Understanding Canonical Correlation through the General Linear Model and Principal Components

Canonical correlation has been little used and little understood, even by otherwise sophisticated analysts. An alternative approach to canonical correlation, based on a general linear multivariate model, is presented. Properties of principal component analysis are used to help explain the method. Standard computational methods for full rank canonical correlation, techniques for canonical correlation on component scores, and canonical correlation with less than full rank are discussed. They are seen to be essentially equivalent when the model equation for canonical correlation on component scores is presented. The two approaches to less than full rank situations are equivalent in some senses, but quite different in usefulness, depending on the application. An example dataset is analyzed in detail to help demonstrate the conclusions.     

Ranking paired contestants

The ranking of paired contestants (players) after a series of contests is difficult when every player does not play every other player. In the 1975 JASA Mark Thompson presented a maximum likelihood solution based on the assumption that the probability of any one player defeating any other is a function only of the difference in their ranks. Here the linear approximation to that likelihood is shown to lead to a nonparametric measure of the efficacy of the ranking, called the net difference in ranks (NDR) , which is the sum of the differences in ranks of the paired players in the observed contests that agree with the ranking minus the sum of the differences in ranks in the observed contests that disagree with the ranking (upsets) . The subject is part of a large literature that has been consolidated by H.A. David in The Method of Paired Comparisons (1963, 1988). The method was introduced by the psychophysicist Fechner in 1860 and has been widely applied to sensory testing,     

Diagnostics for elliptical linear mixed models with first-order autoregressive errors

For longitudinal time series data, linear mixed models that contain both random effects across individuals and first-order autoregressive errors within individuals may be appropriate. Some statistical diagnostics based on the models under a proposed elliptical error structure are developed in this work. It is well known that the class of elliptical distributions offers a more flexible framework for modelling since it contains both light- and heavy-tailed distributions. Iterative procedures for the maximum-likelihood estimates of the model parameters are presented. Score tests for the presence of autocorrelation and the homogeneity of autocorrelation coefficients among individuals are constructed. The properties of test statistics are investigated through Monte Carlo simulations. The local influence method for the models is also given. The analysed results of a real data set illustrate the values of the models and diagnostic statistics.     

Comparison of causal effect estimators under exposure misclassification

Over the past decades, various principles for causal effect estimation have been proposed, all differing in terms of how they adjust for measured confounders: either via traditional regression adjustment, by adjusting for the expected exposure given those confounders (e.g., the propensity score), or by inversely weighting each subject's data by the likelihood of the observed exposure, given those confounders. When the exposure is measured with error, this raises the question whether these different estimation strategies might be differently affected and whether one of them is to be preferred for that reason. In this article, we investigate this by comparing inverse probability of treatment weighted (IPTW) estimators and doubly robust estimators for the exposure effect in linear marginal structural mean models (MSM) with G-estimators, propensity score (PS) adjusted estimators and ordinary least squares (OLS) estimators for the exposure effect in linear regression models. We find analytically that these estimators are equally affected when exposure misclassification is independent of the confounders, but not otherwise. Simulation studies reveal similar results for time-varying exposures and when the model of interest includes a logistic link.     

The efficacy and safety of short-acting testosterone ointment (Glowmin) for late-onset hypogonadism in accordance with testosterone circadian rhythm

Introduction: It is well known that there is a reduction of circadian rhythm in blood testosterone levels with aging. Our previous report revealed that 3?mg of short-acting testosterone ointment (Glowmin: GL) elevated serum testosterone levels to within the physiological range for 4–6?h. The aim of this study was to clarify the clinical efficacy and safety of GL used topically once every morning, to enhance the circadian rhythm of testosterone, for late-onset hypogonadism (LOH).

Methods: A total of 61 LOH patients received 3?mg of GL topically once a day in the morning on scrotal skin for 24 weeks. The clinical efficacy of GL was evaluated by the aging males symptoms (AMS) scale, and blood sampling tests were measured before and after GL treatment.

Results: Mean patients age was 55.3?±?9.2 years old. Total AMS scores at 4, 12, and 24 weeks after GL treatments significantly decreased. The results of sub-analysis of AMS, including psychological, physical, and sexual factors also significantly improved after GL treatments. No severe adverse reactions or abnormal laboratory data were reported.

Conclusions: This study shows that TRT for LOH with once daily GL treatment supports testosterone circadian rhythm and should be considered to be an effective and safe therapy for LOH.     

On shrinkage m-estimators of location parameters

For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.     

Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods

Summary.  Recently several studies have analysed active labour market policies by using a recently proposed matching estimator for multiple programmes. Since there is only very limited practical experience with this estimator, this paper checks its sensitivity with respect to issues that are of practical importance in this kind of evaluation study. The estimator turns out to be fairly robust to several features that concern its implementation. Furthermore, the paper demonstrates that the matching approach per se is no panacea for solving all the problems of evaluation studies, but that its success depends critically on the information that is available in the data. Finally, a comparison with a bootstrap distribution provides some justification for using a simplified approximation of the distribution of the estimator that ignores its sequential nature.     

A General Model of Some Inverse Combinatorial Optimization Problems and Its Solution Method Under l ∞ Norm

This paper proposes an optimization model and shows that most inverse combinatorial optimization problems so far discussed can be fit into this model as special cases. We propose a Newton-type algorithm for this model under l norm. This algorithm can solve the model in strongly polynomial time if the subproblem involved is solvable in strongly polynomial time for any fixed value of the parameter appearing in the subproblem, and it is shown that most particular inverse optimization problems encountered are this kind. Therefore, through this paper we show that a large group of inverse optimization problems can be handled in a uniform way and solved in strongly polynomial time.     

On Inverse Problems of Optimum Perfect Matching

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l ₁ or l norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l ₁ and l norms. It has been proved that the inverse maximum-weight perfect matching under l norm can be formulated as a maximum-mean alternating cycle problem of an undirected network, and can be solved in polynomial time by a binary search algorithm and in strongly polynomial time by an ascending algorithm, and under l ₁ norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l ₁ and l norms are solvable in polynomial time.