The response ratio hypothesis for magnitude estimation

Assume that each presentation of a signal produces two independent random variable representations and that the ratio of responses on successive trials of a magnitude estimation experiment are proportional to the ratio of a representation from the present trial, which representation is then lost, to the remaining one from the previous trial. The mean response to a particular signal depends on the mean of the representation used, but in general exhibits drift over trials and sequential effects due to the preceeding trial; the mean response ratio does not exhibit drift, but it has a simple form only when there are no sequential effects; however, a modified mean ratio function has a simple form. A model suggested by D. V. Cross is a special case of this one. Simple timing and counting models for the representations fail to exhibit sequential effects, contrary to considerable data. However, data of the authors have suggested a version of the timing model in which the sample size of the representation varies by an order of magnitude depending on how close the signal is to the preceding one; this hypothesis accounts for the observed sequential effects and other aspects of the data.     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

Multilevel mediation analysis: The effects of omitted variables in the 1–1–1 model

Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1–1–1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c – c′) are equivalent at the between‐ and within‐cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within‐cluster ab and c – c′ no longer holds. Correlation between random slopes implies that the within‐cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.     

A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

Goodness of fit of trend curves and significance of trend differences

Experimental studies of the successive changes (frequently represented by curves describing laws of learning and other similar functional relationships) in a criterion variable accompanying experimental variations in a given treatment, and experimental comparisons of such changes for different populations or for different treatments, constitute a large and important class of psychological experiments. In most such experiments, no attempt has been made to analyze or to make allowance for errors of sampling or of observation. In many others, the techniques of error analysis that have been employed have been inefficient, inexact, or inappropriate. This paper suggests tests, using the methods of analysis of variance, of certain hypotheses concerning trends and trend differences in sample means obtained in experiments of this general type. For means of successive independent samples, tests are provided of the hypotheses: (H ₁) that there is no trend, or that the trend is a horizontal straight line, (H ₃) that there is a linear trend, (H ₅) that the trend is as described by a line not derived from the observed means, and (H ₇) that the trend is as described by a line fitted to the observed means. Tests are also provided of similar hypotheses (H ₂,H ₄,H ₆, andH ₈, respectively) for means of successive measurements of the same sample. Finally, tests are provided of the null hypotheses that there is no difference in trend in two series of means: (H ₉) when each mean in each series is based on an independent sample, (H ₁₀) when each pair of corresponding means is based on an independent sample, (H ₁₁) when each series of means is based on an independent sample, and (H ₁₂) when both series are based on a single sample.     

A comparison of visual tilt illusions measured by the techniques of verticle setting, parallel matching, and dot alignment.

The tilt illusion (TI) was investigated by using both short (19 min) and long (2 deg 6 min) test lines, at three angles of test line-inducing line separation (15 degrees, 45 degrees, and 75 degrees). Three groups of ten observers each provided data under one of three task conditions: vertical judgment, parallel matching, and dot alignment on a common visual display. The main result was that both the vertical judgment and the parallel matching task provided similar, classic TI angular functions with the means ordered 15 degrees greater than 45 degrees greater than 75 degrees and with small attraction effects at 75 degrees in three of the four relevant functions. The third task, dot alignment, yielded results different from the average of the other two: no attraction effects occurred and, with the short test line, the obtained mean illusion at 45 degrees exceeded those at the other intersect angles. These results are consistent with alignment data reported by others. One explanation is that the inducing line produces an apparent bowing of the test line which would be reflected in dot alignments but not in vertical setting or in parallel matching. However, direct evidence does not support this hypothesis. An alternate hypothesis, for which independent evidence exists, is that alignment errors reflect perceptual mistracking but that the origin of these errors is not the tip of the test line but within it. Although this does not explain dot alignment errors, it highlights their complexity and the need to interpret them with caution.     

How accurate are interpretations of curriculum-based measurement progress monitoring data? Visual analysis versus decision rules

Curriculum based measurement of oral reading (CBM-R) is used to monitor the effects of academic interventions for individual students. Decisions to continue, modify, or terminate these interventions are made by interpreting time series CBM-R data. Such interpretation is founded upon visual analysis or the application of decision rules. The purpose of this study was to compare the accuracy of visual analysis and decision rules. Visual analysts interpreted 108 CBM-R progress monitoring graphs one of three ways: (a) without graphic aids, (b) with a goal line, or (c) with a goal line and a trend line. Graphs differed along three dimensions, including trend magnitude, variability of observations, and duration of data collection. Automated trend line and data point decision rules were also applied to each graph. Inferential analyses permitted the estimation of the probability of a correct decision (i.e., the student is improving – continue the intervention, or the student is not improving – discontinue the intervention) for each evaluation method as a function of trend magnitude, variability of observations, and duration of data collection. All evaluation methods performed better when students made adequate progress. Visual analysis and decision rules performed similarly when observations were less variable. Results suggest that educators should collect data for more than six weeks, take steps to control measurement error, and visually analyze graphs when data are variable. Implications for practice and research are discussed.     

Assessing the driving distraction effect of vehicle HMI displays using data mining techniques

With the rapid development of human–machine interface (HMI) systems in vehicles, driving distraction caused by HMI displays affects road safety. This study presents a data mining technique to model the four driving distraction indicators: speed deviation, lane departure standard deviation, dwell time, and mean glance time. Driving distraction data was collected on a real-car driving simulator. 3 secondary tasks in 13 mass produced cars were tested by 24 drivers. The random forest algorithm outperformed linear regression, extreme gradient boosting, and multi-layer perceptron as the best model, demonstrating good regression performance as well as good interpretability. The result of random forest showed that the importance of target speed is large for all driving distraction indicators. Among the variables of interaction and user interface design, less step and less on-screen distance of finger movement are efficient for lowering lane departure standard deviation and dwell time. The position of right point is another important variable, and should be between 37 and 47 degrees on a typical sample in this study. A larger angle leads to bigger lane departure, while a smaller angle leads to bigger mean glance time. Most variables of HMI display positioning themselves are not important. This study provides one driving distraction assessment method with a variable impact trend analysis for HMI secondary tasks in an early phase of product development.     

The role of “irrelevant” derogation in vicarious aggression catharsis: A field experiment

In order to test hypotheses about the occurence of aggression catharsis, a field experiment was conducted in which passengers in taxi cabs served as subjects. En route to each subject's destination, the taxi driver left the cab with the meter operating for an amount of time which resulted in a small or large overcharge (the first independent variable). When the driver returned, subjects read one of four letters which either praised or derogated the driver (the second independent variable) on a relevant or irrelevant dimension (the third independent variable). Subjects' responses confirmed the principal hypothesis on several different atitudinal and behavioral dependent measures: angered subjects tended to complain less often, more often paid the overcharge, and more often left a tip, when they read the irrelevant derogation letter. The results contribute to the delineation of a set of conditions under which vicarious catharsis can be clearly observed.     

Instructions and reinforcement in the observing behavior of adults and children

Observing responses of college students and children of different ages (4 to 5, 9 to 10, and 13 to 14 years) were studied using two-component schedules of reinforcement. Different frequencies or numbers of points were given in the components and points were backed by either money or instructions about getting points (e.g., “points are for the experimenter's information only”). Stimuli that were either correlated or uncorrelated with the components were contingent on presses on either of two concurrently available levers (observing responses). In each of three experiments, preferences for stimuli were consistent with the conditioned-reinforcement hypothesis of observing but inconsistent with the uncertainty-reduction hypothesis. Stimulus preferences were established, eliminated, or reversed by instructions about the significance of getting points not backed with money. Instructions to in effect ignore points with no monetary value eliminated stimulus preference provided that money was not associated with points in other conditions for the same subjects. Stimulus preferences were otherwise independent of monetary point value. Instructions that described reinforcement contingencies promoted more rapid adjustment to the contingencies than occurred without them, and preferences were less variable across sessions within subjects and were on the average more extreme. Although some results involving absolute rates of observing depended upon the age of subjects, stimulus preferences did not. The data suggest that the conditioned-reinforcement hypothesis of observing has considerable generality for humans in choice procedures in the laboratory. That monetary value of points did not affect preferences in a graded fashion is consistent with versions of the conditioned-reinforcement hypothesis which emphasize reduction in delay to reinforcement over other reinforcement parameters.     

A Propensity Score Adjustment for Multiple Group Structural Equation Modeling

In the behavioral and social sciences, quasi-experimental and observational studies are used due to the difficulty achieving a random assignment. However, the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates. To estimate average treatment effects when the treatment variable is binary, Rosenbaum and Rubin (1983a) proposed adjustment methods for pretreatment variables using the propensity score. However, these studies were interested only in estimating the average causal effect and/or marginal means. In the behavioral and social sciences, a general estimation method is required to estimate parameters in multiple group structural equation modeling where the differences of covariates are adjusted. We show that a Horvitz–Thompson-type estimator, propensity score weighted M estimator (PWME) is consistent, even when we use estimated propensity scores, and the asymptotic variance of the PWME is shown to be less than that with true propensity scores. Furthermore, we show that the asymptotic distribution of the propensity score weighted statistic under a null hypothesis is a weighted sum of independent χ² ₁ variables. We show the method can compare latent variable means with covariates adjusted using propensity scores, which was not feasible by previous methods. We also apply the proposed method for correlated longitudinal binary responses with informative dropout using data from the Longitudinal Study of Aging (LSOA). The results of a simulation study indicate that the proposed estimation method is more robust than the maximum likelihood (ML) estimation method, in that PWME does not require the knowledge of the relationships among dependent variables and covariates.     

两类常见的类别变量调节效应分析

类别变量在心理学和其他社科研究领域经常遇到,当自变量或调节变量为类别变量时,应当如何分析调节效应呢？详述了多类别变量的被试间设计和两水平被试内设计（因变量重复测量2次）的调节效应分析方法,并给出了分析流程。先进行调节效应的显著性检验,后用选点法或Johnson-Neyman法进行简单斜率检验。多类别变量被试间设计的简单斜率检验是先进行整体检验,后进行配对检验。用两个实际例子演示如何进行类别变量的调节效应分析,最后展望了两类设计的类别变量调节研究的拓展方向,例如更复杂的类别变量的调节模型等。     

Multilevel Modeling with Correlated Effects

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized method of moments (GMM) estimation techniques in multilevel modeling, the authors present a series of estimators along a robust to efficient continuum. This continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects. It is shown that the GMM approach provides an overarching framework that encompasses well-known estimators such as fixed and random effects estimators and also provides more options. These GMM estimators can be expressed as instrumental variable (IV) estimators which enhances their interpretability. Moreover, by exploiting the hierarchical structure of the data, the current technique does not require additional variables unlike traditional IV methods. Further, statistical tests are developed to compare the different estimators. A simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency. It further shows that not only are regression coefficients biased, but variance components may be severely underestimated in the presence of correlated effects. Empirical standard errors are employed as they are less sensitive to correlated effects when compared to model-based standard errors. An example using student achievement data shows that GMM estimators can be effectively used in a search for the most efficient among unbiased estimators. This research was supported by the National Academy of Education/Spencer Foundation and the National Science Foundation, grant number SES-0436274. We thank the editor, associate editor, and referees for detailed feedback that helped improve the paper.     

A Truncated-Probit Item Response Model for Estimating Psychophysical Thresholds

Human abilities in perceptual domains have conventionally been described with reference to a threshold that may be defined as the maximum amount of stimulation which leads to baseline performance. Traditional psychometric links, such as the probit, logit, and t, are incompatible with a threshold as there are no true scores corresponding to baseline performance. We introduce a truncated probit link for modeling thresholds and develop a two-parameter IRT model based on this link. The model is Bayesian and analysis is performed with MCMC sampling. Through simulation, we show that the model provides for accurate measurement of performance with thresholds. The model is applied to a digit-classification experiment in which digits are briefly flashed and then subsequently masked. Using parameter estimates from the model, individuals’ thresholds for flashed-digit discrimination is estimated.     

基于人工神经网络的一种效度凭证求取方法

针对基于统计学的效度凭证求取方法所存在的问题,提出了基于人工神经网络的效度凭证求取方法。蒙特卡罗模拟实验和对实际数据的分析表明,当测验分数和效标分数为单变量且非线性关系时,或者测验分数和效标分数为多变量时,运用神经网络方法可以比统计学方法更好地求取心理测验效度的基于和其他变量关系的凭证。     

Syllable similarity: The effects of differences in vowels, consonants, and order

In five experiments with synthetic and natural speech syllables, a rating task we used to study the effects of differences in vowels, consonants, and segment order on judged syllable similarity. The results of Experiments I-IV support neither a purely phonemic model of speech representation, in which vowel, consonant, and order are represented independently, nor a purely syllabic model, in which the three factors are integrated. Instead, the data indicate that subjects compare representations in which adjacent vowel and consonant are independent of one another but are not independent of their positions in the syllable. Experiment V provided no support for the hypothesis that this position-sensitive coding is due to acoustic differences in formant transitions.     

多层多项Logit模型：原理与应用

常用的多层线性模型要求因变量是服从正态分布的连续变量,却无法处理因变量为离散变量的嵌套数据.多层多项Logit模型能够处理因变量是无序多分类的多层嵌套数据,但这一模型在我国心理学研究中却鲜有介绍和应用.研究简要介绍了多层多项Logit模型的原理、参数估计和假设检验,然后分别用该模型和传统Logistic回归模型探讨个体因素和区域因素对35721名学生进入不同高校就读机会的影响并对结果进行了解释,结果表明多层多项Logit模型比传统Logistic回归模型更拟合数据.     

Schema: the variability of practice hypothesis

An experiment is presented which tested the variability of practice hypothesis of Schmidt's (1975) schema theory. Children served as subjects and a complex motor task was used. The results supported the variability of practice hypothesis in that the group that had more variable practice did perform better on the average on a novel variation of the task than did the group with less variable practice. There was no support for the suggestion that variability of practice would increase the rate of improvement on the novel variation. The results are discussed in relation to the differential importance of the four subcomponents of the schema in its development.