Statistical Test of the Rule Assessment Methodology by Latent Class Analysis

A problem of Siegler's (1981) rule assessment methodology is that the assignment of subjects to rules takes place by an arbitrary criterion. This problem can be solved by latent class analysis by which we can test statistically how many rules are needed to fit the data and which these rules are. Two data sets of the balance scale test are analyzed. The first empirical data set stems from a study of Van Maanen, Been & Sijtsma (1989) and consists of 484 subjects in Grade 7 and Grade 8. The second data set is derived from the simulation of the PDP model of McClelland (1989). According to McClelland and Jenkins (1991), this connectionistic model simulates the saltatory acquisition of rules for tasks like the balance scale. The fit of the latent class models to the empirical data shows that rules can be found, that some are different from the ones Siegler proposes, that the correct rule is not acquired by the subjects in this sample, and that the rules in the transitional period are difficult to identify. The latent class models do not fit the PDP data, indicating that the behavior of the PDP model can not be characterized by rules.