Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

Probabilistic multidimensional scaling: Complete and incomplete data

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets. This research was supported by National Science Grant No. SOC76-20517. The first author would especially like to express his gratitude to the Netherlands Institute for Advanced Study for its very substantial help with this research.     

On Green's best linear composites with a specified structure,and oblique estimates of factor scores

Green solved the problem of least-squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix. In the present paper an omission in Green's proof is discussed and resolved. Furthermore, it is shown that some recently published solutions for estimating oblique factor scores are special cases of Green's solution for the case of fixed covariance matrices.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

Response–reinforcer contiguity versus response-rate–reinforcer-rate covariance in rats' lever pressing: Support for a multiscale view

The multiscale molar view sees behavior as a flow, like a river, extended in time. Matching theory expresses the way activities compete for time. Relative time taken by any activity depends on relative induction. The present experiment tested matching theory applied to concurrent contingent and noncontingent food. As adjunctive activities that compete with operant activity, we recorded hopper head entries and presses on a lever near the food hopper that had no programmed consequences. Eight naïve rats were first exposed to a variable-time 60 s schedule, which across conditions was gradually transformed into a variable-interval 60 s schedule by increasing the proportion of food that was delivered contingent on pressing a lever far from the hopper. Another group of 4 rats that had been trained to press a lever near a food hopper were introduced in the second condition, in which one food delivery was contingent on far-lever pressing. We found induction following a power function to describe pressing on the far lever (operant activity). Matching theory combined with power-function induction also accounted for adjunctive activity. Results with single contingent food deliveries provided little support for the molecular view that behavior consists of discrete responses “strengthened” by immediately following reinforcers.     

Avoidance,induction, and the illusion of reinforcement

Environmental events that impact reproductive success may be called phylogenetically important events (PIEs). Some promote reproductive success, like mates and food; others threaten reproductive success, like predators and injury. Beneficial PIEs induce activities that enhance them, and detrimental PIEs induce activities that mitigate or avoid them. Free-operant avoidance relies on electric shock as a proxy for injury, a PIE. One theory takes avoidance behavior to be reinforced by its reducing shock rate. A more complete explanation is that avoidance both reduces shock rate and is induced by the PIEs it usually prevents. Shocks received act in concert with shock-rate reduction, in a feedback system. Four parametric data sets were analyzed to show that avoidance is induced by received shock rate according to power functions. Avoidance is not reinforced at all; avoidance is induced by its failures. Induction explains not only avoidance itself, but also phenomena unique to avoidance, like warmup and effects of unavoidable shock. Induction explains behavior more generally than reinforcement, because induction explains not only food-maintained operant and nonoperant behavior, but also shock-maintained behavior, including avoidance. Reinforcement fails to explain behavior when reinforcement is defined as strengthening by consequences. Induction erases the distinction between consequences and antecedents.     

4~8年级学生分数数量表征的准确性及形式

在分数学习中,分数数量表征是非常重要的方面。本研究利用数字线估计任务对四到八年级学生分数数量表征的情况进行探索。研究结果表明：随着年级升高,被试分数数量表征的准确性也随之提高;被试对单位分数和非单位分数表征的准确性存在显著差异,表现为对单位分数表征的准确性显著高于对非单位分数的表征,这种差异在低年级显著,随着年级的增长,差异逐渐消失;四到八年级学生在0~3数字线上,对分数数量的表征表现为线性形式而非对数形式,且这种线性表征形式是在六年级开始出现并随着年龄增长逐渐发展起来的。中西方儿童在分数数量表征的准确性和形式上有相似的发展路径,但是在表征准确性上中国儿童更高、线性形式出现年级上中国儿童可能更早。     

时间赋义对数字空间表征的影响：来自数字线估计任务的证据

数字线估计任务的大量研究以纯数字为研究对象而忽视了赋义数字。本研究以Siegler等的数字线估计任务为原型,探讨在对数字时间赋义条件下小学二、四和六年级儿童的数字表征形式是否发生变化。结果表明,小学二年级是0-1000范围内数字表征从对数形式转换为线性形式的转折点,对数字赋予时间含义后,三个年级均出现了赋义效应。在线性模型和对数模型中时间赋义的作用相反,时间赋义表现出抑线升对（抑制线性模型提升对数模型解释力）的效果。     

Plasticity associated with escalated operant ethanol self-administration during acute withdrawal in ethanol-dependent rats requires intact matrix metalloproteinase systems

Repeated cycles of ethanol intoxication and withdrawal associated with dependence induce neuroadaptations in a variety of brain systems. Withdrawal-induced negative emotional states can be ameliorated by ethanol consumption; a learned process termed negative reinforcement. Accordingly, a dependence-induced phenotype is escalated ethanol self-administration. Matrix metalloproteinases (MMPs) are proteolytic enzymes which degrade the extracellular matrix to allow for synaptic reorganization and plasticity. To test the hypothesis that an intact MMP system is required for animals to learn about the negative reinforcing effects of ethanol and display escalated self-administration during acute withdrawal when ethanol-dependent, male Wistar rats were trained to self-administer ethanol and then assigned to either acute or chronic MMP inhibition treatment groups. The chronic treatment group received intracerebroventricular (ICV) infusions of the broad spectrum MMP inhibitor FN-439 or artificial cerebrospinal fluid (aCSF) via osmotic minipumps during a 1 month ethanol dependence induction period and subsequent post-dependence induction self-administration sessions that occurred during acute withdrawal. The acute treatment group only received ICV FN-439 or aCSF on the day of self-administration sessions following dependence induction during acute withdrawal. The results showed that inhibition of MMPs attenuated escalated ethanol self-administration following chronic and acute exposure conditions. Furthermore, once learning (i.e., plasticity) had occurred, MMP inhibition had no impact on escalated response patterns and animals previously subjected to MMP inhibition that did not escalate evidenced normal escalations in operant ethanol self-administration once FN-439 treatments were terminated. Thus, the present data identified that an intact MMP system is required for the escalated responding that occurs during acute withdrawal in dependent animals and implicate such escalation as a learned response.