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.     

Testing for independence between pairs of autocorrelated binomial data sequences

A problem arises in analyzing the existence of interdependence between the behavioral sequences of two individuals: tests involving a statistic such as chi-square assume independent observations within each behavioral sequence, a condition which may not exist in actual practice. Using Monte Carlo simulations of binomial data sequences, we found that the use of a chi-square test frequently results in unacceptable Type I error rates when the data sequences are autocorrelated. We compared these results to those from two other methods designed specifically for testing for intersequence independence in the presence of intrasequence autocorrelation. The first method directly tests the intersequence correlation using an approximation of the variance of the intersequence correlation estimated from the sample autocorrelations. The second method uses tables of critical values of the intersequence correlation computed by Nakamuraet al. (J. Am. Stat. Assoc., 1976,71, 214–222). Although these methods were originally designed for normally distributed data, we found that both methods produced much better results than the uncorrected chi-square test when applied to binomial autocorrelated sequences. The superior method appears to be the variance approximation method, which resulted in Type I error rates that were generally less than or equal to 5% when the level of significance was set at .05.     

Response to name in children with autism: Treatment,generalization, and maintenance

Deficits in response to name (RTN) are an early indicator of autism spectrum disorder (ASD), and RTN is a treatment goal in many early intervention curricula for children with ASD. However, little research has empirically evaluated methods for increasing RTN in children with ASD. We evaluated a series of conditions designed to increase RTN for 4 children with ASD using a multielement experimental design. The schedules of tangible reinforcement were thinned after mastery and generalization was tested across people and contexts. Tangible reinforcers were necessary to increase RTN for all 4 participants, and the schedule of reinforcement was successfully thinned with all participants after intervention. Generalization was also observed across people and experimental contexts.     

Investigating Individual Differences in Toddler Search with Mixture Models

Children's performance on cognitive tasks is often described in categorical terms in that a child is described as either passing or failing a test, or knowing or not knowing some concept. We used binomial mixture models to determine whether individual children could be classified as passing or failing two search tasks, the DeLoache model room task and the Berthier et al. door task. The data support categorical classification of the children and suggest that the increase in average proportion correct with age is the result of an increasing proportion of children who can solve the tasks. Performance on the two tasks was concordant, and improving performance could be due to advances in a single psychological ability, such as cognitive control. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessing the generality and durability of interview‐informed functional analyses and treatment

Due to the limited research demonstrating socially valid outcomes of function‐based treatments in ecologically relevant environments (Santiago, Hanley, Moore, & Jin, 2016), we replicated and extended the effects of the interview‐informed functional analysis and skill‐based treatment procedure described by Hanley, Jin, Vanselow, and Hanratty (2014) with two children diagnosed with autism in a home setting. The assessment and treatment was implemented by a home‐based service provider and treatment was extended to the participants’ parents. Following the interview‐informed functional analyses, we taught the participants functional communication responses and to engage in less‐preferred activities when functional communication outcomes were delayed. We observed large reductions in problem behavior following the introduction of the function‐based treatment. The effects extended to novel settings, stimuli, and caregivers and the results maintained at 6‐week follow‐ups.     

A binomial test for hierarchical dependency

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. This hypothesis is basic to the writings of several prominent theorists, such as Gagné and Piaget. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative example is also provided.     

The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective

It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies.     

Empirical bayes estimates of domain scores under binomial and hypergeometric distributions for test scores

We introduce two simple empirical approximate Bayes estimators (EABEs)— and —for estimating domain scores under binomial and hypergeometric distributions, respectively. Both EABEs (derived from corresponding marginal distributions of observed test scorex without relying on knowledge of prior domain score distributions) have been proven to hold -asymptotic optimality in Robbins' sense of convergence in mean. We found that, where and are the monotonized versions of and under Van Houwelingen's monotonization method, respectively, the convergence rate of the overall expected loss of Bayes risk in either or depends on test length, sample size, and ratio of test length to size of domain items. In terms of conditional Bayes risk, and outperform their maximum likelihood counterparts over the middle range of domain scales. In terms of mean-squared error, we also found that: (a) given a unimodal prior distribution of domain scores, performs better than both and a linear EBE of the beta-binomial model when domain item size is small or when test items reflect a high degree of heterogeneity; (b) performs as well as when prior distribution is bimodal and test items are homogeneous; and (c) the linear EBE is extremely robust when a large pool of homogeneous items plus a unimodal prior distribution exists.The authors are indebted to both anonymous reviewers, especially Reviewer 2, and the Editor for their invaluable comments and suggestions. Thanks are also due to Yuan-Chin Chang and Chin-Fu Hsiao for their help with our simulation and programming work.