A modified signed likelihood ratio test in elliptical structural models

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

A conditional likelihood ratio test for structural models

This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reducedform covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson- Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

A comparison of discriminant logistic regression and Item Response Theory Likelihood-Ratio Tests for Differential Item Functioning (IRTLRDIF) in polytomous short tests

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A likelihood ratio appropach to family-based association studies with covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

The use of the likelihood ratio for evaluative and investigative purposes in comparative forensic handwriting examination

This paper extends previous research and discussion on the use of multivariate continuous data, which are about to become more prevalent in forensic science. As an illustrative example, attention is drawn here on the area of comparative handwriting examinations. Multivariate continuous data can be obtained in this field by analysing the contour shape of loop characters through Fourier analysis. This methodology, based on existing research in this area, allows one describe in detail the morphology of character contours throughout a set of variables. This paper uses data collected from female and male writers to conduct a comparative analysis of likelihood ratio based evidence assessment procedures in both, evaluative and investigative proceedings. While the use of likelihood ratios in the former situation is now rather well established (typically, in order to discriminate between propositions of authorship of a given individual versus another, unknown individual), focus on the investigative setting still remains rather beyond considerations in practice. This paper seeks to highlight that investigative settings, too, can represent an area of application for which the likelihood ratio can offer a logical support. As an example, the inference of gender of the writer of an incriminated handwritten text is forwarded, analysed and discussed in this paper. The more general viewpoint according to which likelihood ratio analyses can be helpful for investigative proceedings is supported here through various simulations. These offer a characterisation of the robustness of the proposed likelihood ratio methodology.

Uncertainty about the true source. A note on the likelihood ratio at the activity level.

This paper focuses on likelihood ratio based evaluations of fibre evidence in cases in which there is uncertainty about whether or not the reference item available for analysis - that is, an item typically taken from the suspect or seized at his home - is the item actually worn at the time of the offence. A likelihood ratio approach is proposed that, for situations in which certain categorical assumptions can be made about additionally introduced parameters, converges to formula described in existing literature. The properties of the proposed likelihood ratio approach are analysed through sensitivity analyses and discussed with respect to possible argumentative implications that arise in practice.

Influence of Bacille Calmette-Guérin vaccination on size of tuberculin skin test reaction : to what size ?

RESUME Le diagnostic d'infection tuberculeuse repose essentiellement sur le test tuberculinique (test de Mantoux). Cependant, le résultat de ce dernier est également influencé par d'autres facteurs, le plus important étant la vaccination par le Bacille Calmette-Guérin (BCG), interaction connue depuis de nombreuses années. Il est généralement admis que l'effet de la vaccination peut entraîner des réactions positives jusqu'à un diamètre d'induration de 15 mm. Au-delà, la positivité du test est en général attribuée à une primo-infection tuberculeuse. Peu d'études se sont réellement penchées sur le sujet. Chez le personnel de soins soumis à des Mantoux répétés, cette notion revêt une importance particulière pour interpréter correctement une réaction fortement positive en l'absence de facteurs de risque tuberculeux, dans un pays à faible endémie tuberculeuse. Notre étude a cherché à déterminer si le diamètre transversal de l'induration du Mantoux était un critère fiable pour distinguer une positivité associée à une infection tuberculeuse de celle associée à une ancienne vaccination. Elle s'est attachée à rechercher un seuil au-delà duquel l'infection tuberculeuse pourrait être considérée comme probable. Entre janvier 1991 et mars 1998, tous les nouveaux employés du CHUV ont été invités à recevoir un test tuberculinique à l'occasion de leur visite d'entrée à la Médecine du personnel. En cas de réponse négative, un deuxième test a été pratiqué une semaine plus tard, pour détecter un éventuel effet booster. Lors de la première visite, l'infirmière a rempli un questionnaire comprenant les données démographiques usuelles, des informations concernant les facteurs pouvant influencer la positivité du test, notamment les antécédents de vaccination par le BCG, les expositions à la tuberculose et l'existence d'antécédents d'infection tuberculeuse. Parmi les 5117 sujets inclus dans l'étude, nous avons trouvé que l'influence de la vaccination variait en fonction de l'âge. Chez les sujets de moins de 40 ans, la vaccination par le BCG était le prédicteur le plus important d'un Mantoux positif inférieur à 18 mm, de loin supérieur aux facteurs de risque habituels pour une infection tuberculeuse, eux aussi significatifs. L'effet du BCG était présent pour des réactions allant jusqu'à 20 mm. Pour les Mantoux supérieurs à 20 mm, l'odds ratio (OR) relatif au BCG demeure clairement élevé (supérieur à 3,4) bien que non significatif. Par contre, pour les employés âgés de plus de 40 ans, le BCG est un facteur prédictif pour les tests supérieurs à 10 mm (OR 2.4) mais n'est plus un facteur significatif pour une taille supérieure à 15 mm. Ces résultats montrent que l'interprétation d'un test tuberculinique même fortement positif, doit être faite avec prudence et discernement. En effet, notre étude démontre que chez les sujets vaccinés de moins de 40 ans, dans les zones de faible endémie tuberculeuse particulièrement en l'absence de facteurs de risque pour une infection tuberculeuse, un Mantoux positif jusqu'à 18 mm est dû, le plus probablement, à une ancienne vaccination par le BCG, plutôt qu'à une infection par M tuberczilosis. L'interprétation des Mantoux de taille inférieure à 18 mm et les Mantoux effectués chez des sujets de moins de 40 ans, doit prendre en compte l'existence d'un BCG antérieur. En conséquence, la mise en évidence d'une réaction de Mantoux fortement positive ne devrait pas conduire systématiquement à un traitement préventif. L'absence de spécificité du test Mantoux, utilisé pour le dépistage de la tuberculose depuis bientôt une centaine d'année, est un problème connu. Nous démontrons que la taille de l'induration ne peut pas être utilisée de façon fiable comme critère pour identifier une infection tuberculeuse chez une personne vaccinée avec le BCG, avec le risque de sui-traiter un nombre important de sujets. Dans notre étude, 21% des sujets avaient un Mantoux supérieur ou égal à 15 mm et auraient dû être traités selon les recommandations en vigueur en Suisse si l'on ne tenait pas compte du BCG antérieur. Des tests plus spécifiques sont actuellement à l'étude et permettront vraisemblablement, à l'avenir, de palier au problème de l'absence de spécificité du test de Mantoux. Abstract : Background. Previous bacillus Calmette-Guerin (BCG) vaccination can confound the results of a tuberculin skin test (TST). We sought to determine a cutoff diameter of TST induration beyond which the influence of BCG vaccination was negligible in evaluating potential Mycobacterium tuberculosis infection in a population of health care workers with a high vaccination rate and low incidence of tuberculosis. Methods. From 1991 through 1998, all new employees at the University Hospital of Lausanne, Switzerland, underwent a 2-step TST at entry visit. We also gathered information on demographic characteristics, along with factors commonly associated with tuberculin positivity, including previous BCG vaccination, history of latent M. tuberculosis infection, and predictors for M. tuberculosis infection. Results. Among the 5117 investigated subjects, we found that influence of BCG vaccination on TST results varied across categories of age (likelihood ratio test, 0.0001). Prior BCG vaccination had a strong influence on skin test results of mm in diameter among persons <40 years old, compared with the influence of factors predictive of M. tuberculosis infection. Prior latent M. tuberculosis infection and travel or employment in a country in which tuberculosis is endemic also had significant influences. Conclusions. Interpretation of TST reactions of mm among BCG-vaccinated persons <40 years of age must be done with caution in areas with a low incidence of tuberculosis. In such a population, except for persons who have never been vaccinated, TST reactions of ---518 mm are more likely to be the result of prior vaccination than infection and should not systematically lead to preventive treatment.

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

On the use of the likelihood ratio for forensic evaluation: response to Fenton et al.

This letter to the Editor comments on the article When 'neutral' evidence still has probative value (with implications from the Barry George Case) by N. Fenton et al. [[1], 2014].

HIERFSTAT, a package for R to compute and test hierarchical F-statistics

The package HIERFSTAT for the statistical software R, created by the R Development Core Team, allows the estimate of hierarchical F-statistics from a hierarchy with any numbers of levels. In addition, it allows testing the statistical significance of population differentiation for these different levels, using a generalized likelihood-ratio test. The package HIERFSTAT is available at http://www.unil.ch/popgen/softwares/hierfstat.htm.