Some Results Based on a General Stochastic Model for Mental Tests
William H. Meredith · Psychometrika · 1965
There have been a number of important developments by several authors which are based on the assumption that test taking behavior is stochastic. That is, it is assumed that the probability that an individual will “endorse” or “pass” a dichotomous item can be represented by some function of an underlying, “latent” attribute (possibly multivariate) called the item trace line or item characteristic curve. Various forms for trace lines have been postulated such as polynomial [9, 11], step function [9], normal ogive [13, 19], and logistic [1, 2]. An interesting model due to Rasch [18] utilizes only a subject parameter and item parameter to determine the probability of passing an item. The only model which does not make some formal assumptions about trace lines is Lazarsfeld's latent class model. All of these models for test behavior are unified by two basic assumptions. One is the stochastic assumption of a probability of passing or endorsing an item.