Using regression mixture models with non-normal data: examining an ordered polytomous approach

Mild to moderate skew in errors can substantially impact regression mixture model results; one approach for overcoming this includes transforming the outcome into an ordered categorical variable and using a polytomous regression mixture model. This is effective for retaining differential effects in the population; however, bias in parameter estimates and model fit warrant further examination of this approach at higher levels of skew. The current study used Monte Carlo simulations; 3000 observations were drawn from each of two subpopulations differing in the effect of X on Y. Five hundred simulations were performed in each of the 10 scenarios varying in levels of skew in one or both classes. Model comparison criteria supported the accurate two-class model, preserving the differential effects, while parameter estimates were notably biased. The appropriate number of effects can be captured with this approach but we suggest caution when interpreting the magnitude of the effects.     

Gaining insight with recursive partitioning of generalized linear models

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles. Then, usually, a constant in every partition is fitted. While this is a simple and intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and independent variables may look. Or it may be that a certain model is assumed or of interest and there is a number of candidate variables that may non-linearly give rise to different model parameter values. We present an approach that combines generalized linear models (GLM) with recursive partitioning that offers enhanced interpretability of classical trees as well as providing an explorative way to assess a candidate variable's influence on a parametric model. This method conducts recursive partitioning of a GLM by (1) fitting the model to the data set, (2) testing for parameter instability over a set of partitioning variables, (3) splitting the data set with respect to the variable associated with the highest instability. The outcome is a tree where each terminal node is associated with a GLM. We will show the method's versatility and suitability to gain additional insight into the relationship of dependent and independent variables by two examples, modelling voting behaviour and a failure model for debt amortization, and compare it to alternative approaches.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

A Theory for Coloring Bivariate Statistical Maps

Consideration of some practical uses of statistical bivariate maps—for example, display of association between variables—leads to principles for making effective use of color to represent data values. Effective color schemes for bivariate maps are viewed as continuous transformations from color models to the unit square with appropriate restrictions involving hue, saturation, and brightness. Several schemes, including those used by the U.S. Census Bureau, are criticized on the basis of this theory.     

In Search of the Optimum Harvey Wallbanger Recipe via Mixture Experiment Techniques

A Harvey Wallbanger is an alcoholic drink composed of three ingredients: orange juice, vodka, and Galliano. One of the authors (Sahrmann), a connoisseur of the libation, was perplexed upon discovering that different bartender handbooks listed different recipes for the drink. Determined to shed some light on this irksome problem, he issued invitations for an evening workshop session (party) to former and current attendees of an experimental-design training course taught within his company. A mixture experiment was designed and data collected using the class participants. This article describes the experimental design and the analysis of the data. The results of the experiment indicate that reducing the proportion of vodka produces better-flavored drinks. The results of the experiment were not entirely conclusive, however, so recommendations are made for future experimentation.     

“Serials at Warp Speed: Navigating Transitions,” the 2007 North Carolina Serials Conference

Abstract

Reports on four major serials conferences, the 2007 North Carolina Serials Conference, the 2007 meeting of the Ohio Valley Group of Technical Services Librarians, the Canadian Library Association’s 2007 Pre-Conference, and the 2007 North American Serials Interest Group Conference.     

An Empirical Comparison of Estimating Methods for the Ramberg–Osgood EIV Model

The standard tensile test is one of the most frequent tools performed for the evaluation of mechanical properties of metals. An empirical model proposed by Ramberg and Osgood fits the tensile test data using a nonlinear model for the strain in terms of the stress. It is an Error-In-Variables (EIV) model because of the uncertainty affecting both strain and stress measurement instruments. The SIMEX, a simulation-based method for the estimation of model parameters, is powerful in order to reduce bias due to the measurement error in EIV models. The plan of this article is the following. In Sec. 2, we introduce the Ramberg–Osgood model and another reparametrization according to different assumptions on the independent variable. In Sec. 3, there is a summary of SIMEX method for the case at hand. Section 4 is a comparison between SIMEX and others estimating methods in order to highlight the peculiarities of the different approaches. In the last section, there are some concluding remarks.     

Confidence Intervals for the Hyperparameters in Structural Models

This article deals with the bootstrap as an alternative method to construct confidence intervals for the hyperparameters of structural models. The bootstrap procedure considered is the classical nonparametric bootstrap in the residuals of the fitted model using a well-known approach. The performance of this procedure is empirically obtained through Monte Carlo simulations implemented in Ox. Asymptotic and percentile bootstrap confidence intervals for the hyperparameters are built and compared by means of the coverage percentages. The results are similar but the bootstrap procedure is better for small sample sizes. The methods are applied to a real time series and confidence intervals are built for the hyperparameters.     

Two Moments of the Logitnormal Distribution

We display the first two moment functions of the Logitnormal(μ, σ²) family of distributions, conveniently described in terms of the Normal mean, μ, and the Normal signal-to-noise ratio, μ/σ, parameters that generate the family. Long neglected on account of the numerical integrations required to compute them, awareness of these moment functions should aid the sensible interpretation of logistic regression statistics and the specification of “diffuse” prior distributions in hierarchical models, which can be deceiving. We also use numerical integration to compare the correlation between bivariate Logitnormal variables with the correlation between the bivariate Normal variables from which they are transformed.