Linking across forms in vertical scaling under the common-item nonequvalent groups design

The purposes of this dissertation are to compare how different the resulting proficiency estimates are by using two scale maintenance approaches, the horizontal and vertical approaches, in supporting scale stability across grade within form, within grade across forms, and across grades and across forms, and to thus investigate under which conditions of within-grade variability patterns and examinee sample characteristics one approach is preferable to the other.

Since there is no universally accepted growth model in the literature, three different distribution sets were specified and generated with regard to within-grade variability patterns in the simulation data: constant across grades, decreasing variability as grade increases, and increasing variability as grade increases. In addition, two sets of examinee sample characteristics were also specified in the simulation data: small examinee group difference and large examinee group difference. Thus six proficiency distribution conditions were used to generate data in this dissertation. Under the six conditions of proficiency distributions, the performances of the two scale maintenance approaches on the resulting proficiency estimates across multiple forms were the foci in this dissertation.

One major implication of this study is that the accuracy in recovering the true examinee proficiencies on the new form across multiple linking appeared to be an interaction among the number of forms or years involved in the linking process, the within-grade variability patterns, and the examinee group differences, but they did not appear to be a function of the maintenance approach implemented.

The findings from this study provide important empirical guidance to practitioners on how the vertical scale can be maintained, once a vertical scale is established. If the desired output of a maintained scale is to continue to capture the characteristics of the established scale in terms of grade separation, within-grade variability, and growth implications, the vertical approach appears to be marginally better in achieving these goals. However, the differences observed across three forms are marginal, and in some cases neither approach demonstrates superiority in preserving the same patterns at the baseline scale. Both approaches are able to reasonably well capture the trend of the baseline scale, at least across three forms.