Stochastic Models
Guttman's deterministic model is brought within a probabilistic framework in item response theory models, and especially Rasch measurement. The Rasch model requires a probabilistic Guttman structure when items have dichotomous responses (e.g. right/wrong). In the Rasch model, the Guttman response pattern is the most probable response pattern for a person when items are ordered from least difficult to most difficult (Andrich, 1985). In addition, the Polytomous Rasch model is premised on a deterministic latent Guttman response subspace, and this is the basis for integer scoring in the model (Andrich, 1978, 2005). Analysis of data using item response theory requires comparatively longer instruments and larger datasets to scale item and person locations and evaluate the fit of data to model.
In practice, actual data from respondents do not closely match Guttman's deterministic model. Several probabilistic models of Guttman implicatory scales were developed by Krus (1977) and Krus and Bart (1974).
Read more about this topic: Guttman Scale
Famous quotes containing the word models:
“Grandparents can be role models about areas that may not be significant to young children directly but that can teach them about patience and courage when we are ill, or handicapped by problems of aging. Our attitudes toward retirement, marriage, recreation, even our feelings about death and dying may make much more of an impression than we realize.”
—Eda Le Shan (20th century)