New multinomial models for the Chechile-Meyer task

This paper provides a critique of the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) multinomial processing tree (MPT) models that were generated for the measurement of storage and retrieval components of the correct recall rate. These models were developed for a specific test procedure that involved the random mixing of recall and recognition trials. A key problem with the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) models is the validity of an assumption made for foil recognition test trials. Three new MPT models for obtaining separate storage and retrieval measures are provided. These new models circumvent the difficulties of the Chechile and Meyer (J. Math. Psychol. 13 (1976) 269) models. Both maximum likelihood estimates (MLE) and population-parameter mapping (PPM) estimates (discussed in Chechile (J. Math. Psychol. 42 (1998) 432)) are provided for the model parameters. Monte Carlo studies were conducted to compare the relative accuracy of the MLE and PPM storage estimates. Both methods have the same average error rate for samples that are very large in size; however, for all the more practical sample sizes, the PPM estimates were more accurate. Statistical methods for model selection were also developed and tested. Finally, the new models were used to reanalyze some existing data. The new analyses provide strong validation evidence for the new models.