Lattice square approach to construction of mutually orthogonalF-squares

Summary Factorial design theory has been effectively used in solving problems associated with many combinatorial structures. Hedayat, Raghavarao and Seiden [7] clearly demonstrated this in obtaining various results onF(n, λ)-squares. Indeed, both theorems in their paper are cute observations if knowledge of factorial design theory is assumed. The objective of this paper is to present the lattice square method for obtaining sets of mutually orthogonalF(n, λ)-squares of given ordern. As a by-product a generalization of a theorem, due to the above authors, is obtained and a lower bound is presented for the number of mutually orthogonalF(n, λ)-squares on sets of various cardinalities associated with the canonical decomposition ofn as a product of powers of distinct primes.     

混合水平正交设计的最优选择

利用矩阵象方法,首先将强度2下混合水平正交设计的混杂度量,推广到强度t下混合水平正交设计的混杂度量,然后通过这些混杂度量指标,给出了强度t下混合水平正交设计的四个分辨度指标,其具有水平置换不变性,并能同时用于等水平情形和混合水平情形。最后对混合水平正交表OA(18,6~13~6,2)进行了实例计算,并讨论四个分辨度的差异性。     

Relations among homogeneity,collapsibility and nonconfounding in distribution effects

In this paper, the concept of distribution effect is proposed without the causal diagram. Following the notation of Stone [11], we assume that the exposure treatment X is an unknown deterministic function of the confounder set Pa(X) and a random error ε. We discuss sufficient and necessary conditions for homogeneity, collapsibility and nonconfounding for distribution effects and discuss relations among them.     

一般最小低阶混杂设计的统计性质

本文旨在研究满足N/4+2≤n≤5N/16的GMC 2n-m设计的统计性质(N=2n-m),首先通过研究这些设计别名关系来讨论其估计能力,然后提出了一种新的理论方法用以得到这些设计的混杂信息,最后给出了可供实际使用的试验表格.     

A theory on constructing blocked two-level designs with general minimum lower order confounding

Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.     

copCAR: A Flexible Regression Model for Areal Data

Non-Gaussian spatial data are common in many fields. When fitting regressions for such data, one needs to account for spatial dependence to ensure reliable inference for the regression coefficients. The two most commonly used regression models for spatially aggregated data are the automodel and the areal generalized linear mixed model (GLMM). These models induce spatial dependence in different ways but share the smoothing approach, which is intuitive but problematic. This article develops a new regression model for areal data. The new model is called copCAR because it is copula-based and employs the areal GLMM’s conditional autoregression (CAR). copCAR overcomes many of the drawbacks of the automodel and the areal GLMM. Specifically, copCAR (1) is flexible and intuitive, (2) permits positive spatial dependence for all types of data, (3) permits efficient computation, and (4) provides reliable spatial regression inference and information about dependence strength. An implementation is provided by R package copCAR, which is available from the Comprehensive R Archive Network, and supplementary materials are available online.     

临床医学论文中的统计问题

本文对中华医学会主办的１４种临床医学和基础医学杂志发表的１５５篇论著，从医学统计的角度，按２２项指标，进行了一次调查研究。结果表明，与１９８０年中华医学会召开医学科研设计座谈会以前的情况相比，论文质量有了明显提高，但仍存在不少不可忽视的问题。常见的问题有：试验设计不良，缺少防止偏性的有力措施，组间可比性差，样本含量不足；对两类错误的控制、置信限的应用和排除混杂因子的影响重视不够；统计软件、统计图和多元分析方法的利用率还不够高。针对存在问题提出了一些见解和建议。     

Beyond Simpson's paradox: A descriptive approach

In considering the strength of association of particular variables, we cannot ignore the effects of confounding factors that cause Simpson's paradox. Many methods for adjusting these effects have been proposed, and a great deal of effort has been devoted to statistical tests. Apart from the statistical tests, the aim of the present study is to examine the strength of association of two categorical variables without reference to any explicit confounding factors. In other words, our aim is to specify the conditions under which Simpson's paradox does not occur, where the idea of classifying the original universe into groups is adopted. Let us begin by focusing our attention on a 2 × 2 contingency table (cross-classification table) and considering the association of X with Y, where X and Y denote dichotomous variables with classes A and B for X and classes + and − for Y. To examine the strength of association between these variables, the index k = q/p is used, where p denotes the proportion of A + in A and q denotes that of B + in B. Using the maximum and minimum values of the index k obtained by numerical calculation, the strength of association is examined. The results are discussed and examples given. © 1996 John Wiley & Sons, Ltd.     

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction; our methods also compare favorably to existing “reduced-rank” approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types. Supplementary material for this article is available online.