Probabilistic test theory
The probabilistic test theory ( item response theory , also English latent trait theory , strong true score theory or modern mental test theory ) examines how one can convert underlying manifest categorical data (e.g. the answers to test items) to underlying latent variables (e.g. B. Personality traits of the test persons ). The word “probabilistic” is derived from the stochastic relationship between the respondents' response behavior and the latent variable.
Depending on whether the latent property is conceived as a metric (e.g. intelligence) or as a categorical variable (e.g. clinical syndromes), a distinction is made between the latent trait and latent class models described here (see also Latentes Variable model ).
requirements
For most of the following models, two essential requirements must be made:
- One-dimensionality : There is exactly one latent variable that determines the response behavior for an item. So there are no other latent variables that have a systematic influence. This requirement can e.g. B. be examined with a suitable confirmatory factor analysis of the items.
- Conditional independence : For a given value of the latent variable, the response probability for several items can be broken down as the product of the response probabilities of the individual items. This means that the correlation between the items is only determined by the latent variable and that there are no other systematic influencing variables. Test tasks that build on each other violate this assumption - in this case, other models, e.g. B. testlet models can be used.
Rasch model
Probably the most well-known and mathematically and statistically best founded latent trait model is the Rasch model , which goes back to Georg Rasch and models the probability density of the response variables as a logistic function of two parameters, one of which is the underlying ability of the test subject and the other the difficulty the items are measuring. This model assumption has a number of consequences that distinguish the Rasch model from all other latent trait models in pragmatic, statistical and epistemological terms:
The Rasch model is necessary and sufficient to ensure that all information about the latent person variable is contained in the test subjects' total scores; it is necessary and sufficient for the estimation of the model parameters using the conditional maximum likelihood method ; and it is necessary and sufficient for the mutual independence (specific objectivity) of the comparisons between measurement objects (test persons) and measurement instruments (items): The statements that are obtained about the relationships between n = 1,2,3 ... test persons are independent of this which items were selected and used as a basis for the comparison. Conversely, the statements that are obtained from the relation between k = 1, 2, 3… items are independent of the sample of persons from which they were obtained.
If the model assumptions of the Rasch model are violated, the use of the total score is associated with a loss of information, which can go so far that the diagnostically relevant information contained in the responses of the test persons is completely lost. Instead of the scores, the diagnostic decision must then be based on the respondents' response patterns. This is done by the latent class analysis, which goes back to Paul Lazarsfeld , by means of which typical response patterns are identified and the test persons are classified according to which of these types their response behavior corresponds best. Especially in attitude measurement, where even slight semantic variations in the item formulation can trigger completely different reaction tendencies in the test subjects, this approach has proven to be significantly more effective than the still common use of scoring.
In response to Siegfried Kracauer's criticism, according to which it is not so much the frequency of certain text features that make up the meaning of a text as the patterns they form, the latent class analysis has not only psychological diagnostics but also quantitative content analysis found an important field of application.
literature
- S. Embretson, S. Reise: Item response theory for psychologists . Erlbaum, Mahwah NJ 2000.
- GH Fischer: Introduction to the theory of psychological tests. Basics and Applications . Huber, Bern [a. a.] 1974.
- F. Gernot: Probabilistic test models in personality diagnostics . Lang, Frankfurt am Main [a. a.] 1993.
- D. Heyer: Boolean and probabilistic measurement theory: Methods of error handling in psychophysical theories . Lang, Frankfurt am Main [a. a.] 1990.
- W. Kempf: Research methods in psychology. Volume II. Quantity and Quality . regener, Berlin 2008.
- W. Kempf, R. Langeheine: Item Response Models in Social Science Research . regener, Berlin 2012.
- PF Lazarsfeld, NW Henry: Latent structure analysis . Houghton Mifflin, Boston 1968.
- D. Lind: Probabilistic test models in empirical pedagogy . BI-Wiss.-Verlag, Mannheim [u. a.] 1994.
- FM Lord: Applications of item response theory to practical testing problems . Erlbaum, Mahwah NJ 1980.
- H. Müller: Probabilistic test models for discrete and continuous rating scales . Huber, Bern 1999.
- G. Rasc: Probabilistic models for some intelligence and attainment tests . Danish Institute for Educational Research, Copenhagen 1960; expanded edition with foreword and afterword by BD Wright. The University of Chicago Press, Chicago 1980
- J. Rost: Textbook test theory - test construction . Huber, Bern [a. a.] 1996; 2., completely revised and exp. Edition 2004.
- R. Steyer, M. Eid: Measuring and testing . Springer, Berlin 2001 [chap. 16-18]
See also
Web links
- D. Lind: Models for performance evaluation (PDF; 548 kB) Lecture notes
- Ivailo Partchev: A visual guide to item response theory . (PDF; 515 kB)
Individual evidence
- ^ Howard Wainer, Eric T. Bradlow, Xiaohui Wang: Testlet Response Theory and Its Applications . Cambridge University Press, 2007, ISBN 978-0-521-68126-1 .