Separability of item and person parameters in response time models

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is separate sufficiency: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is ranking independence: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.I am indebted to Wim van der Linden for bringing Thissen's (1983) paper to my notice, and to Martijn Berger, Frans Tan, and the anonymous reviewers for their constructive comments on earlier drafts of this paper.     

Semi‐parametric proportional hazards models with crossed random effects for psychometric response times

The semi‐parametric proportional hazards model with crossed random effects has two important characteristics: it avoids explicit specification of the response time distribution by using semi‐parametric models, and it captures heterogeneity that is due to subjects and items. The proposed model has a proportionality parameter for the speed of each test taker, for the time intensity of each item, and for subject or item characteristics of interest. It is shown how all these parameters can be estimated by Markov chain Monte Carlo methods (Gibbs sampling). The performance of the estimation procedure is assessed with simulations and the model is further illustrated with the analysis of response times from a visual recognition task.     

How Long Do Offenders Escape Arrest? Using DNA Traces to Analyse when Serial Offenders Are Caught

Why is it that some serial offenders are arrested quickly and others only after a long period, or never at all? What characterises offenders who continue to escape arrest despite their continued involvement in crime? To be able to answer these questions, arrested (identified) offenders must be compared with never arrested (unidentified) offenders. In this paper, data from the Dutch DNA database are used to assess which characteristics of the criminal behaviour of unidentified offenders influence the probability that they will subsequently be arrested. DNA data offer a unique opportunity to compare crime series of identified offenders with crime series of yet unidentified offenders. Using the Cox proportional hazards model, we tested whether the number of crimes committed, offence specialization, and offence seriousness affect the probability of arrest of serial offenders. Results showed that as an offender commits more crimes, the probability that he will be arrested increases and that offence specialization decreases the probability of arrest. Another conclusion drawn is that DNA traces offer unique opportunities for criminological research. We discuss the limitations of this new data source and make suggestions for future research using DNA traces and for future research that might improve the current study. Copyright © 2012 John Wiley & Sons, Ltd.     

An accumulator model for responses and response times in tests based on the proportional hazards model

Latent trait models for responses and response times in tests often lack a substantial interpretation in terms of a cognitive process model. This is a drawback because process models are helpful in clarifying the meaning of the latent traits. In the present paper, a new model for responses and response times in tests is presented. The model is based on the proportional hazards model for competing risks. Two processes are assumed, one reflecting the increase in knowledge and the second the tendency to discontinue. The processes can be characterized by two proportional hazards models whose baseline hazard functions correspond to the temporary increase in knowledge and discouragement. The model can be calibrated with marginal maximum likelihood estimation and an application of the ECM algorithm. Two tests of model fit are proposed. The amenability of the proposed approaches to model calibration and model evaluation is demonstrated in a simulation study. Finally, the model is used for the analysis of two empirical data sets.     

Psychometric Modeling of response speed and accuracy with mixed and conditional regression

Human performance in cognitive testing and experimental psychology is expressed in terms of response speed and accuracy. Data analysis is often limited to either speed or accuracy, and/or to crude summary measures like mean response time (RT) or the percentage correct responses. This paper proposes the use of mixed regression for the psychometric modeling of response speed and accuracy in testing and experiments. Mixed logistic regression of response accuracy extends logistic item response theory modeling to multidimensional models with covariates and interactions. Mixed linear regression of response time extends mixed ANOVA to unbalanced designs with covariates and heterogeneity of variance. Related to mixed regression is conditional regression, which requires no normality assumption, but is limited to unidimensional models. Mixed and conditional methods are both applied to an experimental study of mental rotation. Univariate and bivariate analyzes show how within-subject correlation between response and RT can be distinguished from between-subject correlation, and how latent traits can be detected, given careful item design or content analysis. It is concluded that both response and RT must be recorded in cognitive testing, and that mixed regression is a versatile method for analyzing test data.I am grateful to Rogier Donders for putting his data at my disposal.     

Psychometric and information processing properties of selected response time models

This paper discusses the compatibility of some response time (RT) models with psychometric and with information processing approaches to response times. First, three psychometrically desirable properties of probabilistic models for binary data, related to the principle of specific objectivity, are adapted to the domain of RT models. One of these is the separability of item and subject parameters, and another is double monotonicity. Next, the compatibility of these psychometric properties with one very popular information processing approach, the serial-additive model, is discussed. Finally, five RT models are analyzed with respect to their compatibility with the psychometric properties, with serial-additive processing and with some alternative types of processing. It is concluded that (a) current psychometric models each satisfy one or more of the psychometric properties, but are not (easily) compatible with serial-additive processing, (b) at least one serial-additive processing model satisfies separability of item and subject parameters, and (c) RT models will more easily satisfy double monotonicity than the other two psychometric properties.     

Predictors of Length of Stay Among Youths Hospitalized in State Hospitals in Illinois

Using data from the Integrated Database on Children and Family Services in Illinois, we examined factors associated with the length of psychiatric hospitalization of youths in state hospitals between July 1, 1987 and June 30, 1992. Univariate analysis indicated that those diagnosed with attention deficit, psychotic, and conduct disorder experienced longer hospitalizations. In contrast, youths diagnosed with depressive disorders, drug and alcohol disorders, and adjustment disorders had shorter hospitalizations. Youths receiving services from multiple sectors of the human service delivery system experienced longer hospitalizations. Youths living in communities with state hospital linked community-based mental health services had shorter hospitalizations. Males experienced longer hospitalizations than females and African American youths experienced longer hospitalizations than White youths. Hispanic youths experienced shorter stays than either White or African American youths. The proportional hazards model indicated that being female, a history of previous admissions, multiservice use, and dangerousness were all associated with the decreased likelihood of discharge. Psychotic, attention deficit, and bipolar disorders were also associated with a decreased likelihood of hospital discharge. Youths with depressive disorders and African Americans with psychotic disorders had an increased likelihood of discharge. Increased age was also associated with the increased likelihood of discharge.     

Models for the statistics and mechanisms of response speed and accuracy

Van Breukelen offers a promising method for modeling both response speed and response accuracy. However, the underlying conception of both dependent measures is somewhat flawed, leading the author to conclude that the approach possesses limitations that, under revised assumptions, may not hold. The central misconception, and a set of related misconceptions, is addressed, and it is suggested that this approach holds a good deal of promise for application in the perceptual and cognitive sciences.     

Estimating an unobserved component of a serial response time model

A method is developed for estimating the response time distribution of an unobserved component in a two-component serial model, assuming the components are stochastically independent. The estimate of the component's density function is constrained only to be unimodal and non-negative. Numerical examples suggest that the method can yield reasonably accurate estimates with sample sizes of 300 and, in some cases, with sample sizes as small as 100.The author wishes to thank David Kohfeld, Jim Ramsay, Jim Townsend and two anonymous referees for a number of useful and stimulating comments on an earlier version of this paper.     

Effects of age and the relationship between response time measures and psychometric intelligence in younger adults

The major goal of the present study was to investigate the potential influence of age on the relationship among performance measures derived from a Hick reaction time task and general intelligence (psychometric g). Participants were 130 male and 130 female younger adults (mean age: 24.6 years) covering a wide range of individual levels of intelligence. Results from structural-equation modelling analyses clearly indicate that there is no evidence for the notion of a general speed factor underlying psychometric g. A much more sufficient model is provided by the assumption that median reaction time (RTmd) and intraindividual variability of reaction time (RTSD), though highly correlated, reflect two distinct sources of variance for psychometric g. While age was negatively associated with RTmd, no such relationship could be established for RTSD.     

Rotation in the dynamic factor modeling of multivariate stationary time series

A special rotation procedure is proposed for the exploratory dynamic factor model for stationary multivariate time series. The rotation procedure applies separately to each univariate component series of aq-variate latent factor series and transforms such a component, initially represented as white noise, into a univariate moving-average. This is accomplished by minimizing a so-called state-space criterion that penalizes deviations of the rotated solution from a generalized state-space model with only instantaneous factor loadings. Alternative criteria are discussed in the closing section. The results of an empirical application are presented in some detail.This research was supported by the Institute for Developmental and Health Research Methodology, University of Virginia.     

Bayesian modeling of measurement error in predictor variables using item response theory

It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.This paper is part of the dissertation by Fox (2001) that won the 2002 Psychometric Society Dissertation Award.     

项目间多维测验作答时间数据分析：潜在特质速度间效应建模

随着计算机测验使用的普及化,被试在心理与教育测验上的作答反应时的获取也越发便利。为了充分利用项目反应时信息,单维与多维的反应时模型相继被提出。然后,在项目间多维反应时数据中,潜在特质速度之间可能存在共同关系（比如,层阶关系）,此时现有的反应时模型并不能适用。基于此,本研究提出了高阶对数正态反应时模型与双因子对数正态反应时模型。在模拟研究中,高阶对数正态反应时模型与双因子对数正态反应时模型的各参数都能被准确估计。在瑞文标准推理测验的三组测验项目的反应时数据中,双因子对数正态反应时模型表现出更为优秀的拟合效果,同时基于多个统计量说明了局部与全局潜在特质速度同时存在的必要性。因此,在项目间多维测验反应时数据分析中,非常有必要考虑多维潜在特质速度之间的共同效应。     

心理与教育测验中反应时模型应用的优势与举例

基于计算机形式的测验使得收集作答反应时信息成为可能,这些信息的有效利用对心理与教育测验的理论研究和实际应用产生了重大影响。首先,归纳并总结了测验中使用反应时信息的五大优势。其次,分别介绍了4种不同取向下较典型的反应时模型与模型特征,并分别进行评价。再次,较系统地梳理了反应时模型在实践中的应用,使读者了解反应时信息在测验中所发挥的作用。最后,探讨了未来将反应时应用于心理与教育测量领域的几个研究方向。     

From Poisson shot noise to the integrated Ornstein-Uhlenbeck process: Neurally principled models of information accumulation in decision-making and response time

In the diffusion model of decision-making, evidence is accumulated by a Wiener diffusion process. A neurally motivated account of diffusive evidence accumulation is given, in which diffusive accumulation arises from an interaction between neural integration processes operating on short and long time scales. The short time scale process is modeled as a Poisson shot noise process with exponential decay. Stimulus information is coded by excitatory-inhibitory shot noise pairs. The long time scale process is modeled as algebraic integration, possibly implemented as a first-order autoregressive process realized by recurrent connections within a population of neurons. At high intensities, an excitatory-inhibitory shot noise pair converges weakly to an Ornstein-Uhlenbeck (OU) velocity process. The integrated OU process, or OU displacement process, obtained by integrating the velocity process over time, is indistinguishable at long times from the Wiener process. Diffusive information accumulation may therefore be characterized as an integrated OU process whose properties mimic those of the Wiener process.     

Predicting Romantic Interest at Zero Acquaintance: Evidence of Sex Differences in Trait Perception but Not in Predictors of Interest

We evaluated five competing hypotheses about what predicts romantic interest. Through a half‐block quasi‐experimental design, a large sample of young adults (i.e. responders; n = 335) viewed videos of opposite‐sex persons (i.e. targets) talking about themselves, and responders rated the targets' traits and their romantic interest in the target. We tested whether similarity, dissimilarity or overall trait levels on mate value, physical attractiveness, life history strategy and the Big Five personality factors predicted romantic interest at zero acquaintance and whether sex acted as a moderator. We tested the responders' individual perception of the targets' traits, in addition to the targets' own self‐reported trait levels and a consensus rating of the targets made by the responders. We used polynomial regression with response surface analysis within multilevel modelling to test support for each of the hypotheses. Results suggest a large sex difference in trait perception; when women rated men, they agreed in their perception more often than when men rated women. However, as a predictor of romantic interest, there were no sex differences. Only the responders' perception of the targets' physical attractiveness predicted romantic interest; specifically, responders' who rated the targets' physical attractiveness as higher than themselves reported more romantic interest. Copyright © 2017 European Association of Personality Psychology