关联规则方法在心理测量中的应用

探讨了当相关系数对变量之间相关程度不易进行度量或者无法度量的情况下,是否可以采用关联规则方法来考察变量之间的相互关系。从理论上分析了关联规则方法在心理测量中应用的可能性,并运用Apriori算法挖掘频繁项集,对来华留学生跨文化适应性数据进行了分析,将关联规则方法分析结果与Pearson相关、Spearman相关结果进行比较,发现当使用关联规则方法进行相互关系分析时,能够更加简易、有效地获得变量间的相关规则。研究结果表明关联规则方法可以获得变量各个水平具体的支持度和置信度,推导出多变量之间的相关规则,并且对于处理非线性的多变量以及多分类变量的相关是非常有用的方法。     

Canonical versus factor analytic perspectives on the structure of associations between the MMPI and the Buss-Durkee Hostility Inventory

A canonical correlational analysis of MMPI profiles versus Buss-Durkee hostility and aggression scales was conducted, resulting in the identification of a general hostility-aggression-maladjustment dimension and three relatively specific aggression-personality relationships. These findings were contrasted with those obtained from a factor analysis of the combination of both sets of scores. Though often used in previous studies of associations between the Buss-Durkee Hostility Inventory and other measures, factor analysis was seen to be less than optimally suited to such a purpose. It was concluded that canonical correlation is preferable to factor analysis when seeking to clarify the multivariate structure of relationships between two sets of variables.     

PERSON-SITUATION SELECTION: A REVIEW OF SOME ABILITY-SITUATION INTERACTION RESEARCH

A review of literatures thought to be relevant for understanding situational contributions to ability-performance relationships was conducted. The review suggested that only three sets of variables, incentive systems, job characteristics, and leadership style/management philosophy ("climates") have recieved research attention from an ability/situation vantage point. It was also shown that in both experimental and survey research these three factors can moderate ability-performance relationships. Because these same three sets of variables are also known to have main effects on average performance levels, an hypothesis is presented that when organizations establish work conditions which facilitate the display of task-relevant individual ability, then validity for ability measures, average performance levels, and general levels of satisfaction will all be high.     

The effect of affine transformation on redundancy analysis

Canonical redundancy analysis provides an estimate of the amount of shared variance between two sets of variables and provides an alternative to canonical correlation. The proof that the total redundancy is equal to the average squared multiple correlation coefficient obtained by regressing each variable in the criterion set on all variables in the predictor set is generalized to the case in which there are a larger number of criterion than predictor variables. It is then shown that the redundancy for the criterion set of variables is invariant under affine transformation of the predictor variables, but not invariant under transformation of the criterion variables.     

Fitting and Testing Conditional Multinormal Partial Credit Models

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in Psychometrika 55:5?C18, 1990). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores, which are sufficient statistics. Attention is paid to maximum likelihood estimation of item parameters, multivariate moments of latent variables, and person parameters. It is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques. More general models are discussed which can be used for testing the model, and it is shown how models with different numbers of latent variables can be tested against each other. In addition, multi-group extensions are proposed, which can be used for testing both measurement invariance and latent population differences. Models and procedures discussed are demonstrated in an empirical data example.     

Global optimality of the successive Maxbet algorithm

The Maxbet method is an alternative to the method of generalized canonical correlation analysis and of Procrustes analysis. Contrary to these methods, it does not maximize the inner products (covariances) between linear composites, but also takes their sums of squares (variances) into account. It is well-known that the Maxbet algorithm, which has been proven to converge monotonically, may converge to local maxima. The present paper discusses an eigenvalue criterion which is sufficient, but not necessary for global optimality. However, in two special cases, the eigenvalue criterion is shown to be necessary and sufficient for global optimality. The first case is when there are only two data sets involved; the second case is when the inner products between all variables involved are positive, regardless of the number of data sets.The authors are obliged to Henk Kiers for critical comments on a previous draft.     

Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features

Homogeneity analysis, or multiple correspondence analysis, is usually applied tok separate variables. In this paper we apply it to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological survey is presented.This research was partly supported by SWOV (Institute for Road Safety Research) in Leidschendam, The Netherlands.     

Bayesian modeling of measurement error in predictor variables using item response theory

It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.This paper is part of the dissertation by Fox (2001) that won the 2002 Psychometric Society Dissertation Award.     

Multivariate repeated measures designs

In the social, behavioral, and health researches it is a common strategy to collect data along time on more than one group of participants on multiple dependent variables. To analyse this kind of data is very complicated due to the correlations between the measures taken in different points of the time, and between the answers. Usually to analyse these data the multivariate mixed model, or the doubly multivariate model, are the most frequent approaches. Both of them require combined multivariate normality, equal covariance matrices, independence between the observations of different participants, complete measurements on all subjects, and time-independent covariates. When one ore more of these assumptions are not accomplished these approaches do not control in the correct way the Type I error, and this affects the validity and the accuracy of the inferences. In this paper some solutions that solve the problems with the error Type I will be shown. Several programs for a correct realization of the analyses through the SAS Proc Mixed procedure are presented.     

Random Item IRT Models

It is common practice in IRT to consider items as fixed and persons as random. Both, continuous and categorical person parameters are most often random variables, whereas for items only continuous parameters are used and they are commonly of the fixed type, although exceptions occur. It is shown in the present article that random item parameters make sense theoretically, and that in practice the random item approach is promising to handle several issues, such as the measurement of persons, the explanation of item difficulties, and trouble shooting with respect to DIF. In correspondence with these issues, three parts are included. All three rely on the Rasch model as the simplest model to study, and the same data set is used for all applications. First, it is shown that the Rasch model with fixed persons and random items is an interesting measurement model, both, in theory, and for its goodness of fit. Second, the linear logistic test model with an error term is introduced, so that the explanation of the item difficulties based on the item properties does not need to be perfect. Finally, two more models are presented: the random item profile model (RIP) and the random item mixture model (RIM). In the RIP, DIF is not considered a discrete phenomenon, and when a robust regression approach based on the RIP difficulties is applied, quite good DIF identification results are obtained. In the RIM, no prior anchor sets are defined, but instead a latent DIF class of items is used, so that posterior anchoring is realized (anchoring based on the item mixture). It is shown that both approaches are promising for the identification of DIF.     

A family of association coefficients for metric scales

Four types of metric scales are distinguished: the absolute scale, the ratio scale, the difference scale and the interval scale. A general coefficient of association for two variables of the same metric scale type is developed. Some properties of this general coefficient are discussed. It is shown that the matrix containing these coefficients between any number of variables is Gramian. The general coefficient reduces to specific coefficients of association for each of the four metric scales. Two of these coefficients are well known, the product-moment correlation and Tucker's congruence coefficient. Applications of the new coefficients are discussed.     

Latent structure in measures of associative,semantic, and thematic knowledge

There has been much debate about the relation between knowledge for meaning (semantic memory) and knowledge for words in context (associative memory). Many measures of that knowledge exist, but do they all measure the same thing? In this study, scaling, clustering, and factor-analytic techniques were used to reveal the structure underlying 13 variables. Semantic similarity determined from lexicographic measures is shown to be separable from the associative strength determined from word association norms, and these semantic and associative measures are in turn separable from abstract representations derived from computational analyses of large bodies of text. The three-factor structure is at odds with traditional views of word knowledge. The expression of long-term knowledge about words and the concepts they represent may be better viewed in terms of associative, semantic, and thematic information.     

Gender-Differentiated Associations among Objectified Body Consciousness, Self-Conceptions and Physical Activity

The nature of relationships among objectified body consciousness (OBC), a model of physical self-conceptions, and self-reported physical activity were examined in a cross-sectional study with U.S. undergraduate women (n?=?231) and men (n?=?163). As hypothesized, women reported significantly higher levels of OBC body surveillance and body shame than men with no significant difference in OBC appearance control beliefs levels between women and men. Canonical correlation analysis revealed significant and different relationships between the set of OBC variables and the set of physical self-concept variables for women and men. The strength of association between the two sets of variables accounted for 48% of the shared variance for women and 29% for men. The multivariate relationship between OBC and physical activity was non-significant.     

Two Studies Examining the Error Theory Underlying the Measurement Model of the Verbal Aggressiveness Scale

Meta‐analysis indicates moderate correlations between the Verbal Aggressiveness Scale (VAS) and other self‐report measures but near‐zero correlations with behavioral measures. Accurately interpreting correlations between the VAS and other variables, however, requires an examination of the untested error theory underlying the measurement model for the VAS. In two separate studies, the results of single‐factor correlated uniqueness confirmatory factor analytic models revealed a pattern of significant error covariances indicating that VAS item scores are confounded by systematic error attributable to multiple unspecified latent effects. After pruning the item sets, we identified 4 items that were free of latent variable influences other than trait verbal aggressiveness. Implications for interpreting the verbal aggressiveness literature are discussed along with recommendations for revising the VAS.     

Orthogonal dreams in an oblique world: A meta-analysis of the association between attachment anxiety and avoidance

The association between attachment dimensions (anxiety and avoidance) can influence measurement creation and statistical analyses. Our goal was to test the assumption that anxiety and avoidance was orthogonal in two popular measures: the ‘Experience in Close Relationships Scale - Revised’ (ECR-R) and the original ‘Experiences in Close Relationships Scale’ (ECR). Our meta-analysis of 242 studies revealed that despite both scales being highly reliable, the anxiety-avoidance correlation was higher for the ECR-R than the ECR. Other variables also moderated the association. Implications include methods of statistical analysis and recommendations for future measurement creation and use.     

A family of chance-corrected association coefficients for metric scales

A chance-corrected version of the family of association coefficients for metric scales proposed by Zegers and ten Berge is presented. It is shown that a matrix with chance-corrected coefficients between a number of variables is Gramian. The members of the chance-corrected family are shown to be partially ordered. The author is obliged to Jos ten Berge for helpful comments.     

Relationships between redundancy analysis,canonical correlation,and multivariate regression

This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. Stewart and Love introduced redundancy analysis to provide non-symmetric measures of the dependence of one set of variables on the other, as channeled through the canonical variates. Van den Wollenberg derived sets of variates which directly maximize the between set redundancy. Multivariate multiple linear regression on component scores (such as principal components) is considered. The problem is extended to include an orthogonal rotation of the components. The solution is shown to be identical to van den Wollenberg's maximum redundancy solution.This research was supported in part by U.S. Environmental Protection Agency contract 68-02-3402. The author gratefully acknowledges the stimulation of Maurice Tatsuoka and Beth Dawson-Saunders in first interesting him in redundancy analysis, as well as a useful change suggested by Warren Sarle.     

The Problem of Units and the Circumstance for POMP

Many areas of the behavioral sciences have few measures that are accepted as the standard for the operationalization of a construct. One consequence is that there is hardly ever an articulated and understood framework for the units of the measures that are employed. Without meaningful measurement units, theoretical formulations are limited to statements of the direction of an effect or association, or to effects expressed in standardized units. Thus the long term scientific goal of generation of laws expressing the relationships among variables in scale units is greatly hindered. This article reviews alternative methods of scoring a scale. Two recent journal volumes are surveyed with regard to current scoring practices. Alternative methods of scoring are evaluated against seven articulated criteria representing the information conveyed by each in an illustrative example. Converting scores to the percent of maximum possible score (POMP) is shown to provide useful additional information in many cases.     

The effect of representations of binary variables on judgment of influence

Studies concerned with judgments of contingency between binary variables have often ignored what the variables stand for. The two values of a binary variable can be represented as a prevailing state (nonevent) or as an active state (event). Judgments under the four conditions resulting from the combination of a binary input variable that can be represented as event-nonevent or event-event with an outcome variable that can be represented in the same way were obtained. It is shown in Experiment 1, that judgments of data sets which exhibit the same degree of covariation depend upon how the input and output variables are represented. In Experiment 2 the case where both the input and output variables are represented as event-nonevent is examined. Judgments were higher when the pairing of the input event was with the output event and the input nonevent with the output nonevent that when the pairing was of event with nonevent, suggesting a causal compatibility of event-event pairings and a causal incompatibility of event-nonevent pairings. Experiment 3 demonstrates that judgments of the strength of the relation between binary input and output variables is not based on the appropriate statistical measure, the difference between two conditional probabilities. The overall pattern of judgments in the three experiments is mainly explicable on the basis of two principles: (1) judgments tend to be based on the difference between confirming and disconfirming cases and (2) causal compatibility in the representation of the input and output variables plays a critical role.     

Multiple causation,indirect measurement and generalizability in the social sciences

The fact that causal laws in the social sciences are most realistically expressed as both multivariate and stochastic has a number of very important implications for indirect measurement and generalizability. It becomes difficult to link theoretical definitions of general constructs in a one-to-one relationship to research operations, with the result that there is conceptual slippage in both experimental and nonexperimental research. It is argued that problems of this nature can be approached by developing specific multivariate causal models that incorporate sources of measurement bias, along with the theoretical variables of interest. Many general concepts are defined in such a way that causal assumptions are built into the definitions themselves. Additionally, in any given piece of research it is necessary to omit many variables from consideration, and this is often done without careful consideration of the assumptions required to justify such omissions. Finally, generalization to more inclusive populations or a diversity of settings ordinarily requires one to replace constants by variables. It is concluded that the criteria of parsimony, generalizability, and precision are incompatible, given the multivariate nature of social causation, and the author expresses his own preference for sacrificing parsimony in favor of the objectives of achieving increased precision and generalizability of social science laws.