Theories, Models, and Standard Systems of MeasurementAftanas, Marion S.
doi: 10.1177/014662168801200401pmid: N/A
Measurement theories in psychology may be classi fied in terms of whether they begin from a general measurement framework or from a specific area of measurement. Points of contact between theories and different specific measurement areas have been limited by the choice of focus in discussions of general mea surement theories and specific theories or models. This presentation outlines a metatheoretical framework that begins with the obvious common factor in all areas, the standard system of measurement. Just as a stan dard is a commonly accepted unit of measurement, a standard system is a commonly accepted mechanism of measurement for a given area. The concept of a standard system amplifies general definitions of mea surement and clarifies metatheoretical statements con cerning the requirements for measurement. Differences between measurement situations may be categorized by the type of standard system used and by features of the attribute measured. Identification of different stan dard systems and elements of the measurement process provides a focus for comparisons between measure ment theories and models in different measurement situations. Index terms: applied measurement models, comparison of measurement models, definition of measurement, measurement process, measurement theory, metatheoretical framework for applied mea surement models, standard systems of measurement.
Acquiescence in Components Analysis and Multidimensional Scaling of Self-Rating ItemsDavison, Mark L.; Srichantra, Niyada
doi: 10.1177/014662168801200402pmid: N/A
Earlier work has shown that when multidimensional scaling (MDS) is applied to item intercorrelations, met ric MDS implicitly subtracts the standardized person mean (SPM) from responses. As a result, when a met ric or nonmetric MDS solution is compared to a com ponents solution, the components solution often con tains one component with no counterpart among the scaling dimensions. If self-report items form a bal anced scale and negatively worded items are not re verse scored, the SPM is closely related to several con cepts of acquiescence and disacquiescence. In this paper, MDS and components solutions are compared using two balanced self-report item sets. In the Likert self-report attitude item set, the MDS and components solutions were essentially the same. In a set of affec tive well-being items, the components solution con tained a general component with no counterpart among the scaling dimensions. Scores along the general com ponent were substantially correlated with measures of acquiescence and disacquiescence. Results in the sec ond dataset suggest that when the self-report items are balanced and the negatively worded items have not been reverse scored, MDS and components solutions can differ largely with respect to a component closely associated with certain measures of acquiescence. In dex terms: acquiescence, attitude measurement, factor analysis, multidimensional scaling, personality mea surement, response bias, self-report items.
Detecting and Interpreting Local Item Dependence Using a Fannily of Rasch ModelsWilson, Mark
doi: 10.1177/014662168801200403pmid: N/A
This paper describes a method for detecting and in terpreting disturbances of the local independence as sumption among items that share common stimulus material or other substantive features. Dichotomous and polytomous Rasch models are used in an example to analyze Structure of the Learning Outcome (SOLO) superitems and examine the results for local independ ence problems. The results indicate that some disturb ances were present among particular subsets of the items. Index terms: local independence, partial credit model, one-parameter logistic model, Rasch model, rating scale model.
IRT Item Bias Detection Procedures: Issues of Model Misspecification, Robustness, and Parameter LinkingLautenschiager, Gary J.; Park, Dong-Gun
doi: 10.1177/014662168801200404pmid: N/A
This article examines the consequences of employ ing IRT item bias detection procedures with multidi mensional IRT item data. Parameter linking methods used in previous studies of item bias were investigated in a simulation that minimized the need for such link ing. The results illustrate shortcomings of two linking methods that have been employed in IRT item bias de tection studies. The effectiveness of these methods de pended on several factors, including the number of biased items in a fixed-length test, whether bias was against only one group or more than one group, and the correlation between the two latent abilities. The findings indicated that some current IRT-based statisti cal procedures for detecting item bias were not gener ally effective at differentiating biased from unbiased items. Index terms: item bias, item response theory, multidimensional IRT data, parameter linking, reverse bias, statistical artifacts.
Unidimensionality Versus Statistical Accuracy: A Note on Beiar's Method for Detecting Dimensionality of Achievement TestsLiou, Michelle
doi: 10.1177/014662168801200406pmid: N/A
A simulation investigated use of the difficulty pa rameter (Bejar, 1980) to evaluate item unidimensional ity. Artificial tests were designed to be nonequivalent in both length and dimensionality. Simulated item re sponses to the tests were analyzed with the LOGIST computer program. Two indices were calculated: the slope of the principal axis between the content-area- based item difficulty estimates and corresponding to tal-test-based estimates, and the correlation between the two sets of estimates. Results show that the mag nitude of the correlation coefficient provides no infor mation about dimensionality of a set of test items. The slope of the principal axis, on the other hand, is sensi tive to multidimensionality in the data as well as test length. The size of the slope adequately detects the di mensionality of items for relatively long tests. Index terms: equating, item difficulty parameters, item re sponse theory, unidimensionality.
The Item Log-Likelihood Surface for Two- and Three-Parameter Item Characteristic Curve ModelsBaker, Frank B.
doi: 10.1177/014662168801200407pmid: N/A
This article investigated the form of item log-likeli hood surface under two- and three-parameter logistic models. Graphs of the log-likelihood surfaces for items under two-parameter and three-parameter (with a fixed value of c) models were very similar, but were characterized by the presence of a ridge. These graphs suggest that the task of finding the maximum of the surface should be roughly equivalent under these two models when c is fixed in the three-parameter model. For two items, the item log-likelihood surface was plotted for several values of c to obtain the contour line of the maxima. For an item whose value of Lord's b — 2/ a index was less than the criterion value, the contour line was relatively flat. The item having an index value above the criterion value had a contour line with a very sharp peak. Thus, under a three-pa rameter model, finding the maximum of the item log- likelihood is more difficult when the criterion for Lord's index is not met. These results confirm that the LOGIST program procedures used to locate the maxi mum of the likelihood function are consistent with the form of the item log-likelihood surface. Index terms: estimation, item parameter; likelihood surfaces; LOGIST procedures; log-likelihood; maximum likelihood estimation.
Measuring Attitudes With a Threshold Model Drawing on a Traditional Scaling ConceptRost, Jürgen
doi: 10.1177/014662168801200408pmid: N/A
This paper presents a generalized Rasch model for measuring attitudes which is based on the concepts of Thurstone's method of successive intervals. The model combines the rating scale and the dispersion model proposed by Andrich and a submodel of the partial credit model proposed by Masters. An estimation pro cedure for unconditional maximum likelihood (ML) es timates is outlined. A recursion formula for the sym metric functions, which is needed for conditional ML procedures, is given. The benefits of the model are il lustrated with a study on students' interest in physics. The fit of different threshold models can be compared using conditional likelihood values and conditional likelihood ratio tests. Index terms: attitude measure ment, conditional likelihood ratio test, partial credit model, Rasch model, rating scales, successive inter vals, threshold model.
Set Correlation and Contingency TablesCohen, Jacob
doi: 10.1177/014662168801200410pmid: N/A
Set correlation is a realization of the general multi variate linear model, can be viewed as a multivariate generalization of multiple correlation analysis, and may be employed in the analysis of multivariate data in any form. Set correlation supplements the four methods for analyzing two-way contingency tables de scribed by Zwick and Cramer (1986), and its applica tion to their example is illustrated. It gives the same results for the overall association, and in addition, by the use of nominal scale coding and partialling, it as sesses specific hypotheses about the details of the as sociation. Set correlation includes measures of strength of association (including correlations and proportions of variance), significance tests and estimation, power analysis, and computer programs to implement the calculations. Index terms: canonical analysis, con tingency table analysis, correspondence analysis, gen eral multivariate linear model, multivariate analysis of variance, Pearson chi-square, set correlation.