A multinomial model to assess central characteristics of mental operators

Knowledge about potential operators, about the preconditions of their applicability, and about their effects is essential to interact effectively with the physical world. Four classes of representational units of this knowledge can be distinguished: I) rules, II) structures, III) instances, and IV) episodes. Two important characteristics of these units are the abstractness of content and the directionality of access. A multinomial model is presented that enables the measurement of these characteristics. Three experiments were conducted to validate the parameters of the model. The multinomial model could be fitted very well to the empirical data of each experiment. Moreover, the parameter estimates showed the expected effects. The model allows the investigation of the influence of important variables (for example, knowledge domain, type of instruction, or amount of practice) on characteristics of mental operators without a strong commitment to any specific process theory. Debates regarding the contribution of different kinds of knowledge can be converted into statistical tests of the corresponding model parameters.