Tree Models

Tree models, also known as multinomial process tree models, are data-analysis tools widely used in behavioral sciences to measure the contribution of different cognitive processes underlying observed data. They are developed exclusively for categorical data, with each observation belonging to exactly one of a finite set of categories. For categorical data, the most general statistical distribution is the multinomial distribution, where observations are independent and identically distributed over categories, and each category has associated with it a parameter representing the probability that a random observation falls within that category. These probability parameters are generally expressed as functions of the statistical model’s parameters, i.e., they redefine the parameters of the multinomial distribution. Linear (e.g., analysis of variance) and nonlinear (e.g., log-linear and logit) models are routinely used for categorical data in a number of fields in the social, behavioral, and biological sciences. All that is required in these models is a suitable factorial experimental design, upon which a model can be selected without regard to the substantive nature of the paradigm being modeled.