Measurement Theories

Classical Test Theory (CTT)

True score theory.

Item Response Theory (IRT)

May be known as modern latent trait theory.

Rasch model

The development of the Rasch model, and the broader class of models to which it belongs, was explicitly founded on requirements of measurement in the physical sciences.

Psychometricians have also developed methods for working with large matrices of correlations and covariances. Techniques in this general tradition include:factor analysis,^[5] a method of determining the underlying dimensions of data; multidimensional scaling,^[6] a method for finding a simple representation for data with a large number of latent dimensions; and data clustering, an approach to finding objects that are like each other. All these multivariate descriptive methods try to distill large amounts of data into simpler structures. More recently, structural equation modeling^[7] and path analysis represent more sophisticated approaches to working with large covariance matrices. These methods allow statistically sophisticated models to be fitted to data and tested to determine if they are adequate fits.

One of the main deficiencies in various factor analyses is a lack of consensus in cutting points for determining the number of latent factors. A usual procedure is to stop factoring when eigenvalues drop below one because the original sphere shrinks. The lack of the cutting points concerns other multivariate methods, also.