Comparing alternating logistic regressions to other approaches to modelling correlated binary data

Alternating logistic regressions (ALRs) seem to offer some of the advantages of marginal models estimated via generalized estimating equations (GEE) and generalized linear mixed models (GLMMs). Via simulation study we compared ALRs to marginal models estimated via GEE and subject-specific models estimated via GLMMs, with a focus on estimation of the correlation structure in three-level data sets (e.g. students in classes in schools). Data set size and structure, and amount of correlation in the data sets were varied. For simple correlation structures, ALRs performed well. For three-level correlation structures, all approaches, but especially ALRs, had difficulty assigning the correlation to the correct level, though sample sizes used were small. In addition, ALRs and GEEs had trouble attaching correct inference to the mean effects, though this improved as overall sample size improved. ALRs are a valuable addition to the data analyst's toolkit, though care should be taken when modelling data with three-level structures.     

制冷剂在毛细管内流动过程的数值模拟及程序实用化

本文给出了一个既考虑热力学非平衡的影响,又考虑汽、液相间相对速度的毛细管内带有汽化过程的两相流数学模型。模型计算结果与试验数据的一致性及计算程序的实用化处理表明,它不仅可用来分析制冷剂在毛细管内的流动机理和特性,还可应用于小型制冷系统设计中毛细管几何参数的选择及系统的参数匹配。     

Discrete approximations to continuous univariate distributions—an alternative to simulation

A method to replace a continuous univariate distribution with a discrete distribution that takes MN different values is analysed. Both distributions share the same r th moments for r =0, . . ., 2 N −1 and their corresonding distribution functions coincide at least at M +1 points. Several statistical and engineering examples are considered in which the discrete approximation may be used to avoid a simulation study that would be much more demanding computationally.     

Parameter estimation for partially observed hypoelliptic diffusions

Summary.  Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small intersample times Δ t and large total observation times N  Δ t . Hypoellipticity together with partial observation leads to ill conditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with an application of the Gibbs sampler to molecular dynamics data.     

On the effect of the number of quadrature points in a logistic random effects model: an example

Although generalized linear mixed models are recognized to be of major practical importance, it is also known that they can be computationally demanding. The problem is the evaluation of the integral in calculating the marginalized likelihood. The straightforward method is based on the Gauss–Hermite technique, based on Gaussian quadrature points. Another approach is provided by the class of penalized quasi-likelihood methods. It is commonly believed that the Gauss–Hermite method works relatively well in simple situations but fails in more complicated structures. However, we present here a strikingly simple example of a logistic random-intercepts model in the context of a longitudinal clinical trial where the method gives valid results only for a high number of quadrature points ( Q ). As a consequence, this result warns the practitioner to examine routinely the dependence of the results on Q . The adaptive Gaussian quadrature, as implemented in the new SAS procedure NLMIXED, offered the solution to our problem. However, even the adaptive version of Gaussian quadrature needs careful handling to ensure convergence.     

Even More Direct Calculation of the Variance of a Maximum Penalized-Likelihood Estimator

We discuss here two examples of estimation by numerical maximization of penalized likelihood. We show that, in these examples, it is simpler not to use the EM algorithm for computation of the estimates or their standard errors. We discuss also confidence and credibility intervals based on penalized likelihood and a chi-squared approximate distribution, and compare such intervals with intervals of Wald type.

[Received July 2014. Revised September 2015.]     

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

We review and discuss numerical inversion of the characteristic function as a tool for obtaining cumulative distribution functions. With the availability of high-speed computing and symbolic computation software, the method is ideally suited for instructional purposes, particularly in the illustration of the inversion theorems covered in graduate probability courses. The method is also available as an alternative to asymptotic approximations, Monte Carlo, or bootstrap techniques when analytic expressions for the distribution function are not available. We illustrate the method with several examples, including one which is concerned with the detection of possible clusters of disease in an epidemiologic study.     

Discussion

A number of studies have investigated the numerical reliability of the GAUSS Mathematical and Statistical System by Aptech Inc. Those studies identified several critical accuracy errors for different computational methods. We conducted comprehensive tests of this widely used package on estimation, statistical distributions, and random number generation and found that GAUSS 8.0 still has serious problems, especially with statistical distributions and random number generation.     

Gibbs sampling in DP-based nonlinear mixed effects models

This article uses several approaches to deal with the difficulty involved in evaluating the intractable integral when using Gibbs sampling to estimate the nonlinear mixed effects model (NLMM) based on the Dirichlet process (DP). For illustration, we applied these approaches to real data and simulations. Comparisons are then made between these methods with respect to estimation accuracy and computing efficiency.     

Random effects regression models for count data with excess zeros in caries research

We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.