From model to measurement with dichotomous items

Psychometric models typically represent encounters between persons and dichotomous items as a random variable with two possible outcomes, one of which can be labeled success. For a given item, the stipulation that each person has a probability of success defines a construct on persons. This model specification defines the construct, but measurement is not yet achieved. The path to measurement must involve replication; unlike coin-tossing, this cannot be attained by repeating the encounter between the same person and the same item. Such replication can only be achieved with more items whose features are included in the model specifications. That is, the model must incorporate multiple items. This chapter examines multi-item model specifications that support the goal of measurement. The objective is to select the model that best facilitates the development of reliable measuring instruments. From this perspective, the Rasch model has important features compared to other models.