correlation and Multiple Regression Analysis
SAS and SPSS computer programs are made available to permit researchers to select sample size for levels of accuracy, probabilities, and parameter values and for Type I error rates other than those used in constructing the tables.
Cost-Benefit Considerations in Choosing among Cross-Validation Methods.
There are two general methods of cross-validation: (a) empirical estimation, and (b) formula estimation. In choosing a specific cross-validation procedure, one should consider both costs (eg.