Combined Rasch Hierarchical Models: A Preliminary Application to Autobiographical Memory

The Rasch model, from its original dichotomous form, was extended to versions adapted to analysing ordinal responses like measurements on Likert scales, such as the partial credit model (Masters, 1982). In order to improve the accuracy of estimates of standard errors of parameters, a partial credit model can be combined with a hierarchical linear model (Bryk & Raudenbush, 1992). The result is a partial credit hierarchical measurement model (HMM), that frames item responses as a within-student model and the population distribution as a between-subjects model. This perspective enables a simultaneous estimation of a two level model rather than a two-step estimation and it allows the population model to include covariates. The partial credit HMM is illustrated in an application to data on autobiographical memory, consisting of responses on a Likert scale to a set of items, in terms of individuals' ratings of the phenomenological properties of past events. The inclusion of covariates allows one to explore the effect of gender. A further development introduces a third level in the HMM, taking into account the same pattern of responses given to the same items aforementioned for studying past events, now applied to the imagining of future events. Recent theories of autobiographical memory contend that the same memory system subsumes recall of specific past events and the imagining of future events. Gender can be analyzed with respect to the hypothesized symmetry between the recall of the past and conjectures about the future.