FITTING FINITE MIXTURE MODELS IN A REGRESSION CONTEXT

Suppose data are collected in a three-mode fashion (individuals x items X attributes), and it is sought to cluster the individuals into groups on the basis of lineat relations between scores on the attributes for each item and auxiliary measurements made on the same items. A mixture model is pro posed and the EM algorithm is used to fit it to the data by simultaneously estimating the group parameters and allocating individuals to groups. The method is illustrated by a simulation study and a real example in which consumers are clustered on the basis of product scores that are related to a sensory laboratory measurement.     

Bayesian sequential methods for choosing the best multinomial cell: some simulation results

Suboptimal Bayesian sequential methods for choosing the best (i.e. largest probability) multinomial cell are considered and their performance is studied using Monte Carlo simulation. Performance characteristics, such as the probability of correct selection and some other associated with the sample size distribution, are evaluated assuming a maximum sample size. Single observation sequential rules as well as rules, where groups of observations are taken, and fixed sample size rules are discussed.     

The Use of Multiplicity in a Household Survey of Disabilities

The multiplicity technique has been proposed (Sirken, 1970) as a means of improving estimates of the number of rare “events” in a population. This paper describes one use of this technique, namely estimation of the number of persons with certain types of disability living in private dwellings in Canberra. The results are taken from three household surveys conducted in Canberra during 1978–79 in which a multiplicity rule linking parents, siblings and children of residents of sample households who were also living in private dwellings in Canberra was used. While no direct evidence on the level of non-sampling error is available here, it appears that net response errors at least are not substantial using this multiplicity rule and that a reasonable gain in sampling efficiency results from the use of multiplicity.     

Do expressive mothers have expressive children? The role of socialization in children's affect expression

The effects of maternal expressiveness and children's gender on children's nonverbal expressiveness were assessed in two settings. In the laboratory, 30 boys and 30 girls of kindergarten age were unobtrusively videotaped while talking about happy, sad, and fearful experiences and while experiencing three social situations designed to elicit happy, disappointed, and apprehensive feelings. Videotapes were rated for emotion expression, using global ratings and EMFACS codes. In school, teachers rated these children's expression of four discrete emotions. In both the laboratory and school settings children were more positively expressive than negatively so, and positive and negative expressiveness were unrelated. In the laboratory children's positive expressiveness was consistent across the three social situations, but negative expressiveness varied across affective context. In both settings, children of low-expressive mothers were more positively expressive than children of high-expressive mothers, who tended to be more negatively expressive than children of low-expressive mothers. The difference in negative expression appeared most striking for anger. Gender was not predictive of children's expressiveness in either setting     

Community exercise program for older adults recovering from hip fracture: a pilot study

Community-based rehabilitative exercise programs might be an effective means to improve functional outcomes for hip-fracture patients. The purpose of this study was to evaluate the effectiveness of a community exercise program (CEP) for older adults recovering from hip fracture. Twenty-five older adults (mean age 80.0 +/- 6.0 years; 24 women; 71 +/- 23 days post-hip fracture) participated in this pilot study (17 exercise, 8 control). The CEP involved functional stepping and lower extremity-strengthening exercises. Control participants received only standard outpatient therapy. Measures of functional mobility, balance confidence, falls efficacy, lower extremity strength, and daily physical activity were evaluated at baseline and at 16 weeks. Improvements for self-reported physical activity, mobility, balance, and knee-extensor strength were observed for the CEP group. This study demonstrated that a CEP is beneficial for community-dwelling older adults post-hip fracture.     

On Blest’s Measure of Kurtosis Adjusted for Skewness

We reconsider the derivation of Blest’s (2003) skewness adjusted version of the classical moment-based coefficient of kurtosis and propose an adaptation of it which generally eliminates the effects of asymmetry a little more successfully. Lower bounds are provided for the two skewness adjusted kurtosis moment measures as functions of the classical coefficient of skewness. The results from a Monte Carlo experiment designed to investigate the sampling properties of numerous moment-based estimators of the two skewness adjusted kurtosis measures are used to identify those estimators with lowest mean squared error for small to medium sized samples drawn from distributions with varying levels of asymmetry and tailweight.     

An Improved Test for Continuous Local Martingales

We present a new test for the “continuous martingale hypothesis”. That is, a test for the hypothesis that observed data are from a process which is a continuous local martingale. The basis of the test is an embedded random walk at first passage times, obtained from the well-known representation of a continuous local martingale as a continuous time-change of Brownian motion. With a variety of simulated diffusion processes our new test shows higher power than existing tests using either the crossing tree or the quadratic variation, including the situation where non-negligible drift is present. The power of the test in the presence of jumps is also explored with a variety of simulated jump diffusion processes. The test is also applied to two sequences of high-frequency foreign exchange trade-by-trade data. In both cases the continuous martingale hypothesis is rejected at times less than hourly and we identify significant dependence in price movements at these small scales.     

On a Class of Distributions Defined by the Relationship Between Their Density and Distribution Functions

Knowledge concerning the family of univariate continuous distributions with density function f and distribution function F defined through the relation f(x) = F ^α(x)(1 ? F(x))^β, α, β ? , is reviewed and modestly extended. Symmetry, modality, tail behavior, order statistics, shape properties based on the mode, L-moments, and—for the first time—transformations between members of the family are the general properties considered. Fully tractable special cases include all the complementary beta distributions (including uniform, power law and cosine distributions), the logistic, exponential and Pareto distributions, the Student t distribution on 2 degrees of freedom and, newly, the distribution corresponding to α = β = 5/2. The logistic distribution is central to some of the developments of the article.