A Parametric Bootstrap Test for Comparing Heteroscedastic Regression Models

Testing equality of regression coefficients in several regression models is a common problem encountered in many applied fields. This article presents a parametric bootstrap (PB) approach and compares its performance to that of another simulation-based approach, namely, the generalized variable approach. Simulation studies indicate that the PB approach controls the Type I error rates satisfactorily regardless of the number of regression models and sample sizes whereas the generalized variable approach tends to be very liberal as the number of regression models goes up. The proposed PB approach is illustrated using a data set from stability study.     

A MCMC algorithm to fit a general exchangeable model

Consider the exchangeable Bayesian hierarchical model where observations y_i are independently distributed from sampling densities with unknown means, the means µi, are a random sample from a distribution g, and the parameters of g are assigned a known distribution h. A simple algorithm is presented for summarizing the posterior distribution based on Gibbs sampling and the Metropolis algorithm. The software program Matlab is used to implement the algorithm and provide a graphical output analysis. An binomial example is used to illustrate the flexibility of modeling possible using this algorithm. Methods of model checking and extensions to hierarchical regression modeling are discussed.     

Average Most Powerful Tests for a Segmented Regression

To improve the goodness of fit between a regression model and observations, the model can be complicated; however, that can reduce the statistical power when the complication does not lead significantly to an improved model. In the context of two-phase (segmented) logistic regressions, the model evaluation needs to include testing for simple (one-phase) versus two-phase logistic regression models. In this article, we propose and examine a class of likelihood ratio type tests for detecting a change in logistic regression parameters that splits the model into two-phases. We show that the proposed tests, based on Shiryayev–Roberts type statistics, are on average the most powerful. The article argues in favor of a new approach for fixing Type I errors of tests when the parameters of null hypotheses are unknown. Although the suggested approach is partly based on Bayes–Factor-type testing procedures, the classical significance levels of the proposed tests are under control. We demonstrate applications of the average most powerful tests to an epidemiologic study entitled “Time to pregnancy and multiple births.”     

A Bayesian Analysis of a Poisson Random Effects Model for Home Run Hitters

The problem of interest is to estimate the home run ability of 12 great major league players. The usual career home run statistics are the total number of home runs hit and the overall rate at which the players hit them. The observed rate provides a point estimate for a player's “true” rate of hitting a home run. However, this point estimate is incomplete in that it ignores sampling errors, it includes seasons where the player has unusually good or poor performances, and it ignores the general pattern of performance of a player over his career. The observed rate statistic also does not distinguish between the peak and career performance of a given player. Given the random effects model of West (1985), one can detect aberrant seasons and estimate parameters of interest by the inspection of various posterior distributions. Posterior moments of interest are easily computed by the application of the Gibbs sampling algorithm (Gelfand and Smith 1990). A player's career performance is modeled using a log-linear model, and peak and career home run measures for the 12 players are estimated.     

Modelling longitudinal semicontinuous emesis volume data with serial correlation in an acupuncture clinical trial

Summary.  In longitudinal studies, we are often interested in modelling repeated assessments of volume over time. Our motivating example is an acupuncture clinical trial in which we compare the effects of active acupuncture, sham acupuncture and standard medical care on chemotherapy-induced nausea in patients being treated for advanced stage breast cancer. An important end point for this study was the daily measurement of the volume of emesis over a 14-day follow-up period. The repeated volume data contained many 0s, had apparent serial correlation and had missing observations, making analysis challenging. The paper proposes a two-part latent process model for analysing the emesis volume data which addresses these challenges. We propose a Monte Carlo EM algorithm for parameter estimation and we use this methodology to show the beneficial effects of acupuncture on reducing the volume of emesis in women being treated for breast cancer with chemotherapy. Through simulations, we demonstrate the importance of correctly modelling the serial correlation for making conditional inference. Further, we show that the correct model for the correlation structure is less important for making correct inference on marginal means.     

Characterizations of distributions through coincidences of semiparametric families

Semiparametric families are families that have both a real parameter and a parameter that is itself a distribution. A number of semiparametric families suitable for lifetime data are introduced: scale, power, frailty (proportional hazards), age, moment, Laplace transform, and convolution parameter families. The coincidence of two families provides a characterization of the underlying distribution. Characterizations of the Weibull, gamma, lognormal, and Gompertz distributions are obtained.     

Picture Perception in Infants: Do 9‐Month‐Olds Attempt to Grasp Objects Depicted in Photographs?

Two experiments tested the DeLoache, Pierroutsakos, Uttal, Rosengren, and Gottlieb (1998 claim that 9‐month‐old infants attempt to grasp objects depicted in photographs. In Experiment 1, 9‐month‐olds viewed an object, a photograph of the object, and 2 flat, nonpictorial displays. On average, they reached for the photograph and nonpictorial displays with their hands approximately horizontal and close to the display surfaces, but reached for the object with their hands oriented obliquely and at significantly higher heights. The infants also exhibited similar behaviors when touching the photograph and nonpictorial displays. In Experiment 2, 9‐month‐olds exhibited similar behaviors when touching a photograph of an object and a photograph of textured carpet. The results of both experiments suggest that 9‐month‐olds treat photographs of objects as 2‐dimensional surfaces and not as graspable objects.     

Short happiness and affect research protocol (sharp)

Issues in the measurement of subjective well-being (SWB) include the relative balance between scale brevity and measurement accuracy. Because accuracy is expected to vary negatively with the length of a scale, the brevity/accuracy trade-off has pragmatic implications for survey research. This article begins by examining minimal psychometric criteria to evaluate short measures of SWB. These criteria include content validity (i.e., four basic categories are cited), criterion validity, internal consistency, and test-retest reliability. Several measures frequently used in large-scale surveys are shown to fail against one or more of these criteria. Consequently, a new brief measure was developed and shown to satisfy all the criteria. It is termed the Short Happiness and Affect Research Protocol (SHARP). This measure contains 12-items derived from the Memorial University of Newfoundland Scale of Happiness (MUNSH), with the content balanced over positive and negative, and short-term (affective) and long-term (dispositional) components. The internal consistency, temporal stability, and criterion validity coefficients for the SHARP are comparable to those of the MUNSH, which is among the most accurate measures of self-reported SWB.     

The multilevel dependence of contraceptive use on socioeconomic development and family planning program strength

Using World Fertility Survey data for 15 developing countries, we estimate an equation in which the dependent variable—whether the respondent has ever used an efficient contraceptive method—depends on the respondent’s education and location of childhood residence. All of the coefficients of this equation, including the intercept, vary over countries. Analysis based on new methodology shows that the intercept and education effects vary as a function of national family planning program efforts and that none of the parameters of the equation depend on gross national product per capita. The results demonstrate the efficacy of multilevel analysis, provide a partial test of the theory underlying the analysis, and refocus discussion of the contributions of development and policy variables to fertility reduction.     

Bayesian selection of log-linear models

A general methodology is presented for finding suitable Poisson log-linear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two- and three-way contingency tables, in which the regression coefficients are interpretable in terms of odds ratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of two-way simulated tables and for two three-way tables. These methods appear to be useful in selecting the best log-linear model and in estimating parameters of interest that reflect uncertainty in the true model.