Item response theory

The probabilistic test theory ( Item Response Theory, and Engl. Latent trait theory, strong true score theory, or modern mental test theory ) examines how to get out underlying manifest categorical data (eg the responses to test items ) to underlying latent variables (z. example can close back personality characteristics of the subjects ). The word " probabilistic " is derived from it from the stochastic relationship between the response of the subject and the latent variable.

Coverage: Depending on whether the latent capacity as a metric (eg, intelligence) or as a categorical variable (eg, clinical syndromes ) is designed to distinguish the latent trait and latent class models described here (see also latent variable model).

Requirements

For most models the following two essential conditions must be made:

Rasch model

The most famous and mathematical- statistical best informed latent trait model is the going back to Georg Rasch Rasch model that models the probability density of the response variable as a logistic function of two parameters, one of which is the underlying ability of the subjects and the other the difficulty of items measures. This model assumption has a number of consequences that characterize the Rasch model in a pragmatic, statistical and epistemological respect to all other latent trait models:

The Rasch model is necessary and sufficient that all the information on the latent variable persons is included in the total scores of the subjects; it is necessary and sufficient for the estimation of the model parameters using the conditional ( conditional ) maximum likelihood method; and it is necessary and sufficient for the mutual independence (specific objective ) of the comparisons between the measured objects ( subjects) and measuring instruments (items): The statements which are obtained about the relations between n = 1,2,3 ... subjects are independent of which items are selected and was based on the comparison. Conversely, the statements which are obtained via the relation between k = 1,2,3 ... items, regardless of the basis of which people sample it originates.

Are the model assumptions of the Rasch model is violated, then the use of the sum score is associated with a loss of information which can go so far that the diagnostically relevant information contained in the responses of the subjects lost completely. Instead of the scores, the diagnostic decision must then be based on the response patterns of the subjects. This makes going back to Paul Lazarsfeld latent class analysis, identified by means of which typical response patterns and the subjects are classified according to which of these types corresponds to its response at best. Especially in the setting of measurement, where even slight variations in the semantic Itemformulierung can trigger completely different reaction tendencies of the subjects, this approach has proven to be compared with the usual still score education as significantly more powerful.

In response to Siegfried Kracauer's criticism that it is so much the frequency of certain textual features is not making up the meaning of a text, as the pattern which they form, has the latent -class analysis of the psychological assessment also in the quantitative content analysis an important application found.