Background

This paper extends a recent study by Kaplan and Su (J Educ Behav Stat 41: 51–80, 2016) examining the problem of matrix sampling of context questionnaire scales with respect to the generation of plausible values of cognitive outcomes in large-scale assessments.

Methods

Following Weirich et al. (Nested multiple imputation in large-scale assessments. In: Large-scale assessments in education, 2. http://www.largescaleassessmentsineducation.com/content/2/1/9, 2014) we examine single + multiple imputation and multiple + multiple imputation methods using predictive mean matching imputation under three different context questionnaire matrix sampling designs: a two-form design studied by Adams et al. (On the use of rotated context questionnaires in conjunction with multilevel item response models. In: Large-scale assessments in education. http://www.largescaleassessmentsineducation.com/content/1/1/5, 2013), a three-form design implemented in PISA 2012, and a partially-balanced incomplete design studied by Kaplan and Su (J Educ Behav Stat 41: 51–80, 2016).

Results

Our results show that the choice of design has a larger impact on the reduction of bias than the choice of imputation method. Specifically, the three-form design used in PISA 2012 yields considerably less bias compared to the two-form design and the partially balanced incomplete design. We further show that the partially balanced incomplete block design produces less bias than the two-form design despite having the same amount of missing data.

Conclusions

We discuss the results in terms of implications for the design of context questionnaires in large-scale assessments.