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The effectiveness of multidimensional scaling (MDS) techniques in recovering the underlying dimensionality of dichotomously-scored data was examined for unidimensional and multidimensional data. Thirty-three data sets of varying numbers of dimensions with differing patterns of item discrimination were generated using a multidimensional latent trait model in a Monte Carlo simulation study. Margin-sensitive measures (agreement, phi, and kappa) and margin-free measures (Φ/ Φ(max), Yule's Q, and the tetrachoric correlation) were used as measures of similarity and the resulting matrices were scaled in one through five dimensions. Values of the stress coefficient, S₁, S₁ by dimensionality plots, and plot configurations were examined to determine the dimensionality of the item set. Principal components analyses (PCAs) of phi and tetrachoric matrices were carried out as a basis for comparison. In addition, MDS and PCA were used to examine a data set comprised of items obtained from the routing tests of the Head Start Measures Battery. Two effects of item discrimination on MDS results were especially noteworthy. First, factors tended to be located equally distant from each other in the MDS space. Items were located closest to the factor for which the primary factor loading occurred. Second, as item discrimination decreased, items tended to be more widely dispersed from their appropriate locations in space. Extra dimensions in the MDS representational space were required for margin-sensitive coefficients to accommodate difficulty effects. Margin-free coefficients generally eliminated difficulty-related dimensions, although occasional problems were noted with the tetrachoric correlation. Analysis of the HSMB revealed that the data were primarily unidimensional, although specific effects due to each subtest were clearly present in the analysis. MDS was found to be a useful technique and its use in conjunction with PCA or factor analysis is recommended.

The present study was a systematic investigation of hierarchical skill sequences in the beginning reading domain. The hierarchies included skills from the traditional approach to reading which reflect bottom-up processing and skills from the conceptual area of print awareness which reflect top-down processing. Researchers supporting the bottom-up approach view reading as a process in which the child extracts information from the text to gain knowledge of the print. The bottom-up processes examined were in the areas of letter recognition and letter naming, and identification of letter sounds and phonemes. The top-down processing approach views reading as a task in which the child brings his/her past experiences and knowledge about the world to gain information about print. The top-down processes examined were in the areas of print identification, inferring a word in context, and print directionality rules. Hierarchical skill sequences were developed within each of the specific areas reflecting the top-down and bottom-up processing theories. Items were developed to reflect the skill sequences based on the cognitive processes that are necessary for correct performance. This involved varying the task demands imposing various requirements of cognitive processing. The data were from 13,189 Head Start children ranging from 3 to 6 years of age. Latent trait models were constructed to reflect the viii ix hypothesized skill sequences by allowing the aj (discrimination) and bj (difficulty) parameters to be free to vary or by constraining them to be equal to other parameters. To arrive at a preferred model, each latent trait model that represented a hypothesized skill sequence was statistically compared against alternative latent trait models. The results from the present investigation supported the hierarchical skill sequences reflecting skills within the traditional area of reading. However, some of the skill sequences from the conceptual area of print awareness were not clearly supported. While the results provide a deeper understanding of beginning reading skill sequences reflecting top-down and bottom-up processing theories, future research is needed to delineate the specific skills which promote later reading ability once the child is in formal reading instruction.

No description available.

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