Assessing The Adequacy Of Split-Plot Design Models

This paper assesses the adequacy of model fit of the split-plot design models, that is the whole plot (WP) sub-design model with WP error and the split-plot (SP) sub-design model with SP error for comparing the effectiveness of resistant measures that use medians instead of means, resulting in a coefficient that is more resistant to outliers or extreme data points. This paper presents empirical application of four measures of model adequacy check and they are coefficient of determination (R2), modelling efficiency (MEF) statistic, prediction coefficient of determination (R2prod), and mean square error prediction (MSEP). These four measures were explored using their mean and median form. A 2(1+3) replicated two-level SP design and a 31 × 42 replicated mixed level SP design were used for computing the measures of model adequacy of fit for each WP and SP sub-design models. These measures in their median form described the predictive performance of each WP and SP sub-design models adequately.

[1]  Sergio Bermejo,et al.  Oriented principal component analysis for large margin classifiers , 2001, Neural Networks.

[2]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[3]  D. M. Allen.  Mean Square Error of Prediction as a Criterion for Selecting Variables , 1971 .

[4]  Murat Kulahci,et al.  Checking the Adequacy of Fit of Models from Split-Plot Designs , 2009 .

[5]  J. E. Sheehy,et al.  Comparison of predictions and observations to assess model performance: a method of empirical validation , 1997 .

[6]  P. L. Mitchell.  Misuse of regression for empirical validation of models , 1997 .

[7]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[8]  Taylor Francis Online,et al.  The American statistician , 1947 .

[9]  Luis Orlindo Tedeschi,et al.  Assessment of the adequacy of mathematical models , 2006 .

[10]  David M. Allen,et al.  The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction , 1974 .

[11]  Karen A. F. Copeland.  Design and Analysis of Experiments, 5th Ed. , 2001 .

[12]  C. Willmott.  Some Comments on the Evaluation of Model Performance , 1982 .

[13]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[14]  K. Loague,et al.  Statistical and graphical methods for evaluating solute transport models: Overview and application , 1991 .

[15]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[16]  J. B. Dent,et al.  Systems Simulation in Agriculture , 1979, Springer Netherlands.

[17]  T. O. Kvålseth.  Cautionary Note about R 2 , 1985 .

[18]  Daniel Wallach,et al.  Mean squared error of prediction as a criterion for evaluating and comparing system models , 1989 .

[19]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.