The purpose of this investigation was to study the nature of the item and ability estimates obtained when the modified three-parameter logistic model is used with two-dimensional data. To examine the effects of two-dimensional data on unidimensional parameter estimates, the relative potency of the two dimensions was systematically varied by changing the correlations between the two ability dimensions. Data sets based on correlations of .0, .3, .6, .9, and .95 were generated for each of four combinations of sample size and test length. Also, for each of these four combinations, five unidimensional data sets were simulated for comparison purposes. Relative to the nature of the unidimensional estimates, it was found that the â value seemed best considered as the average of the true a values. The b value seemed best thought of as an overestimate of the true b 1 values. The & t h e t a s ; value seemed best considered as the average of the true ability parameters. Although there was a consistent trend for these relationships to strengthen as the ability dimensions became more highly correlated, there was always a substantial disparity between the magnitudes of these values and of those derived from the unidimensional data. Sample size and test length had very little effect on these relationships.Research related to item response theory (IRT) has dominated the psychometric literature in recent years. This is not surprising since this theory has the potential to resolve many problems frequently encountered in psychological and educational measurement (Lord, 1980). However, the mathematical models on which this theory is founded are based on some very strong assumptions. In particular, IRT models most commonly used assume that the response data are unidimensional in the reference population.The importance of the unidimensionality assumption has been stressed by many authors (see e.g., H~rrlbiet®r~ ~ Murray, 1983;Traub, 1983). Several researchers have hypothesized that failure to satisfy the assumption of unidimensionality was a major reason IRT models did not adequately fit their data. For example, Loyd and Hoover (1980) reported that multidimensional data might have contributed to the lack of fit of the Rasch model in a vertical equating setting. In comparing the fit of the one-and three-parameter logistic models to actual standardized test data, Hutten (1980) found that the potency of the major dimension (as assessed by the ratio of the first two eigenvalues of the matrix of inter-item tetrachoric correlations) was significantly related to the degree of fit.

This study compared the effects of using a unidi mensional IRT model with two-dimensional data gener ated by noncompensatory and compensatory multidi mensional IRT models. Within each model, simulated datasets differed according to the degree of correlation between two vectors of θ parameters, ranging from 0 to .95. Results showed that the number-correct distri butions for each group of datasets were generally comparable, although factor analyses of tetrachoric correlations suggested that differences existed in the structure of the data from the two models. For the uni dimensional parameter estimates, it was found that the â values from the noncompensatory model appeared to be averages of the a1 and a2 values, while the â values from the compensatory model were best considered as an estimate of the sum of the a1 and a2 values. Con versely, the b values for the noncompensatory data were consistently greater than the b1 values, while the b values from the compensatory model were best con sidered as the average of the b1 and b2 values. For both models the θ estimates were most highly related to the average of the two θ parameters. However, for the noncompensatory model there was a general in crease in the strength of this relationship with in creases in ρ(θ1,θ 2). For the compensatory model, the strength of this relationship did not show a great deal of change with differences in ρ(θ1,θ 2). Index terms: Compensatory multidimensional IRT models, Item response theory, Multidimensional IRT models, Noncompensatory multidimensional IRT models, Pa rameter estimation, Violations of unidimensionality.

EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1969, 29, 61-71. THE appropriate applications, idiosyncrasies, and potential misuses of correlations corrected for attenuation have been the subject of debate for over fifty years. A number of prominent research workers

The purpose of this study was to investigate the nature and characteristics of the measurement scales developed using Thurstone and item response theory (IRT) methods of scaling achievement tests for the same set of data. Expanded standard score scales were created using Thurstone, one‐parameter IRT, and three‐parameter IRT models, and descriptive information on achievement growth and variability was obtained for examinees in Grades 9 through 12 in the subject areas of vocabulary, reading, and mathematics. The results indicated increasing variability in all three test areas for all three scaling methods as grade level increased. In addition, greater average growth across grades was observed at the 90th percentile as compared to the 10th percentile, even with the IRT‐based scales.

What are some of the ways that the NAEP scales have been interpreted? Are such interpretations valid? What conditions are necessary before valid criterion‐referenced interpretations can be made for the NAEP Proficiency Scales? Does the NAEP test development process meet these conditions?