A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.     

Effects of fixed-ratio sample and choice response requirements upon oddity matching

Three pigeons were trained on oddity matching in which either 1, 4, 8, 16, or 32 sample-key observing responses were required to turn off the sample stimuli and turn on the comparison stimuli. Oddity accuracy increased when the observing-response requirement was raised and decreased when the requirement was lowered. Next, while the observing requirement was maintained at one response, the number of responses required to the comparison stimuli was either 1, 4, 8, 16, or 32. Under these conditions, choice was defined as the comparison that first accumulated the required number of responses. In general, increasing the comparison-response requirement decreased accuracy and lowering the comparison requirement increased accuracy. The fixed-ratio observing requirements appeared to facilitate control by stimuli serving an instructional function.     

Demand for food on fixed-ratio schedules as a function of the quality of concurrently available reinforcement

Six rats lever pressed for food on concurrent fixed-ratio schedules, in a two-compartment chamber. In one compartment, mixed diet pellets were delivered on fixed-ratio schedules of 1, 6, 11, and 16; in the other, either no food was delivered, or sucrose or mixed diet pellets were delivered on fixed-ratio 8. The number of pellets obtained in the first compartment declined as a function of fixed-ratio size in that compartment in all three conditions, but the decline was greatest overall with mixed diet pellets concurrently available in the other compartment, and least with no food concurrently available. The result is discussed in terms of economic demand theory, and is consistent with the prediction that elasticity of demand for a commodity (defined in operant terms as the ratio of the proportionate change in number of reinforcements per session to the proportionate change in fixed-ratio size) is greater the more substitutable for that commodity are any concurrently available commodities.     

Producing a change from competition to sharing: effects of large and adjusting response requirements

Pairs of high-school students matched-to-sample for money. On each trial, the first pair member to complete a fixed ratio of knob-pulling responses could work the matching problem on that trial. Competition occurred when both pair members responded for the problem. Sharing occurred when only one pair member responded on each trial, and the subjects alternated trials. Hence, sharing requires less responding and still allows a moderate number of reinforcers for each subject. Recent research has shown that increasing the response requirement to the point that it may have aversive properties will produce a change from competition to sharing. A related variable is an adjusting schedule that adjusts the subjects' response requirements so that their abilities to take reinforcers are equal. In this way, subjects might learn that competition requires more responding but produces no more reinforcers. However, recent research also suggests that competition decreases over sessions without experimental manipulations. Because of this possibility of a time-related variable, ratio size and an adjusting schedule were studied in a group design. Competition did decrease for all groups over sessions, but the large-ratio groups switched from competition to sharing sooner than the low-ratio groups. The adjusting schedule had a similar but smaller effect.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

非符号数量表征和符号分数表征的关系

个体学习符号分数的一个关键是能对其数值形成准确表征。现有研究假设符号分数表征的认知基础是人类自婴幼儿期就具有的非符号数量表征(如表征两个集合各自的数量, 或两个数量的比例)。其证据包括表征非符号数量(尤其是非符号数量比例关系)和表征符号分数在行为和大脑神经活动层面上都表现出相关性。然而要说明非符号数量表征是符号分数表征的认知基础, 还需更多研究表明两者在数量概念上的独特相关和因果联系, 并阐明符号分数表征形成的认知机制。     

Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

得失情境下他人参照点及心理距离对自我-他人利益权衡的影响

以福利权衡率(WTR)为利他程度的指标, 通过3个实验逐步深入地考察了得失情境下他人参照点及心理距离对自我-他人利益权衡的影响。实验1的结果表明, 得失情境并未改变被试的WTR。实验2引入他人底线、现状和目标三个参照点变量, 发现被试获益情境下的WTR高于损失情境, 且WTR从高到低依次为他人临近底线、目标和现状; 他人临近底线时, 被试在获益情境下的WTR高于损失情境, 而他人临近现状和目标时, 个体在得失情境下的WTR无显著差异。实验3进一步引入心理距离变量, 发现心理距离较近他人的WTR高于较远他人, 且与得失情境和参照点发生了复杂的交互效应, 得失情境的主效应消失了, 但总体上并未改变实验2发现的参照点效应。这些结果对于更深入地理解得失不对称效应、三参照点理论及社会折扣和自我-他人决策差异研究的相关发现具有一定的启示意义。