Learning-forgetting independence, unidimensional memory models, and feature models: comment on Bogartz (1990)

In his recent articles, Bogartz offered a definition of what it means for forgetting rate to be independent of degree of original learning. He showed that, given this definition, independence is confirmed by extant data. Bogartz also criticized Loftus's (1985b) proposed method for testing independence. In this commentary, we counter Bogartz's criticisms and then offer two observations. First, we show that Loftus's horizontal-parallelism test distinguishes between two interesting class of memory models: unidimensional models wherein the memory system's state can be specified by a single number and multidimensional models wherein at least two numbers are required to specify the memory system's state. Independence by Loftus's definition is implied by a unidimensional model. Bogartz's definition, in contrast, is consistent with either model. Second, to better understand the constraints on memory mechanisms dictated by the mathematics of the models under consideration, we develop a simple but general feature model of learning and forgetting. We demonstrate what constraints must be placed on this model to make learning and forgetting rate independent by Loftus's and by Bogartz's definitions.