When the component proportions in mixture experiments are restricted by lower and upper bounds, the design space can become an irregular region that can induce multicollinearity among the component proportions. Thus, we suggest the use of ridge regression as a means of stabilizing the estimates of the coefficients in the fitted model. We use fraction of design space plots and violin plots to illustrate and evaluate the effect of ridge regression estimators with respect to the prediction variance and to guide the decision about the value of ridge constant k. We illustrate the methods with three examples from the literature.
When there are constraints on resources, an unreplicated factorial or fractional factorial design can allow efficient exploration of numerous factor and interaction effects. A half‐normal plot is a common graphical tool used to compare the relative magnitude of effects and to identify important effects from these experiments when no estimate of error from the experiment is available. An alternative is to use a least absolute shrinkage and selection operation plot to examine the pattern of model selection terms from an experiment. We examine how both the half‐normal and least absolute shrinkage and selection operation plots are impacted by the absence of individual observations or an outlier, and the robustness of conclusions obtained from these 2 techniques for identifying important effects from factorial experiments. The methods are illustrated with 2 examples from the literature.
Similar to regression, many measures to detect influential data points in discriminant analysis have been developed. Many follow similar principles as the diagnostic measures used in linear regression in the context of discriminant analysis. Here we focus on the impact on the predicted classification posterior probability when a data point is omitted. The new method is intuitive and easily interpretable compared to existing methods. We also propose a graphical display to show the individual movement of the posterior probability of other data points when a specific data point is omitted. This enables the summaries to capture the overall pattern of the change.
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