Three common methods for equating parameter estimates from binary item response theory models are extended to the generalized grading unfolding model (GGUM). The GGUM is an item response model in which single-peaked, nonmonotonic expected value functions are implemented for polytomous responses. GGUM parameter estimates are equated using extended versions of the mean-sigma, mean-mean, and item characteristic curve methods. The former two methods are implemented using two different strategies...

Topics: ERIC Archive, Estimation (Mathematics), Item Response Theory, Simulation, Roberts, James S.

This study explored alternative methods of estimating the number of latent dimensions represented by binary test data. The alternative methods vary in their complexity and include: (1) the minimum average partial correlation technique (MAP; W. Velicer, 1976) applied to phi correlations between binary responses; (2) the bootstrapped parallel analysis method (A. Buja and N. Eyuboglu, 1992) applied to phi correlations; (3) the minimum average partial correlation technique applied to data that has...

Topics: ERIC Archive, Estimation (Mathematics), Responses, Scaling, Simulation, Roberts, James S.,...

Stone and colleagues (C. Stone, R. Ankenman, S. Lane, and M. Liu, 1993; C. Stone, R. Mislevy and J. Mazzeo, 1994; C. Stone, 2000) have proposed a fit index that explicitly accounts for the measurement error inherent in an estimated theta value, here called chi squared superscript 2, subscript i*. The elements of this statistic are natural byproducts of the marginal maximum likelihood procedure used to estimate generalized grading unfolding model (GGUM) parameters. The objective of this study...

Topics: ERIC Archive, Chi Square, Goodness of Fit, Test Items, Roberts, James S.

The purpose of this study was to assess the dimensionality of attitudinal data arising from unfolding models for discrete data and to compute rough estimates of item and individual parameters for use as starting values in other estimation parameters. One- and two-dimensional simulated test data were analyzed in this study. Results of limited analyses performed so far have shown that linear principal components analysis of unfolding data provides a reliable estimate of the underlying...

Topics: ERIC Archive, Attitudes, Estimation (Mathematics), Simulation, Test Items, Nandakumar, Ratna,...

Characteristic curve approaches for linking parameters from the generalized partial credit model were examined for cases in which common (anchor) items are calibrated separately in two groups. Three of these approaches are simple extensions of the test characteristic curve (TCC), item characteristic curve (ICC), and operating characteristic curve (OCC) methods that have been previously developed for other binary item response models. The ICC approach explicitly provides a symmetric solution for...

Topics: ERIC Archive, Estimation (Mathematics), Mathematical Models, Roberts, James S., Bao, Han, Huang,...

The Likert rating scale procedure is often used in conjunction with a graded disagree-agree response scale to measure attitudes. Item characteristic curves associated with graded disagree-agree responses are generally single-peaked, nonmonotonic functions of true attitude. These characteristics are, thus, more generally consistent with an unfolding model like the Thurstone attitude measurement procedure rather than a cumulative model such as the Likert procedure and the typical item...

Topics: ERIC Archive, Attitudes, Likert Scales, Sampling, Test Items, Validity, Roberts, James S., Wedell,...

The generalized graded unfolding model (J. Roberts, J. Donoghue, and J. Laughlin, 1998, 1999) is an item response theory model designed to unfold polytomous responses. The model is based on a proximity relation that postulates higher levels of expected agreement with a given statement to the extent that a respondent is located close to the statement on a unidimensional latent continuum. J. Roberts and others (1998) have examined the recovery of item and person parameters from the generalized...

Topics: ERIC Archive, Attitude Measures, Estimation (Mathematics), Item Response Theory, Simulation,...

The generalized graded unfolding model (GGUM) (J. Roberts, J. Donoghue, and J. Laughlin, 1998) is an item response theory model designed to analyze binary or graded responses that are based on a proximity relation. The purpose of this study was to assess conditions under which item parameter estimation accuracy increases or decreases, with special attention paid to the influence that a given item parameter value has on the estimation of another item parameter. This assessment was based on a...

Topics: ERIC Archive, Estimation (Mathematics), Item Response Theory, Maximum Likelihood Statistics, Sample...

Graded or binary disagree-agree responses to attitude statements are often collected for the purpose of attitude measurement. The empirical characteristics of these responses will generally be inconsistent with the analytical logic that forms the basis of the Likert attitude measurement technique (R. Likert, 1932). As a consequence, the Likert procedure can lead to invalid measurement of a select group of individuals. Likert attitude estimates can substantially misrepresent individuals with the...

Topics: ERIC Archive, Attitude Measures, Attitudes, Comparative Analysis, Error of Measurement, Item...

Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (J. S. Roberts, 1995; W. H. Van Schuur and H. A. L. Kiers, 1994). Advances in item response theory (IRT) have led to the development of several parametric unfolding models for binary data (D. Andrich, 1988; Andrich and G. Luo,...

Topics: ERIC Archive, Attitude Measures, Estimation (Mathematics), Item Response Theory, Mathematical...