A study of algorithms for covariance structure analysis with specific comparisons using factor analysis

Several algorithms for covariance structure analysis are considered in addition to the Fletcher-Powell algorithm. These include the Gauss-Newton, Newton-Raphson, Fisher Scoring, and Fletcher-Reeves algorithms. Two methods of estimation are considered, maximum likelihood and weighted least squares. It is shown that the Gauss-Newton algorithm which in standard form produces weighted least squares estimates can, in iteratively reweighted form, produce maximum likelihood estimates as well. Previously unavailable standard error estimates to be used in conjunction with the Fletcher-Reeves algorithm are derived. Finally all the algorithms are applied to a number of maximum likelihood and weighted least squares factor analysis problems to compare the estimates and the standard errors produced. The algorithms appear to give satisfactory estimates but there are serious discrepancies in the standard errors. Because it is robust to poor starting values, converges rapidly and conveniently produces consistent standard errors for both maximum likelihood and weighted least squares problems, the Gauss-Newton algorithm represents an attractive alternative for at least some covariance structure analyses.Work by the first author has been supported in part by Grant No. Da01070 from the U. S. Public Health Service. Work by the second author has been supported in part by Grant No. MCS 77-02121 from the National Science Foundation.     

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.     

Bias in self-evaluation: Signal probability effects

Two experiments examined apparent signal probability effects in simple verbal self-reports. After each trial of a delayed matching-to-sample task, young adults pressed either a “yes” or a “no” button to answer a computer-presented query about whether the most recent choice met a point contingency requiring both speed and accuracy. A successful matching-to-sample choice served as the “signal” in a signal-detection analysis of self-reports. Difficulty of matching to sample, and thus signal probability, was manipulated via the number of nonmatching sample and comparison stimuli. In Experiment 1, subjects exhibited a bias (log b) for reporting matching-to-sample success when success was frequent, and no bias or a bias for reporting failure when success was infrequent. Contingencies involving equal conditional probabilities of point consequences for “I succeeded” and “I failed” reports had no systematic effect on this pattern. Experiment 2 found signal probability effects to be evident regardless of whether referent-response difficulty was manipulated in different conditions or within sessions. These findings indicate that apparent signal probability effects in self-report bias that were observed in previous studies probably were not an artifact of contingencies intended to improve self-report accuracy or of the means of manipulating signal probability. The findings support an analogy between simple self-reports and psychophysical judgments and bolster the conclusion of Critchfield (1993) that signal probability effects can influence simple self-reports much as they do reports about external stimuli in psychophysical experiments.     

Justification,excuse, and proof beyond reasonable doubt

The law requires criminal guilt to be proved beyond a reasonable doubt. There are two different approaches to construing this legal rule. On an epistemic approach, the rule is construed in terms of justified belief or knowledge; on a probabilistic approach, the rule is construed in terms of satisfying a probabilistic threshold. An epistemic construction of the rule has this advantage over a probabilistic construction: the former can while the latter cannot excuse the state from blame for a false conviction. This claim rests on an understanding of legal rules, legal justification for a finding of guilt and the central purpose of a criminal trial.     

概率估计的趋势效应及其对决策的影响机制——基于心理动量的视角

概率是反映风险与不确定性的重要指标, 概率估计具有趋势效应, 会对决策产生影响。文章描述了概率估计趋势效应的两种表现形式, 概率估计变化的趋势性(即不同时间点概率估计变化产生的趋势作用)与单边概率估计的趋势性(即高于或低于某个概率区间范畴的上界或下界的估计表述所产生的趋势作用), 揭示了概率估计趋势效应对于个体判断、决策行为和非理性决策偏差的影响; 基于心理动量的理论视角提出了一个整合模型, 阐述了概率估计趋势效应催生心理动量体验继而引发后续决策行为的内在机理。未来的研究可进一步关注：多方信息来源主体下概率估计的趋势效应; 动态趋势效应与静态概率估计的交互作用; 风险沟通中的概率估计变化趋势。     

What if I am the one? Measuring individual differences in emotional sensitivity to probability and emotional reactivity to possibility

Current theories of risk perception point to the powerful role of emotion and the neglect of probabilistic information in the face of risk, but these tendencies differ across individuals. We propose a method for measuring individuals' emotional sensitivity to probability to assess how feelings about probabilities, rather than the probabilities themselves, influence decisions. Participants gave affective ratings (worry or excitement) to 14 risky events, each with a specified probability ranging from 1 in 10 to 1 in 10,000,000. For each participant, we regressed these emotional responses against item probabilities, estimating a slope (the degree to which emotional responses change with probability) and an intercept (the emotional reaction to an event with a fixed probability). These two parameters were treated as individual difference scores and included in models predicting reactions to several health risk scenarios. Both emotional sensitivity to probability (slope) and emotional reactivity to possibility (intercept) significantly predicted responses to these scenarios, above and beyond the predictive power of other well‐established individual difference measures.     

Robustness of Parameter Estimation to Assumptions of Normality in the Multidimensional Graded Response Model

A central assumption that is implicit in estimating item parameters in item response theory (IRT) models is the normality of the latent trait distribution, whereas a similar assumption made in categorical confirmatory factor analysis (CCFA) models is the multivariate normality of the latent response variables. Violation of the normality assumption can lead to biased parameter estimates. Although previous studies have focused primarily on unidimensional IRT models, this study extended the literature by considering a multidimensional IRT model for polytomous responses, namely the multidimensional graded response model. Moreover, this study is one of few studies that specifically compared the performance of full-information maximum likelihood (FIML) estimation versus robust weighted least squares (WLS) estimation when the normality assumption is violated. The research also manipulated the number of nonnormal latent trait dimensions. Results showed that FIML consistently outperformed WLS when there were one or multiple skewed latent trait distributions. More interestingly, the bias of the discrimination parameters was non-ignorable only when the corresponding factor was skewed. Having other skewed factors did not further exacerbate the bias, whereas biases of boundary parameters increased as more nonnormal factors were added. The item parameter standard errors recovered well with both estimation algorithms regardless of the number of nonnormal dimensions.     

The roles of delay and probability discounting in texting while driving: Toward the development of a translational scientific program

A sample of 109 college students completed a survey to assess how frequently they send or read text messages while driving. In a novel discounting task with a hypothetical scenario in which participants receive a text message while driving, they rated the likelihood of replying to a text message immediately versus waiting to reply until arriving at a destination. The scenario presented several delays to a destination and probabilities of a motor vehicle crash. The likelihood of waiting to reply decreased as a function of both the delay until the destination and the probability of a motor vehicle crash. Self‐reported higher frequencies of texting while driving were associated with greater rates of both delay and probability discounting. The degree of delay discounting was altered as a function of the probability of a motor vehicle crash and vice versa. These results suggest that both delay and probability discounting are important underlying mechanisms of drivers' decision to text while driving.