Optimal Split-plot Designs for a Mixed Model

Exact tests are given, for the usual hypotheses on split-plot models with random blocks and fixed treatment effects, considering different numbers of blocks for each level of whole-plot treatment and assuming normally distributed observations. U- and D-optimal designs are considered with respect to the tests of main effects and interactions as well as to estimation of parameters.     

Creating Dynamic Images of Short-lived Dopamine Fluctuations with lp-ntPET: Dopamine Movies of Cigarette Smoking

We describe experimental and statistical steps for creating dopamine movies of the brain from dynamic PET data. The movies represent minute-to-minute fluctuations of dopamine induced by smoking a cigarette. The smoker is imaged during a natural smoking experience while other possible confounding effects (such as head motion, expectation, novelty, or aversion to smoking repeatedly) are minimized.We present the details of our unique analysis. Conventional methods for PET analysis estimate time-invariant kinetic model parameters which cannot capture short-term fluctuations in neurotransmitter release. Our analysis - yielding a dopamine movie - is based on our work with kinetic models and other decomposition techniques that allow for time-varying parameters ^1-7. This aspect of the analysis - temporal-variation - is key to our work. Because our model is also linear in parameters, it is practical, computationally, to apply at the voxel level. The analysis technique is comprised of five main steps: pre-processing, modeling, statistical comparison, masking and visualization. Preprocessing is applied to the PET data with a unique ''HYPR'' spatial filter ⁸ that reduces spatial noise but preserves critical temporal information. Modeling identifies the time-varying function that best describes the dopamine effect on ¹¹C-raclopride uptake. The statistical step compares the fit of our (lp-ntPET) model ⁷ to a conventional model ⁹. Masking restricts treatment to those voxels best described by the new model. Visualization maps the dopamine function at each voxel to a color scale and produces a dopamine movie. Interim results and sample dopamine movies of cigarette smoking are presented.     

Size distributions of chylomicrons from human lymph from dynamic light scattering measurements

Chylomicrons, the vehicles for the transport of exogeneous triglycerides and cholesterol in the lymph and the blood, were characterized by their size from dynamic light scattering measurements. To achieve an appropriate resolution, correlation data were collected over several hours. Analysis was performed with an extended version of the regularization method CONTIN, and special attention was given to errors in the experimental baseline and to randomness of the residuals. The solutions selected by means of Fisher's F-test by CONTIN agreed with those obtained with the stability plot of Schnablegger and Glatter, when in the case of data of lower statistical accuracy the solution was taken from the lower part of the confidence interval of the F-test. The intensity-weighted size distributions indicated two classes of particle, their mean diameters being 100–140 nm and 330–350 nm. The ability to resolve two peaks of such a size ratio is demonstrated. The numbers of particles associated with the two peaks were estimated by means of the scattering properties of the particles, which showed that the overwhelming majority were small ones. This estimation also suggested that the mean size of the first peak of the number distribution is significantly smaller than the typical size of chylomicrons. This was consistent with the finding that the sample contained not only apolipoprotein B-48 but also a similar amount of apolipoprotein B-100, which is associated with lipoproteins of smaller size. The larger particles of the second peak are probably dietary triglyceride-rich chylomicrons. Received: 12 October 1997 / Revised version: 26 June 1998 / Accepted: 7 August 1998     

F-tests for Hypotheses with Block Matrices and Under Conditions of Orthogonality in the General Multivariate Gauss-Markoff Model

The multivariate general Gauss-Markoff (MGM) model (U, XB, ∑?σ²V) when the matrices V ≥ 0 and ∑ > 0 are known and the scalar σ² > 0 is unknown, is considered. The present paper is a continuation of two earlier works (Oktaba, 1988a, b). If XB = X₁Σ + X₂Δ, then the F-test for verification the hypothesis WΣA = 0 is presented. Moreover, under conditions of orthogonality the decomposition of the matrix S_A (?BCA)′L^?(?BCA) into the sum of s = r(L) matrices is given, where ?BCA is the estimator of the parametric estimable functions ?BCA, Cov (?BCA) = A′ ∑?σ²L = ?C₄?′, B? = (X′T^?X)^?X′T^?U, C₄ = (X′T^?X)^?M, where M = M′ is any arbitrary matrix such that R(X) ? R(T), T=V+XMX′; T^? is any c-inverse. R(A) is the linear space generated by the colums of A. Then under additional assumption on normality of U the statistics F for testing ?BA = 0 is deduced. Under conditions of normality of U and decomposition of S_A, the statistics F₁, …, F_s for the hypotheses jⁱ BA = 0 (i = 1,…, s) are established.     

On the Effects of Departure from Normality on the F-Ratios in a Nested Random Effect Model by Mixture of Normals

In this paper we consider the following nested random effect model where the α_i's, the β_ij's and the e_ijk are independent random variables. By assuming that these variables follow a mixture of two normal densities, we study the effects of departure from normality on the classical JT-tests for variance components. It is shown that the departure from normality has little effects on the type 1 error and the power function; this indicates that the classical F-tests are quite robust with respect to departure from normality.     

A new approach for obtaining rapid uniformity in rice (Oryza sativa L.) via a 3x x 2x cross

A triploid (2n = 3x = 36) rice plant was obtained by screening a twin seedling population in which each seed germinated to two or three sprouts that were then crossed with diploid plants. One diploid plant was chosen among the various F(1) progenies and developed into an F (2) population via self-pollination. Compared with the control variety Shanyou 63, this F (2) population had a stable agronomical performance in field trials, as confirmed by the F-test. The stability of the F (2) population was further substantiated by molecular analysis with simple sequence repeat markers. Specifically, of 160 markers assayed, 37 (covering all 12 chromosomes) were polymorphic between the parental lines. Testing the F (1) hybrid individually with these markers showed that each PCR product had only a single band instead of two bands from each parent. The bands were identical to either maternal (23 markers) or paternal (eight markers) bands or distinct from both parents (six markers). The amplified bands of all 60 randomly selected F (2) plants were uniform and identical to those of the F (1) hybrid. These results suggest that the F (1) plant is a non-segregating hybrid and that a stable F (2) population was obtained. This novel system provides an efficient means for shortening the cycle of hybrid rice seed production.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.