Regression Analysis, Prediction, and Agreement

Abstract

Evaluations of the regression, prediction, and agreement methods described here are based on the permutation approach. In addition, emphasis is again placed on statistical procedures that closely correspond to the geometrical structure of the data in question. Following some preliminary historical comments regarding linear regression, general descriptions of permutationbased regression analyses are presented. MRPP analyses of least (sum of) absolute deviations (LAD) regression residuals are described for various experimental designs. MRPP regression analyses, Cade-Richards regression analyses, and classical ordinary least (sum of) squared deviations (OLS) regression analyses are compared. Next, MRPP confidence intervals for regression parameters are described. Since the validation of prediction models is a major concern for many fields, the results of recent studies involving drop-one cross-validation and the use of either LAD or OLS regression are discussed. In addition, effects on agreement by various conditions such as sample size, population agreement value, inclusion of redundant predictors, and varying severity of data contamination are examined. Finally, linear and nonlinear multivariate regression models and their applications are discussed.KeywordsRegression ModelDesign MatrixTarget ShapeEffect CodePearson TypeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.