Rasch's multiplicative poisson model with covariates

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values. The author is now affiliated with the Otara University of Commerce. The author is grateful to Yoshio Takane, Haruo Yanai, Eiji Muraki, the editor and referees for their careful readings and helpful suggestions on earlier versions of this paper. Part of this work was presented at the third European Congress of Psychology at Tampere, Finland in 1993.     

Speech parts as Poisson processes

This paper presents evidence that six of the seven parts of speech occur in written text as Poisson processes, simple or recurring. The six major parts are nouns, verbs, adjectives, adverbs, prepositions, and conjunctions, with the interjection occurring too infrequently to support a model. The data consist of more than the first 5000 words of works by four major authors coded to label the parts of speech, as well as periods (sentence terminators). Sentence length is measured via the period and found to be normally distributed with no stochastic model identified for its occurrence. The models for all six speech parts but the noun significantly distinguish some pairs of authors and likewise for the joint use of all words types. Any one author is significantly distinguished from any other by at least one word type and sentence length very significantly distinguishes each from all others. The variety of word type use, measured by Shannon entropy, builds to about 90% of its maximum possible value. The rate constants for nouns are close to the fractions of maximum entropy achieved. This finding together with the stochastic models and the relations among them suggest that the noun may be a primitive organizer of written text.     

Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation. We wish to thank The Research Council of Norway for a grant supporting our collaboration.     

A stochastic model of consideration set sizes

This paper proposes a new model of consideration set sizes, which relies on a stochastic modelling approach to better understand data patterns. The paper combines the Poisson distribution with the lognormal distribution proposed by Hauser and Wernerfelt (1990) to create the Poisson lognormal (PLN) model of consideration set sizes. An advantage of PLN is that it allows variance within a given individual consumer. This is a crucial factor for brand managers who wish to choose a particular market to promote their brand, as a higher within‐individual variance suggests that there is more chance for a consumer to change their consideration set size, whereas a lower within‐individual variance indicates that a consumer tends to stick to his/her consideration set size. The paper then uses 10 datasets including service, durable and fast‐moving consumer goods across four countries to validate the new model and compare it with the lognormal model. The results show that PLN gives a good fit to these data. It outperforms the lognormal model. The average mean absolute percentage error of the PLN model is 12 per cent, whereas that of the lognormal model is 26 per cent. For managerial implications, the paper proposes a better tool to help brand managers analyse the nature and intensity of competition that is facing their brands. Also, relying on its stochastic element, the proposed model can help brand managers predict future brand consideration by their consumers, as well as evaluate any change in brand consideration, caused by marketing activity such as sales promotion and advertising. Copyright © 2014 John Wiley & Sons, Ltd.     

Critical Poisson’s ratio between toughness and brittleness

We have a new understanding on a unified fracture criterion based on two kinds of strain energy density. A definite expression which is a function of Poisson’s ratio to describe a crucial parameter in the unified fracture criterion is derived. The critical value of Poisson’s ratio between brittle and ductile materials can be derived as 2/7 which is verified by experimental data. Besides, the effect of Poisson’s ratio on the fracture loci in stress spaces is studied using unified fracture criterion. It is found that the decrease in Poisson’s ratio increases the asymmetry of fracture loci between tensile stress states and compressive stress states in principal stress spaces and between Lode parameters are 1 and ?1 in deviatoric-stress spaces. In addition, stress triaxiality has a great effect on the fracture behaviour with different Poisson’s ratios.     

Intrinsic factor controlling the deformation and ductile-to-brittle transition of metallic glasses

The energetic driving force and resistance for shearing and cracking in metallic glasses (MGs) are quantitatively evaluated. A universal thermodynamic criterion is proposed for better understanding the intrinsic correlations between fracture toughness and Poisson’s ratio, the competitions between various deformation modes and the ductile-to-brittle transition in MGs and other materials. A new cooperation parameter δ is also introduced to depict quantitatively the relative propensity of shearing versus cracking. This work could provide insights into the long-standing issues of deformation mechanisms of glassy materials, and be helpful in searching for ductile and tough MGs.     

When should clinicians switch treatments? An application of signal detection theory to two treatments for women with alcohol use disorders

Statistical application of signal detection theory has been used to study the clinical utility of early treatment response in a range of treatments and psychiatric disorders. The current study sought to examine the predictive value of weekly within-treatment drinking using receiver operator curves (ROCs) and zero-inflated Poisson (ZIP) regression in 102 women with alcohol use disorders (AUDs) randomized to either alcohol behavioral individual treatment (ABIT; n = 52) or alcohol behavioral couples treatment (ABCT; n = 50). ROC analyses indicated that failure to achieve or sustain abstinence by the end-of-treatment and one-year follow-up was predicted with reasonable accuracy by week 4 percent days abstinent (PDA) in ABIT. ZIP models yielded similar results with evidence for within-treatment PDA with week 6 PDA predicting both the abstinence as well as percent days drinking at the end-of-treatment and one-year follow-up. Within-treatment PDA was a significantly better predictor of outcomes for ABIT than ABCT, despite a better overall treatment response for ABCT. Implications for stepped care models of alcohol treatment are discussed and recommendations for future research made. When Should Clinicians Switch Treatments: An Application of Signal Detection Theory to Two Treatments for Women with Alcohol Use Disorders.     

A multivariate counting process with Weibull-distributed first-arrival times

In this paper, we study a method to construct a multivariate counting process with positive dependencies between the event occurrences. Conditional on a random effect with a positive stable distribution, the univariate counting processes are independent non-homogeneous Poisson processes with a power intensity function. The applicability of the model is illustrated in three examples: a horse race model with several dependent channels, a dependent parallel-counter model and an interactive coactivation model.     

Estimating latent distributions in recurrent choice data

This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by specifying elements of the choice process at the individual level. Probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior. Due to the explicit consideration of random effect sources, the choice models are parsimonious and readily interpretable. An easy to implement EM algorithm is presented for parameter estimation. Two applications illustrate the proposed approach.     

Revisiting dispersion in count data item response theory models: The Conway–Maxwell–Poisson counts model

Count data naturally arise in several areas of cognitive ability testing, such as processing speed, memory, verbal fluency, and divergent thinking. Contemporary count data item response theory models, however, are not flexible enough, especially to account for over- and underdispersion at the same time. For example, the Rasch Poisson counts model (RPCM) assumes equidispersion (conditional mean and variance coincide) which is often violated in empirical data. This work introduces the Conway–Maxwell–Poisson counts model (CMPCM) that can handle underdispersion (variance lower than the mean), equidispersion, and overdispersion (variance larger than the mean) in general and specifically at the item level. A simulation study revealed satisfactory parameter recovery at moderate sample sizes and mostly unbiased standard errors for the proposed estimation approach. In addition, plausible empirical reliability estimates resulted, while those based on the RPCM were biased downwards (underdispersion) and biased upwards (overdispersion) when the simulation model deviated from equidispersion. Finally, verbal fluency data were analysed and the CMPCM with item-specific dispersion parameters fitted the data best. Dispersion parameter estimates indicated underdispersion for three out of four items. Overall, these findings indicate the feasibility and importance of the suggested flexible count data modelling approach.