Multicategorical spline model for item response theory

Additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data. A nonparametric divided-by-total model for joint maximum likelihood estimation of probability-of-choice functions (for particular responses) and of latent ability is proposed. The model approximates probability functions by rational splines. Some illustrative examples of real test data analysis and the results of a Monte Carlo study are presented.The research in this paper was supported by the National Sciences and Engineering Research Council of Canada Grants OGP0105521 and APA 320 awarded to the first and the second author, respectively. The authors are indebted to R. Melzack and A. Baker for making available the data analyzed in this paper. We would also like to thank J. McKenna and B. Cont for their assistance in editing this paper.     

A Monte Carlo investigation of conjoint analysis index-of-fit: Goodness of fit,significance and power

Researchers in the field of conjoint analysis know the index-of-fit values worsen as the judgmental error of evaluation increases. This simulation study provides guidelines on the goodness of fit based on distribution of index-of-fit for different conjoint analysis designs. The study design included the following factors: number of profiles, number of attributes, algorithm used and judgmental model used. Critical values are provided for deciding the statistical significance of conjoint analysis results. Using these cumulative distributions, the power of the test used to reject the null hypothesis of random ranking is calculated. The test is found to be quite powerful except for the case of very small residual degrees of freedom.The authors thank the editor, the three reviewers and Ellen Foxman for helpful comments on the paper. Sanjay Mishra was a doctoral student at Washington State University at the time this research was completed. He is currently in the Department of Marketing at the University of Kansas.     

关于我国学生汉语阅读困难的研究

旨在探讨在我国学生的汉语学习中是否存在阅读困难问题。研究分别采用了目前国外较常使用的两种阅读困难操作定义和新近提出的截点法,对我国学生汉语学习中的阅读困难问题进行了考查。结果揭示出阅读困难在汉语学习者中同样存在,检出率分别为４．５５％和７．９６％．中国学生的阅读困难既表现在词汇上也表现在理解上;研究还发现同为阅读困难者男生和女生呈现出不同的特点。     

Solutions to some nonlinear equations from nonmetric data

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.This work was begun while the author was on sabbatical leave during 1970–71 at the Department of Mathematical Psychology, University of Nijmegen, the Netherlands, where discussions with E. E. Roskam on the problem were very helpful. Support was provided by Grant A0151 from the Natural Sciences and Engineering Council, Canada.     

A statistical analysis of the correlates of compliance and defiance of seatbelt use

With the intent to frame policy recommendations for enhancing the state of road safety, this study employed a binary logit regression approach to examine the factors associated with the compliance/defiance of seatbelt use among drivers of different vehicle types in Islamabad. To this end, a questionnaire survey was conducted to collect data on the respondents’ seatbelt use, demographic characteristics, driving behavior, past penalization history, and perceived effectiveness of enforcement of seatbelt laws. The study results revealed that there is a lower likelihood of wearing seatbelt among male drivers, taxi drivers, drivers with a low level of education, drivers with no crash or injury history, drivers that violate speed limits and are never penalized on seatbelt violation, and drivers with no seatbelt reminder installed in their vehicles. Respondents who believed that there is low effectiveness of the enforcement of seatbelt laws had the highest impact on seatbelt use whereas, the presence of seatbelt reminders in the vehicle had the least impact on seatbelt use. The findings of this study suggest the need for awareness campaigns for taxi drivers with the intent to educate them about the potential benefits of using a seatbelt in the case of a crash event; improved awareness and strict vigilance of male drivers; strict enforcement of posted speed limits and seatbelt laws; legislation for the mandatory installation of a seatbelt in all the new vehicles, and organizing mass outreach campaigns to improve the overall safety environment. Most importantly and widely applicable to the developing world, this study necessitates a depiction of strong resolve on the part of government agencies regarding the strict enforcement of seatbelt laws. Given a substantial difference in the social, cultural, and legislative outfit of the developed and developing worlds, factors influencing the compliance/defiance of seatbelt use among drivers differ significantly. It is, therefore, important to explore the local contributory factors as the results are not necessarily transferable across the regions.     

Editorial

This paper is a response to William Meredith-Owen’s paper presented at the inaugural joint conference on ‘Alchemy, a bridge to Jung’s objective psyche’, for The Society of Analytical Psychology and the West Midlands Institute of Psychotherapy in autumn 2020. The paper presents a way of understanding the collective unconscious through the functioning of the core self, and thus offers a bridge which addresses the indivisibility of the personal and collective psyche/unconscious, referencing Mary Williams’ (1963) classic paper. Specifically, this is applied to Winnicott’s dream of destruction that he had after reviewing Memories, Dreams, Reflections, as well as to parts of the psyche that were dissociated due to significant early deprivation – the primary narcissistic wounds. Alchemical metaphors are shown to relate to the analytic process, which allows the primitive core self (with its identificatory, participatory, connecting nature), when integrated through relationship, to sink back into the unconscious and function as the Self.     

Fungible Correlation Matrices: A Method for Generating Nonsingular,Singular, and Improper Correlation Matrices for Monte Carlo Research

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.     

Estimation Methods for Mixed Logistic Models with Few Clusters

For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.     

Determining the Propensity for Academic Dishonesty Using Decision Tree Analysis

This article investigates the propensity for academic dishonesty by university students using the partitioning method of decision tree analysis. A set of prediction rules are presented, and conclusions are drawn. To provide context for the decision tree approach, the partition process is compared with results of more traditional probit regression models. Results of the decision tree analysis complement the probit models in terms of predictive accuracy and confirm results previously found in the literature. In particular, students’ moral character—whether they believe cheating is acceptable—is found to be the most important factor in determining the propensity for academic dishonesty.     

Pedestrian compliance and cross walking speed adaptation due to countdown timer installations: A self report study

Although they are aware of the possible risk, a high number of pedestrians still violate the red light indication and cross the road illegally. This hazardous behaviour may cause incidents between them and the road vehicles. In order to reduce this illegal behaviour, the traffic signals are equipped with countdown timers, in order to provide more information and decrease pedestrians’ noncompliant behaviour. The main purpose of the present paper is to investigate the influence of countdown timers on pedestrians’ compliance regarding their crossing behaviour at intersections as well as to examine the parameters affecting walking speed adaptation. In the context of this analysis two regression models were developed. The first model is a binary logistic regression model which examines pedestrians’ self reported compliance. The results showed that the gender, the age, the perceived comfort and the seconds remaining for the onset of red light are the main parameters that affect compliance. The second model is an ordinal regression model which examines the factors that make pedestrians adapt their walking speed as they are crossing the road and are informed by the countdown timers about the second remaining for the termination of the green phase. The results of the second model revealed that the age, the compliance and the perceived assistance that the countdown timer provides for the walking speed adaptation affect the minimum remaining time before a pedestrian accelerates.