A Latent Ability Model for Count Data and Application to Processing Speed

Abstract

A new family of item response theory models for count data, based on item characteristic curves (ICCs) of binary models, is presented. These models assume a Poisson distribution for the observed scores where the mean is given by the product of a speed parameter and an ICC, for example, the curve of the one- or two-parameter logistic model. Joint and marginal maximum likelihood parameter estimations are discussed and the proposed procedures are evaluated by computer simulation. As an application, item level data from a test measuring processing speed are analyzed and item fit and test information are explored.

Keywords

count data Rasch Poisson counts model item characteristic curve processing speed

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References

Baker

Kim

(2004). Item response theory: Parameter estimation techniques (2nd ed.). New York, NY: Dekker.

Byrd

R. H.

Nocedal

Zhu

(1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, 1190-1208.

Embretson

Reise

(2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.

Guilford

J. P.

(1967). The nature of human intelligence. New York, NY: McGraw-Hill.

Hambleton

Rogers

Swaminathan

(1995). Fundamentals of item response theory. Thousand Oaks, CA: Sage.

Hung

(2012). A negative binomial regression model for accuracy tests. Applied Psychological Measurement, 36, 88-103.

Jäger

(1967). Dimensionen der Intelligenz [Dimensions of intelligence]. Göttingen, Germany: Hogrefe.

Jäger

(1982). Mehrmodale Klassifikation von Intelligenzleistungen [Multimodal classifications of intelligence achievements]. Diagnostica, 28, 195-225.

Jäger

(1984). Intelligenzstrukturforschung: Konkurrierende Modelle, neue Entwicklungen, Perspektiven [Intelligence structure research: Competing models, new developments, perspectives]. Psychologische Rundschau, 35, 21-25.

10.

Jäger

Holling

Preckel

Schulze

Vock

Süß

H.-M.

Beauducel

(2006). Berliner Intelligenzstruktur-Test für Jugendliche: Begabungs- und Hochbegabungsdiagnostik [Berlin intelligence structure test for adolescents: diagnosis of diftedness and high giftedness] (BIS-HB). Göttingen, Germany: Hogrefe.

11.

Jansen

(1994). Parameters of the latent distribution in Rasch’s Poisson counts model. In Fischer

Laming

(Eds.), Contributions to mathematical psychology, psychometrics, and methodology (pp. 319-326). New York, NY: Springer.

12.

Jansen

(1995). The Rasch Poisson counts model for incomplete data: An application of the EM algorithm. Applied Psychological Measurement, 19, 291-302.

13.

Jansen

van Duijn

(1992). Extensions of Rasch’s multiplicative Poisson model. Psychometrika, 57, 405-414.

14.

Lord

(1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Erlbaum.

15.

Lord

Novick

Birnbaum

(1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

16.

McGrew

(2005). The Cattell-Horn-Carroll theory of cognitive abilities: Past, present, and future. In Flanagan

Harrison

(Eds.), Contemporary intellectual assessment: Theories, tests, and issues (pp. 136-181). New York, NY: Guilford Press.

17.

Ogasawara

(1996). Rasch’s multiplicative Poisson model with covariates. Psychometrika, 61, 73-92.

18.

Rasch

(1960). Studies in mathematical psychology: I. Probabilistic models for some intelligence and attainment tests. Oxford, England: Nielsen & Lydiche.

19.

R Development Core Team. (2012). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.

20.

Thissen

(1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175-186.

21.

Tjur

(1982). A connection between Rasch’s item analysis model and a multiplicative Poisson model. Scandinavian Journal of Statistics, 9, 23-30.

22.

Torrance

E. P.

(1974). Torrance tests of creative thinking: Verbal tests, forms A and B, figurals tests, forms A and B—Norms-technical manual. Princeton, NJ: Personnel Press.

23.

van der Linden

W. J.

(2007). A hierarchical framework for modeling speed and accuracy on test items. Psychometrika, 72, 287-308.

24.

van der Linden

W. J.

Hambleton

(1997). Handbook of modern item response theory. New York, NY: Springer Verlag.

25.

van Duijn

Bockenholt

(1995). Mixture models for the analysis of repeated count data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 44, 473-485.

26.

Verhelst

Kamphuis

(2009). A Poisson-Gamma model for speed tests. Arnhem, The Netherlands: Cito.

27.

Weiss

(1998). Grundintelligenztest Skala 2 (CFT 20) mit Wortschatztest (WS) und Zahlenfolgentest (ZF) - Handanweisung (4th Rev.). [Basic intelligence test scale 2 (CFT 20) with vocabulary test (WS) and number sequence test (ZF) - manual (4th Ed.)] Göttingen, Germany: Hogrefe.

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