Thomas F Suesse

Graphical diagnostics to check model misspecification for the proportional odds regression model.

The cumulative logit or the proportional odds regression model is commonly used to study covariate effects on ordinal responses. This paper provides some graphical and numerical methods for checking the adequacy of the proportional odds regression model. The methods focus on evaluating functional misspecification for specific covariate effects, but misspecification of the link function can also be dealt with under the same framework. For the logistic regression model with binary responses, Arbogast and Lin (Statist. Med. 2005; 24:229-247) developed similar graphical and numerical methods for assessing the adequacy of the model using the cumulative sums of residuals. The paper generalizes their methods to ordinal responses and illustrates them using an example from the VA Normative Aging Study. Simulation studies comparing the performance of the different diagnostic methods indicate that some of the graphical methods are more powerful in detecting model misspecification than the Hosmer-Lemeshow-type goodness-of-fit statistics for the class of models studied.

Bayesian nonparametric reliability analysis for a railway system at component level

Railway system is a typical large-scale complex system with interconnected sub-systems which contain numerous components. System reliability is retained through appropriate maintenance measures and cost-effective asset management requires accurate estimation of reliability at the lowest level. However, real-life reliability data at component level of a railway system is not always available in practice, let alone complete. The component lifetime distributions from the manufacturers are often obscured and complicated by the actual usage and working environments. Reliability analysis thus calls for a suitable methodology to estimate a component lifetime under the conditions of a lack of failure data and unknown and/or mixture lifetime distributions. This paper proposes a nonparametric Bayesian approach with a Dirichlet Process Mixture Model (DPMM) to facilitate reliability analysis in a railway system. Simulation results will be given to illustrate the effectiveness of the proposed approach in lifetime estimation.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Marginalized Exponential Random Graph Models

Exponential random graph models (ERGMs) are a popular tool for modeling social networks representing relational data, such as working relationships or friendships. Data on exogenous variables relating to participants in the network, such as gender or age, are also often collected. ERGMs allow modeling of the effects of such exogenous variables on the joint distribution, specified by the ERGM, but not on the marginal probabilities of observing a relationship. In this article, we consider an approach to modeling a network that uses an ERGM for the joint distribution of the network, but then marginally constrains the fit to agree with a generalized linear model (GLM) defined in terms of this set of exogenous variables. This type of model, which we refer to as a marginalized ERGM, is a natural extension of the standard ERGM that allows a convenient population-averaged interpretation of parameters, for example, in terms of log odds ratios when the GLM includes a logistic link, as well as fast computation of marginal probabilities. Several algorithms to obtain maximum likelihood estimates are presented, with a particular focus on reducing the computational burden. These methods are illustrated using data on the working relationship between 36 partners in a New England law firm. Supplementary materials for the article are available online.

Maximising resource allocation in the teaching laboratory: understanding student evaluations of teaching assistants in a team-based teaching format

ABSTRACT Minimal research papers have investigated the use of student evaluations on the laboratory, a learning medium usually run by teaching assistants with little control of the content, delivery and equipment. Finding the right mix of teaching assistants for the laboratory can be an onerous task due to the many skills required including theoretical and practical know-how, troubleshooting, safety and class management. Using larger classes with multiple teaching assistants, a team-based teaching (TBT) format may be advantageous. A rigorous three-year study across twenty-five courses over repetitive laboratory classes is analysed using a multi-level statistical model considering students, laboratory classes and courses. The study is used to investigate the effectiveness of the TBT format, and quantify the influence each demonstrator has on the laboratory experience. The study found that TBT is effective and the lead demonstrator most influential, influencing up to 55% of the laboratory experience evaluation.

Mantel-Haenszel estimators of odds ratios for stratified dependent binomial data

A standard approach to analyzing n binary matched pairs usually represented in n 2x2 tables is to apply a subject-specific model; for the simplest situation it is the so-called Rasch model. An alternative population-averaged approach is to apply a marginal model to the single 2x2 table formed by n subjects. For the situation of having an additional stratification variable with K levels forming K 2x2 tables, standard fitting approaches, such as generalized estimating equations and maximum likelihood, or, alternatively, the standard Mantel-Haenszel (MH) estimator, can be applied. However, while all these standard approaches are consistent under a large-stratum limiting model, they are not consistent under a sparse-data limiting model. In this paper, we propose a new MH estimator and a variance estimator that are both dually consistent: consistent under both large-stratum and sparse-data limiting situations. In a simulation study, the properties of the proposed estimators are confirmed, and the estimator is compared with standard marginal methods. The simulation study also considers the case when the homogeneity assumption of the odds ratios does not hold, and the asymptotic limit of the proposed MH estimator under this situation is derived. The results show that the proposed MH estimator is generally better than the standard estimator, and the same can be said about the associated Wald-type confidence intervals.

Computational aspects of the EM algorithm for spatial econometric models with missing data

ABSTRACT Maximum likelihood (ML) estimation with spatial econometric models is a long-standing problem that finds application in several areas of economic importance. The problem is particularly challenging in the presence of missing data, since there is an implied dependence between all units, irrespective of whether they are observed or not. Out of the several approaches adopted for ML estimation in this context, that of LeSage and Pace [Models for spatially dependent missing data. J Real Estate Financ Econ. 2004;29(2):233–254] stands out as one of the most commonly used with spatial econometric models due to its ability to scale with the number of units. Here, we review their algorithm, and consider several similar alternatives that are also suitable for large datasets. We compare the methods through an extensive empirical study and conclude that, while the approximate approaches are suitable for large sampling ratios, for small sampling ratios the only reliable algorithms are those that yield exact ML or restricted ML estimates.

Wilson confidence intervals for the two-sample log-odds-ratio in stratified 2 x 2 contingency tables

Large-sample Wilson-type confidence intervals (CIs) are derived for a parameter of interest in many clinical trials situations: the log-odds-ratio, in a two-sample experiment comparing binomial success proportions, say between cases and controls. The methods cover several scenarios: (i) results embedded in a single 2 × 2 contingency table; (ii) a series of K 2 × 2 tables with common parameter; or (iii) K tables, where the parameter may change across tables under the influence of a covariate. The calculations of the Wilson CI require only simple numerical assistance, and for example are easily carried out using Excel. The main competitor, the exact CI, has two disadvantages: It requires burdensome search algorithms for the multi-table case and results in strong over-coverage associated with long confidence intervals. All the application cases are illustrated through a well-known example. A simulation study then investigates how the Wilson CI performs among several competing methods. The Wilson interval is shortest, except for very large odds ratios, while maintaining coverage similar to Wald-type intervals. An alternative to the Wald CI is the Agresti-Coull CI, calculated from the Wilson and Wald CIs, which has same length as the Wald CI but improved coverage.

Mantel–Haenszel estimators of a common odds ratio for multiple response data

For a two-way contingency table, odds ratios are commonly used to describe the relationships between the row and column variables. In the ordinary case cells are mutually exclusive, that is each subject must fit into one and only one cell. However, in many surveys respondents may select more than one outcome category, commonly referred to as multiple responses. We discuss model-based and Mantel–Haenszel estimators of an assumed common odds ratio for several