Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence

To model an hypothesis of double monotone dependence between two ordinal categorical variables A and B usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined, respectively, on the conditional distributions of A given B and on the conditional distributions of B given A are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non-standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model.This work has been supported by the COFIN 2002 project, references 2002133957_002, 2002133957_004. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Bari, 2004.     

Comparing diagnostic tests: test of hypothesis for likelihood ratios

Likelihood ratios (LRs) are used to characterize the efficiency of diagnostic tests. In this paper, we use the classical weighted least squares (CWLS) test procedure, which was originally used for testing the homogeneity of relative risks, for comparing the LRs of two or more binary diagnostic tests. We compare the performance of this method with the relative diagnostic likelihood ratio (rDLR) method and the diagnostic likelihood ratio regression (DLRReg) approach in terms of size and power, and we observe that the performances of CWLS and rDLR are the same when used to compare two diagnostic tests, while DLRReg method has higher type I error rates and powers. We also examine the performances of the CWLS and DLRReg methods for comparing three diagnostic tests in various sample size and prevalence combinations. On the basis of Monte Carlo simulations, we conclude that all of the tests are generally conservative and have low power, especially in settings of small sample size and low prevalence.     

Evidential inference for diffusion-type processes

This article analyses diffusion-type processes from a new point-of-view. Consider two statistical hypotheses on a diffusion process. We do not use a classical test to reject or accept one hypothesis using the Neyman–Pearson procedure and do not involve Bayesian approach. As an alternative, we propose using a likelihood paradigm to characterizing the statistical evidence in support of these hypotheses. The method is based on evidential inference introduced and described by Royall [Royall R. Statistical evidence: a likelihood paradigm. London: Chapman and Hall; 1997]. In this paper, we extend the theory of Royall to the case when data are observations from a diffusion-type process instead of iid observations. The empirical distribution of likelihood ratio is used to formulate the probability of strong, misleading and weak evidences. Since the strength of evidence can be affected by the sampling characteristics, we present a simulation study that demonstrates these effects. Also we try to control misleading evidence and reduce them by adjusting these characteristics. As an illustration, we apply the method to the Microsoft stock prices.     

中国婚姻挤压研究的回顾与评述

通过对检索文献的分析,从婚姻挤压的现状、原因、测度和影响等几个方面对我国学者就婚姻挤压研究取得的成果进行了综述,回顾了主要的研究成果,指出了研究的不足之处,并对未来研究做出展望,笔者最后建议从人口安全与和谐社会这两个角度研究婚姻挤压问题。     

Alone and adrift: The association between mass school shootings,school size,and student support

Background

School shootings have approached epidemic levels in recent years. While mental illness is undoubtedly involved in nearly all cases of mass school violence, we sought to determine how environmental context may exacerbate preexisting personal factors. The present study investigated the associations between mass school shootings, school enrollment size, student–teacher ratios, and student transitions.

Mortality following conjugal bereavement,Belgium 1991-96: The unexpected effect of education

This paper examines excess mortality following spousal bereavement by time since bereavement, sex, age, and education. The main hypothesis challenged is that higher education buffers the harmful effects of spousal loss. Using a log-rate model, death-rate ratios (widowed/married) are estimated for 49,849 and 126,746 Belgian widowers and widows and an equal number of non-bereaved controls matched to the bereaved on their socio-demographic characteristics. The hypothesis that the more educated suffer less excess mortality is not supported. Although higher educational levels are associated with lower mortality in general, they do not alleviate the effects of bereavement. On the contrary, in the period immediately following spousal loss, the more highly educated seem to have more, rather than less, excess mortality. Three possible arguments are suggested to account for this: education-related differences in the partner-relationship, structural differences in the availability of appropriate social support, and cultural differences in potential support networks.     

Modelling two way contingency tables with recursive logits and odds ratios

In this work a new type of logits and odds ratios, which includes as special cases the continuation and the reverse-continuation logits and odds ratios, are defined. We prove that these logits and odds ratios define a parameterization of the joint probabilities of a two way contingency table. The problem of testing equality and inequality constraints on these logits and odds ratios is examined with particular regard to two new hypotheses of monotone dependence. Work partially supported by a MIUR2004 grant. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Torino, 2006.     

A Weighted Composite Dose – Response Model For Human Salmonellosis

This article describes the development of a weighted composite dose – response model for human salmonellosis. Data from previously reported human challenge studies were categorized into two different groups representing low and moderately virulent/pathogenic Salmonella strains based on a disease end point. Because epidemiological data indicate that some Salmonella strains are particularly pathogenic, and in the absence of human feeding study data for such strains, Shigella dysenteriae was used as a proxy for highly virulent strains. Three single-hit dose – response models were applied to the human feeding study data and evaluated for best fit using maximum likelihood estimation: (1) the exponential (E-1pop), (2) the two-subpopulation exponential (E-2pop), and (3) the Beta-Poisson (BP). Based on the goodness-of-fit test, the E-1pop and BP were the best-fit models for low and moderately virulent/pathogenic Salmonella strains, and the E-2pop and BP models were better for highly virulent/pathogenic strains. Epistemic analysis was conducted by determining the degree of confidence associated with the selected models, which was found to be 50%/50% (E-1pop/BP) for low and moderately pathogenic Salmonella strains, and 9.8%/90.2% (E-2pop/BP) for highly virulent strains. The degree of confidence for each component model and variations in the proportion of strains within each virulence/pathogenicity category were incorporated into the overall composite model. This study describes the influence of variation in strain virulence and host susceptibility on the shape of the population dose – response relationship.     

On a statistic useful in dimensionality reduction in multivariable linear stochastic system

In this paper we study the sampling properties of a test statistic which has important applications in the area of linear stochastic control systems with multi-inputs and multi-outputs. The statistic is the ratio of a partial sum of the eigenvalues of a sample covariance matrix and its trace. It turns out that using a method due to Sugiura we may derive a useful approximation for its distribution up to and including terms of order l/n, where n denotes the appropriate size. Numerical illustrations using real data are given.     

Non-Normal Bivariate Distributions with Normal Marginals

The purpose of this note is to indicate that Fieller's Theorem can be expressed in the matrix formulation of the general linear model. The practical consequence is that one general computer program which can estimate the parameters and test the validity of a pertinent model, can also compute confidence limits for the ratios of any linear combinations of the parameters.