Random intercept item factor analysis

The common factor model assumes that the linear coefficients (intercepts and factor loadings) linking the observed variables to the latent factors are fixed coefficients (i.e., common for all participants). When the observed variables are participants' observed responses to stimuli, such as their responses to the items of a questionnaire, the assumption of common linear coefficients may be too restrictive. For instance, this may occur if participants consistently use the response scale idiosyncratically. To account for this phenomenon, the authors partially relax the fixed coefficients assumption by allowing the intercepts in the factor model to change across participants. The model is attractive when m factors are expected on the basis of substantive theory but m + 1 factors are needed in practice to adequately reproduce the data. Also, this model for single-level data can be fitted with conventional software for structural equation modeling. The authors demonstrate the use of this model with an empirical data set on optimism in which they compare it with competing models such as the bifactor and the correlated trait-correlated method minus 1 models.     

"青少年学生生活满意度量表"的概化理论研究

概化理论是用统计调整技术分析测量误差的一种测量理论,它侧重于从宏观方面讨论实测时的测量条件与结论推广应用范围之间的关系来探讨测量的外部效度问题。本文用概化理论对青少年学生生活满意度量表(CASLSS)进行了研究,得到以下研究结果:(1)对于生活满意度的维度数目,就我国青少年学生而言取6到8个维度较为合适,当对CASLSS取2个维度时,CASLSS只适合作常模参照性解释,而不适合作标准参照性解释;(2)CASLSS的各分量表和总量表的信度较高,且它不仅可以作常模参照性解释,还适合作标准参照性解释;(3)CASLSS的环境满意度因子相对其它五个因子而言,量表特性稍差,是今后改进该量表的主要方向。CASLSS无论是各个因子还是总量表均具有非常优良的量表特性,值得在实际的工作和研究中加以推广应用。     

A generalized family of coefficients of relational agreement for numerical scales

A family of coefficients of relational agreement for numerical scales is proposed. The theory is a generalization to multiple judges of the Zegers and ten Berge theory of association coefficients for two variables and is based on the premise that the choice of a coefficient depends on the scale type of the variables, defined by the class of admissible transformations. Coefficients of relational agreement that denote agreement with respect to empirically meaningful relationships are derived for absolute, ratio, interval, and additive scales. The proposed theory is compared to intraclass correlation, and it is shown that the coefficient of additivity is identical to one measure of intraclass correlation.The author thanks the Editor and anonymous reviewers for helpful suggestions.     

Statistical approaches to achieving sufficiently high test score reliabilities for research purposes

The author provides statistical approaches to aid investigators in assuring that sufficiently high test score reliabilities are achieved for specific research purposes. The statistical approaches use tests of statistical significance between the obtained reliability and lowest population reliability that an investigator will tolerate. The statistical approaches work for coefficient alpha and related coefficients and for alternate-forms, split-half (2-part alpha), and retest reliabilities. The author shows that, in some instances, a formula can help to estimate the sample size necessary for the statistical test.     

Biases and Standard Errors of Standardized Regression Coefficients

The paper obtains consistent standard errors (SE) and biases of order O(1/n) for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample standardized regression coefficients are also biased in general, although it should not be a concern in practice when the sample size is not too small. Monte Carlo results imply that, for both standardized and unstandardized sample regression coefficients, SE estimates based on asymptotics tend to under-predict the empirical ones at smaller sample sizes.     

Monte Carlo tests of the Rasch model based on scalability coefficients

For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non‐parametric item response theory a natural starting‐point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using p‐values computed using Markov chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.     

Replies to comments on "Which method delivers greater signal-to-noise ratio: Structural equation modelling or regression analysis with weighted composites?" by Yuan and Fang (2023)

Observational data typically contain measurement errors. Covariance-based structural equation modelling (CB-SEM) is capable of modelling measurement errors and yields consistent parameter estimates. In contrast, methods of regression analysis using weighted composites as well as a partial least squares approach to SEM facilitate the prediction and diagnosis of individuals/participants. But regression analysis with weighted composites has been known to yield attenuated regression coefficients when predictors contain errors. Contrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the signal-to-noise ratio (SNR). In particular, the SNR for the regression coefficient via the least squares (LS) method with equally weighted composites is mathematically greater than that by CB-SEM if the items for each factor are parallel, even when the SEM model is correctly specified and estimated by an efficient method. Analytical, numerical and empirical results also show that LS regression using weighted composites performs as well as or better than the normal maximum likelihood method for CB-SEM under many conditions even when the population distribution is multivariate normal. Results also show that the LS regression coefficients become more efficient when considering the sampling errors in the weights of composites than those that are conditional on weights.     

VIOLATIONS OF BRANCH INDEPENDENCE IN JUDGMENTS OF THE VALUE OF GAMBLES

Abstract —Branch independence is weaker than Savage's "sure thing" principle. It requires that judgments of gambles with a common outcome produced by the same probability-event must not reverse order when that common outcome is changed. Subjects judged 168 gambles from viewpoints of both buyer (highest buying price) and in both viewpoints. Violations also changed systematically between viewpoints, consistent with the theory that viewpoint affects configural weighting but not the utility function. Violations of branch independence were opposite those predicted by the model of cumulative prospect theory. The middle of three equally likely outcomes received the most weight in the seller's viewpoint. In the buyer's, lower outcomes received greater weights. In both viewpoints, the ratio of weights of the middle outcome to the highest outcome exceeded the ratio of weights of the lowest outcome to the middle outcome.     

The Effects of Coaching Subjects in the Recognition of Facial Expressions

A wide range of individual differences in the ability to identify facial expressions of emotion has been reported. As evidence that these inequalities are due in large part to differences of practice in reacting to expressive criteria, rather than to innate factors, F. H. Allport has offered the data from an experimental observation of the effects of training subjects of varying ability for fifteen minutes in the analysis of facial expressions. The gain in score made by his subjects on the facial expression test after the training period was roughly inversely proportional to their original standing; i.e., the less proficient persons gained the most and the more proficient gained the least. Repeating this procedure with larger groups of subjects, both with the same and longer study periods, the writer largely confirmed Allport's data. However, a control experiment, affording no opportunity for study, yielded similar data, except that on the average no gain in score resulted. The inverse relationship between original ability and amount of gain or loss should not, therefore, be attributed to the effects of training. Further analysis shows that when the reliability of the facial expression test, found by retesting a group of subjects, is taken into account, the negative coefficient practically disappears. The negative coefficient, upon which Allport bases his theory, is thus found to result in this study from the erroneous assumption that the reliability of the facial expression test is perfect. The writer, though inclined to agree with Allport's theory, concludes that this type of experimental evidence, when closely scrutinized, fails to support the theory.     

Common language effect size for correlations

The Pearson correlation coefficient can be translated to a common language effect size, which shows the probability of obtaining a certain value on one variable, given the value on the other variable. This common language effect size makes the size of a correlation coefficient understandable to laypeople. Three examples are provided to demonstrate the application of the common language effect size in interpreting Pearson correlation coefficients and multiple correlation coefficients.     

项目特征曲线等值的抽样误差

现在,等值越来越受到各考试测验机构及测量学研究人员的重视,特别是项目反应理论等值的优越性更使他们有了信心。然而,很多人却没有注意到被试能力分布形态可能给等值结果带来的影响效果及程度。本研究以项目反应理论两级记分模型的项目参数等值在不同被试能力分布形态下的结果差异作为重点,探讨被试抽样偏差可能给项目特征曲线等值带来的误差问题。研究结果表明,被试能力分布形态会显著地影响项目参数等值的系数,特别地,能力分布的偏态系数与等值方程的截距存在显著的线性相关关系,但能力分布形态的变化对等值方程中斜率的影响并不明显     

SPSS macros to compare any two fitted values from a regression model

In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant. Therefore, each regression coefficient represents the difference between two fitted values of Y. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests—particularly in more complex models that include interactions, polynomial terms, or regression splines. We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value.     

Test “reliability”: Its meaning and determination

The concept of test reliability is examined in terms of general, group, and specific factors among the items, and the stability of scores in these factors from trial to trial. Four essentially different definitions of reliability are distinguished, which may be called the hypothetical self-correlation, the coefficient of equivalence, the coefficient of stability, and the coefficient of stability and equivalence. The possibility of estimating each of these coefficients is discussed. The coefficients are not interchangeable and have different values in corrections for attentuation, standard errors of measurement, and other practical applications.     

Contrasting Theoretical Approaches to Intergroup Relations

The current forum is designed to assess the strengths and weaknesses of social identity, social dominance, and system justification as theoretical approaches to the study of intergroup relations. Each of these approaches tries to account for variation in the development of ingroup cohesion and outgroup antipathy among individual group members, across groups, and in different societies—three levels at which theorists have commonly sought explanations for variability in intergroup attitudes and behavior. Social dominance theory is the most ambitious of the theories but does not succeed in explaining intergroup relations equally well at all three levels. However, it has excelled in highlighting individual differences in the need and desire to dominate members of lower-status groups and in exploring the interaction between individuals and institutions. Social identity theory is primarily concerned with the attributes of groups that foster the development of ingroup bias and examines the conditions under which this occurs. It is more fully developed in this respect than the other approaches but ignores variation at the individual level and, to a lesser degree, the societal level. System justification theory considers a mix of individual- and societal-level factors, focusing on the role of support for the status quo in producing acceptance of status inequalities among members of low-status groups, even when it is against their own interest to do so. The theory highlights an important problem—the quiescence of low-status groups—but more work is needed to flesh out the theory and its central concepts.     

How to Be a Bayesian Dogmatist

Rational agents have (more or less) consistent beliefs. Bayesianism is a theory of consistency for partial belief states. Rational agents also respond appropriately to experience. Dogmatism is a theory of how to respond appropriately to experience. Hence, Dogmatism and Bayesianism are theories of two very different aspects of rationality. It's surprising, then, that in recent years it has become common to claim that Dogmatism and Bayesianism are jointly inconsistent: how can two independently consistent theories with distinct subject matter be jointly inconsistent? In this essay I argue that Bayesianism and Dogmatism are inconsistent only with the addition of a specific hypothesis about how the appropriate responses to perceptual experience are to be incorporated into the formal models of the Bayesian. That hypothesis isn't essential either to Bayesianism or to Dogmatism, and so Bayesianism and Dogmatism are jointly consistent. That leaves the matter of how experiences and credences are related, and so in the remainder of the essay I offer an alternative account of how perceptual justification, as the Dogmatist understands it, can be incorporated into the Bayesian formalism.     

Rational choice and polynomial measurement models

Rational choice behavior is defined in a manner that subsumes rational choice theory as part of general measurement theory. The special class of polynomial measurement problems are defined, and their solutions are reduced to solving polynomial inequalities. An algebraic criterion is given for the solvability of arbitrary finite sets of polynomial inequalities, resolving a conjecture of Tversky.     

The relation between results obtainable with raw and corrected correlation coefficients in multiple factor analysis

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.     

颜色知觉恒常理论的回顾

本文对早期颜色恒常理论、系数理论、计算理论和 Octant模型作了简要回顾 ,并结合已有的研究成果进行评述。对影响颜色恒常性机制的主要因素进行了探讨。强调了知觉经验、记忆、认知决策等高级意识活动对颜色恒常知觉的作用 ,并尝试性地提出了描述颜色恒常知觉过程的一般参照框架。     

心理治疗中共同要素理论的历史发展

从共同要素的角度,分理论模式化与研究实证化两条线索,追溯了心理治疗中共同要素理论的思想渊源,并自Saul Rosenzweig开始,综述了Carl Rogers、Jerome Frank、Marvin Goldfried、Michael Lambert、Bruce Wampold等学者的观点,探讨了共同要素理论的历史演进、内涵结构、理论模式及当代研究进展。认为它在不久的未来,将与特殊技术说逐步走向整合,加深对心理治疗过程与改变机制的认识,共同提升心理治疗的效果。     

Sampling fluctuations resulting from the sampling of test items

Sampling fluctuations resulting from the sampling of test items rather than of examinees are discussed. It is shown that the Kuder-Richardson reliability coefficients actually are measures of this type of sampling fluctuation. Formulas for certain standard errors are derived; in particular, a simple formula is given for the standard error of measurement of an individual examinee's score. A common misapplication of the Wilks-Votaw criterion for parallel tests is pointed out. It is shown that the Kuder-Richardson formula-21 reliability coefficient should be used instead of the formula-20 coefficient in certain common practical situations.Most of the work reported here was carried out under contract with the Office of Naval Research. The writer is indebted to Professor S. S. Wilks, who has checked over certain critical portions of a draft of this paper.