Contrasts are an important component of the armamentarium of the statistician. In the SAS/STAT R © GLM, ANOVA, MIXED, and GENMOD procedures, the contrasts are used to answer specific additional questions. In many cases, it is difficult to define contrasts which are estimable, or correctly formed. A macro which converts a question about differences between cells (defined in several ways) into es...

In a recent paper on mixed-effects models for confirmatory analysis, Barr et al. (2013) offered the following guideline for testing interactions: “one should have byunit [subject or item] random slopes for any interactions where all factors comprising the interaction are within-unit; if any one factor involved in the interaction is between-unit, then the random slope associated with that intera...

A balanced two-factor ANOVA yields a highly significant effect of watering treatment (F = 10.55, df = 1, 24, P = 0.003) and nonsignificant effects of source (F = 0.47, df = 2, 24, P = 0.628) and the watering treatment x source interaction (F = 0.05, df = 2, 24, P = 0.955). There is one low outlier, and one of the treatment groups (Heeia fresh) had substantially less variation than the others, b...

A new scheme is proposed for fusing multisensor images in which one image is regarded as the main image and the other the complementary, based on the evaluation of certain characteristics in the images. In effect, the scheme is used to fuse an image pair in which one image is superior to the other for interpretation in terms of higher resolution, better image quality, or having more recognizabl...

Abstract: For the balanced ANOVA setup, we propose a new closed form Bayes factor without integral representation, which is however based on fully Bayes method, with reasonable model selection consistency for two asymptotic situations (either number of levels of the factor or number of replication in each level goes to infinity). Exact analytical calculation of the marginal density under a spec...

A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such a...