The Scaling of Mixed-Item-Format Tests With the One-Parameter and Two-Parameter Partial Credit Models

• Published in: Journal of educational measurement Vol. 37; no. 3; pp. 221 - 244
• Main Authors: Sykes, Robert C., Yen, Wendy M.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.09.2000; National Council on Measurement in Education
• Subjects: Achievement Tests; Credit; Discrimination; Elementary Secondary Education; Information economics; Item response theory; Logistics; Mathematical functions; Maximum likelihood estimation; Modeling; One Parameter Model; Parametric models; Partial Credit Model; Prediction; Rasch Model; Scaling; Standard error; Standard errors; State Programs; Statistics; Test Format; Test scores; Testing Programs; Two Parameter Model
• ISSN: 0022-0655; 1745-3984
• DOI: 10.1111/j.1745-3984.2000.tb01084.x

Item response theory scalings were conducted for six tests with mixed item formats. These tests differed in their proportions of constructed response (c.r.) and multiple choice (m.c.) items and in overall difficulty. The scalings included those based on scores for the c.r. items that had maintained the number of levels as the item rubrics, either produced from single ratings or multiple ratings that were averaged and rounded to the nearest integer, as well as scalings for a single form of c.r. items obtained by summing multiple ratings. A one-parameter (1PPC) or two-parameter (2PPC) partial credit model was used for the c.r. items and the one-parameter logistic (1PL) or three-parameter logistic (3PL) model for the m.c. items. Item fit was substantially worse with the combination 1PL/1PPC model than the 3PL/2PPC model due to the former's restrictive assumptions that there would be no guessing on the m.c. items and equal item discrimination across items and item types. The presence of varying item discriminations resulted in the 1PL/1PPC model producing estimates of item information that could be spuriously inflated for c.r. items that had three or more score levels. Information for some items with summed ratings were usually overestimated by 300% or more for the 1PL/1PPC model. These inflated information values resulted in under-estimated standard errors of ability estimates. The constraints posed by the restricted model suggests limitations on the testing contexts in which the 1PL/1PPC model can be accurately applied.