Techniques for rotating two or more loading matrices to optimal agreement and simple structure: A comparison and some technical details

Matrices of factor loadings are often rotated to simple structure. When more than one loading matrix is available for the same variables, the loading matrices can be compared after rotating them all (separately) to simple structure. An alternative procedure is to rotate them to optimal agreement, and then compare them. In the present paper techniques are described that combine these two procedures. Specifically, five techniques that combine the ideals of rotation to optimal agreement and rotation to simple structure are compared on the basis of contrived and empirical data. For the contrived data, it is assessed to what extent the rotations recover the underlying common structure. For both the contrived and the empirical data it is studied to what extent the techniques give well matching rotated matrices, to what extent these have a simple structure, and to what extent the most prominent parts of the different loading matrices agree. It was found that the simple procedure of combining a Generalized Procrustes Analysis (GPA) with Varimax on the mean of the matched loading matrices performs very well on all criteria, and, for most purposes, offers an attractive compromise of rotation to agreement and simple structure. In addition to this comparison, some technical improvements are proposed for Bloxom's rotation to simple structure and maximum similarity.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to René van der Heijden for assistance in programming the procedures in the simulation study reported in this paper, and to Jos ten Berge, three anonymous reviewers and an associate editor for helpful comments on an earlier version of this paper.     

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.     

Sensitivity to reinforcer duration in a self-control procedure

In a concurrent-chains procedure, pigeons' responses on left and right keys were followed by reinforcers of different durations at different delays following the choice responses. Three pairs of reinforcer delays were arranged in each session, and reinforcer durations were varied over conditions. In Experiment 1 reinforcer delays were unequal, and in Experiment 2 reinforcer delays were equal. In Experiment 1 preference reversal was demonstrated in that an immediate short reinforcer was chosen more frequently than a longer reinforcer delayed 6 s from the choice, whereas the longer reinforcer was chosen more frequently when delays to both reinforcers were lengthened. In both experiments, choice responding was more sensitive to variations in reinforcer duration at overall longer reinforcer delays than at overall shorter reinforcer delays, independently of whether fixed-interval or variable-interval schedules were arranged in the choice phase. We concluded that preference reversal results from a change in sensitivity of choice responding to ratios of reinforcer duration as the delays to both reinforcers are lengthened.     

Independence of stimulus discriminability from absolute rate of reinforcement in a signal-detection procedure.

Three experiments are reported in which two pigeons were trained to detect differences in stimulus duration under varying levels of absolute rate of reinforcement. Two red stimuli, differing in duration, were arranged probabilistically on the center key of a three-key chamber. On completion of the center-key duration, the center keylight was extinguished and the two side keys were illuminated white. Correct responses were left-key pecks following the shorter duration and right-key pecks following the longer duration. In Experiment 1, relative rate of reinforcement for correct responses was held constant and absolute rate of reinforcement was varied in seven conditions from continuous reinforcement to a variable-interval 90-second schedule. In Experiment 2, relative rate of reinforcement was manipulated across three different absolute rates of reinforcement (continuous reinforcement, variable-interval 15-second, and variable-interval 45-second). Stimulus discriminability was unaffected by changes in absolute or relative rates of reinforcement. Experiment 3 showed that discriminability was also unaffected by arranging the same consequences (three-second blackout) for unreinforced correct responses and errors.     

Independence of sensitivity to relative reinforcement rate and discriminability in signal detection.

Six pigeons were trained to detect differences between two white stimuli, S1 and S2, differing in duration and arranged probabilistically on the center key of a three-key chamber. Detection performance was measured at two levels of discriminability. At one level, S1 was five seconds and S2 was thirty seconds. At the other level, S1 was twenty seconds and S2 was thirty seconds. The procedure was a standard signal-detection yes-no design in which stimulus-presentation probability was varied from .1 to .9 at both discriminability levels. On completion of the center-key stimulus, a peck on the center key darkened the center-key light and turned on the two red side keys. A left-key response was "correct" on S1 trials, and a right-key response was "correct" on S2 trials. Correct responses produced food reinforcement on a variable-ratio 1.3 schedule. Incorrect responses produced three second blackout. Discriminability was higher for the five-second versus thirty-second conditions than for the twenty-second versus thirty-second conditions, but there were no differences in sensitivity of behavior to reinforcement variation for the two stimulus pairs. Response bias was a function of the relative reinforcement rate for correct choice responses.     

Choice in a variable environment: effects of unequal reinforcer distributions

Six pigeons were trained in a procedure in which sessions included seven unsignaled components, each offering two pecking keys, and each providing a potentially different reinforcer ratio between the two keys. Across conditions, various combinations of reinforcer ratios and reinforcer-magnitude ratios were used to create unequal reinforcer distributions between the two alternatives when averaged across a session. The results extended previous research using the same basic procedure that had included only reinforcer distributions symmetrical around 1:1. Data analyses suggested that the variables controlling choice operated at a number of levels: First, individual reinforcers had local effects on choice; second, sequences of successive reinforcers obtained at the same alternative (continuations) had cumulative effects; and, third, when these sequences themselves occurred with greater frequency, their effects further cumulated. A reinforcer obtained at the other alternative following a sequence of continuations (a discontinuation) had a large effect and apparently reset choice to levels approximating the sessional reinforcer ratio.     

一种基于多阶认知诊断模型测评科学素养的方法

科学素养是指作为一名有反思意识的公民所具有的解决科学问题和运用科学理念的能力。为实现在认知诊断中对科学素养的测评, 本文基于PISA 2015科学素养测评框架首次提出科学素养包含的三阶潜在结构, 使用新提出的多阶认知诊断模型对PISA 2015科学测评数据进行分析, 并通过模拟研究探究新模型的心理测量学性能。结果表明：(1)新模型能够较好地分析包含三阶潜在结构的科学素养; (2)科学知识对科学素养的影响最大, 科学背景次之, 科学能力的影响最小; (3)全贝叶斯MCMC算法能够为新模型提供较精准的参数估计。     

Substitution effects in a generalized token economy with pigeons

Pigeons made repeated choices between earning and exchanging reinforcer‐specific tokens (green tokens exchangeable for food, red tokens exchangeable for water) and reinforcer‐general tokens (white tokens exchangeable for food or water) in a closed token economy. Food and green food tokens could be earned on one panel; water and red water tokens could be earned on a second panel; white generalized tokens could be earned on either panel. Responses on one key produced tokens according to a fixed‐ratio schedule, whereas responses on a second key produced exchange periods, during which all previously earned tokens could be exchanged for the appropriate commodity. Most conditions were conducted in a closed economy, and pigeons distributed their token allocation in ways that permitted food and water consumption. When the price of all tokens was equal and low, most pigeons preferred the generalized tokens. When token‐production prices were manipulated, pigeons reduced production of the tokens that increased in price while increasing production of the generalized tokens that remained at a fixed price. The latter is consistent with a substitution effect: Generalized tokens increased and were exchanged for the more expensive reinforcer. When food and water were made freely available outside the session, token production and exchange was sharply reduced but was not eliminated, even in conditions when it no longer produced tokens. The results join with other recent data in showing sustained generalized functions of token reinforcers, and demonstrate the utility of token‐economic methods for assessing demand for and substitution among multiple commodities in a laboratory context.     

Visual cognitive algorithms for high-dimensional data and super-intelligence challenges

In the long run the cognitive algorithms intend to make super-intelligent machines and super-intelligent humans. This paper presents a technical process to reach specific aspects of super-intelligence that are out of the current human cognitive abilities. These aspects are inabilities to discover patterns in large numeric multidimensional data with a naked eye. This is a long-standing problem in Data Science and Modeling in general. The major obstacle is in human inability to see n-D data by a naked eye and our needs in visualization means to represent n-D data in 2-D losslessly. While these means exist their number and abilities are limited. This paper expands the class of such lossless visual methods, by further developing a new concept of Generalized Shifted Paired Coordinates. It shows the advantages of proposed reversible lossless technique by representing real data and by proving mathematical properties.     

Achievement-oriented and dependency-oriented parental psychological control: An examination of specificity to middle childhood achievement and dependency-related problems

Middle childhood is considered a sensitive phase for the development of both dependency and achievement-related problems. In order to target efficient prevention and treatment, it is necessary to identify unique associations with possible precursors. This study hypothesized that children’s dependency-related problems (i.e., separation anxiety and generalized anxiety) would uniquely relate to parental dependency-oriented psychological control and that children’s achievement-related problems (i.e., extrinsic motivation and maladaptive perfectionism) would uniquely relate to parental achievement-oriented psychological control. The study included 180 elementary school children. Results showed that higher levels of children’s separation anxiety uniquely related to more parental dependency-oriented psychological control, while higher levels of children’s extrinsic motivation uniquely related to more parental achievement-oriented psychological control. Contrary to the expectations, higher levels of children’s maladaptive perfectionism were associated with both dimensions of parental psychological control, and children’s generalized anxiety was not associated with any dimension. Study implications are discussed.