Can items from one module be correlated items from a different module?
No, not directly, since a completely different and non-overlapping subset of students is assigned to each module. Items from modules can only be directly correlated with the items from the core. However, advanced statistical methods permit analysts to impute (estimate) the results from one module to use with the results from another module. Three such approaches are described in: Franklin, Charles H. 1989. “Estimation across Data Sets: Two-Stage Auxiliary Instrumental Variables Estimation (2SAIV).” Political Analysis 1: 1–24. Raghunathan, Trivellore E. and James E. Grizzle. 1995. “A Split Questionnaire Survey Design.” Journal of the American Statistical Association 90: 54–63. Gelman, Andrew, Gary King, and Chuanhai Liu. 1999. “Not Asked and Not Answered: Multiple Imputation for Multiple Surveys.” Journal of the American Statistical Association 93: 846–57; followed by comments by John Brehm, David R. Judkins, Robert L. Santos, and Joseph B. Kadane, and rejoinder by Gelman, King, and Liu
