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Some researchers in psychology have ordinarily relied on traditional linear models when assessing the relationship between predictor(s) and a continuous outcome, even when the assumptions of the traditional model (e.g., normality, homoscedasticity) are not satisfied. Of those who abandon the traditional linear model, some opt for robust versions of the ANOVA and regression statistics that usually focus on relationships for the typical or average case instead of trying to model relationships for the full range of relevant cases. Generalized linear models, on the other hand, model the relationships among variables using all available and relevant data and can be appropriate under certain conditions of non-normality and heteroscedasticity. In this paper, we summarize the advantages and limitations of using generalized linear models with continuous outcomes and provide two simplified examples that highlight the methodology involved in selecting, comparing, and interpreting models for positively skewed outcomes and certain heteroscedastic relationships., Author(s): Victoria K.Y. Ng [sup.1] , Robert A. Cribbie [sup.1] Author Affiliations: (1) 0000 0004 1936 9430grid.21100.32Department of Psychology, York University, 4700 Keele St, M3J 1P3, Toronto, ON, Canada Modeling [...]

We consider the problem of experimental design when the response is modeled by a generalized linear model (GLM) and the experimental plan can be determined sequentially. Most previous research on this problem has been limited either to one-factor, binary response experiments or to augmenting the design when there are already sufficient data to compute parameter estimates. We suggest a new procedure for the sequential choice of observations that offers five important advantages: (1) It can be applied to multifactor experiments and is not limited to the one-factor setting; (2) it can be used with any GLM, not just binary responses; (3) both fully sequential and group sequential settings are treated; (4) it enables efficient design from the outset of the experiment; and (5) the experimenter is not constrained to specify a single model and can use the prior to reflect uncertainty as to the link function and the form of the linear predictor. Our procedure is based on a D-optimality criterion and on a Bayesian analysis that exploits a discretization of the parameter space to efficiently represent the posterior distribution. In the one-factor setting, a simulation study shows that our method is superior in efficiency to commonly used procedures, such as the 'Bruceton' test, Neyer's procedure, or Wu's improved Robbins-Monro method. We also present a comparison of results obtained with the new algorithm versus the 'Bruceton' method on an actual sensitivity test conducted recently at an industrial plant. Source code for the algorithms and examples throughout the article is available at http://www.math.tau.ac.il/~dms/GLM_Design. KEY WORDS: Bayesian; Binary response; D-optimal; Dose-response; Poisson; Sensitivity test.

The development of a score test and constructed residual plots that could be used for checking the scale of a functional predictor in a generalized linear model is reported.

A novel multivariate exponentially weighted moving average scheme to monitor a general linear profile is presented. The schemes include both a polynomial regression and a multiple linear regression model that could be implemented in various industrial processes.