An Evaluation of the Single‐Group Growth Model as an Alternative to Common‐Item Equating

Abstract As an alternative to common‐item equating when common items do not function as expected, the single‐group growth model ( SGGM ) scaling uses common examinees or repeaters to link test scores on different forms. The SGGM scaling assumes that, for repeaters taking adjacent administrations, the conditional distribution of scale scores in later administration, given the scale score in earlier administration, should generalize from previous repeaters to the repeaters taking the current administration. The current repeaters' scale score distribution is estimated from their earlier scale score distribution. The SGGM scaling first uses previous repeaters' data to estimate the conditional distribution of their later scale scores, given their earlier scale scores. Then the repeaters taking both the current and previous administrations are identified, and their scale score distribution on the current form is estimated based on their previous scale score distribution and the estimated conditional distribution. Finally, a single‐group equipercentile equating is performed between the current‐form repeaters' observed raw score distribution and their estimated scale score distribution to obtain the raw‐to‐scale score conversion. This study evaluated the SGGM scaling performance using the common‐item equating results for a language test as the criterion. The study found that the raw‐to‐scale conversions based on SGGM scaling differed from those based on common‐item equating. However, the SGGM scaling results did not show a systematic bias in either the average or the variability of examinees' scale scores.