An Overview of Item Response Theory

An important component of both CAT and MST is the use of item response theory (IRT) as an underlying framework for item bank calibration, ability estimation, and item/module selection. In this chapter, we present a brief overview of this theory, by providing key information and introducing appropriate notation for use in subsequent chapters. Only topics and contents directly related to adaptive and multistage testing will be covered in this chapter; appropriate references for further reading are therefore also mentioned.

[1]  T. A. Warm.  Weighted likelihood estimation of ability in item response theory , 1989 .

[2]  R. D. Bock,et al.  Adaptive EAP Estimation of Ability in a Microcomputer Environment , 1982 .

[3]  Carl P. M. Rijkes,et al.  Loglinear multidimensional IRT models for polytomously scored items , 1988 .

[4]  Fumiko Samejima.  Some critical observations of the test information function as a measure of local accuracy in ability estimation , 1994 .

[5]  M. Reckase.  Multidimensional Item Response Theory , 2009 .

[6]  George Karabatsos,et al.  Comparing the Aberrant Response Detection Performance of Thirty-Six Person-Fit Statistics , 2003 .

[7]  F. Lord.  Applications of Item Response Theory To Practical Testing Problems , 1980 .

[8]  Howard Wainer,et al.  Use of item response theory in the study of group differences in trace lines. , 1988 .

[9]  W. M. Yen.  Using Simulation Results to Choose a Latent Trait Model , 1981 .

[10]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  G. Masters.  A rasch model for partial credit scoring , 1982 .

[12]  M. Reckase.  Unifactor Latent Trait Models Applied to Multifactor Tests: Results and Implications , 1979 .

[13]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm , 1981 .

[14]  F. Lord.  A THEORY OF TEST SCORES AND THEIR RELATION TO THE TRAIT MEASURED , 1951 .

[15]  Raymond J. Adams,et al.  The Multidimensional Random Coefficients Multinomial Logit Model , 1997 .

[16]  E. Muraki.  A Generalized Partial Credit Model: Application of an EM Algorithm , 1992 .

[17]  R. Darrell Bock,et al.  Estimating item parameters and latent ability when responses are scored in two or more nominal categories , 1972 .

[18]  B. Wright,et al.  Best test design , 1979 .

[19]  Howard T. Everson,et al.  Methodology Review: Statistical Approaches for Assessing Measurement Bias , 1993 .

[20]  Fumiko Samejima,et al.  Normal ogive model on the continuous response level in the multidimensional latent space , 1974 .

[21]  P. Holland.  On the sampling theory roundations of item response theory models , 1990 .

[22]  R. Hambleton,et al.  Handbook of Modern Item Response Theory , 1997 .

[23]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[24]  Wendy M. Yen,et al.  Effects of Local Item Dependence on the Fit and Equating Performance of the Three-Parameter Logistic Model , 1984 .

[25]  Bradley A. Hanson,et al.  Development and Calibration of an Item Response Model That Incorporates Response Time , 2005 .

[26]  Edward E. Roskam,et al.  Models for Speed and Time-Limit Tests , 1997 .

[27]  Eric T. Bradlow,et al.  Testlet Response Theory and Its Applications , 2007 .

[28]  E. Maris.  Psychometric latent response models , 1995 .

[29]  M. Gessaroli,et al.  Using an Approximate Chi-Square Statistic to Test the Number of Dimensions Underlying the Responses to a Set of Items , 1996 .

[30]  Martha L. Stocking,et al.  Developing a Common Metric in Item Response Theory , 1983 .

[31]  H. Swaminathan,et al.  Detecting Differential Item Functioning Using Logistic Regression Procedures , 1990 .

[32]  Fritz Drasgow,et al.  Appropriateness measurement with polychotomous item response models and standardized indices , 1984 .

[33]  Lihua Yao,et al.  A Multidimensional Partial Credit Model With Associated Item and Test Statistics: An Application to Mixed-Format Tests , 2006 .

[34]  Tom A. B. Snijders,et al.  Asymptotic null distribution of person fit statistics with estimated person parameter , 2001 .

[35]  Brian Habing,et al.  Performance of DIMTEST- and NOHARM-Based Statistics for Testing Unidimensionality , 2007 .

[36]  Ke-Hai Yuan,et al.  Robust Estimation of Latent Ability in Item Response Models , 2011 .

[37]  Gerhard H. Fischer,et al.  On the existence and uniqueness of maximum-likelihood estimates in the Rasch model , 1981 .

[38]  Frederic M. Lord.  MAXIMUM LIKELIHOOD AND BAYESIAN PARAMETER ESTIMATION IN ITEM RESPONSE THEORY , 1986 .

[39]  R. Mislevy.  Estimating latent distributions , 1984 .

[40]  P. Boeck,et al.  A general framework and an R package for the detection of dichotomous differential item functioning , 2010, Behavior research methods.

[41]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1968 .

[42]  R. Hambleton,et al.  21 Assessing the Fit of Item Response Theory Models , 2006 .

[43]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[44]  A Note on Weighted Likelihood and Jeffreys Modal Estimation of Proficiency Levels in Polytomous Item Response Models , 2015, Psychometrika.

[45]  D. Andrich.  A rating formulation for ordered response categories , 1978 .

[46]  David Magis,et al.  Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models , 2016, Psychometrika.

[47]  Frank B. Baker,et al.  Item Response Theory : Parameter Estimation Techniques, Second Edition , 2004 .

[48]  N. D. Verhelst,et al.  A Logistic Model for Time-Limit Tests , 1992 .

[49]  R. Tate,et al.  A Comparison of Selected Empirical Methods for Assessing the Structure of Responses to Test Items , 2003 .

[50]  W. Velicer,et al.  Comparison of five rules for determining the number of components to retain. , 1986 .

[51]  R. H. Klein Entink,et al.  A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers , 2008, Psychometrika.

[52]  Christine E. DeMars.  Item Response Theory , 2010 .

[53]  C. Glas,et al.  Elements of adaptive testing , 2010 .

[54]  B. Green,et al.  A general solution for the latent class model of latent structure analysis. , 1951, Psychometrika.

[55]  D. Thissen,et al.  Local Dependence Indexes for Item Pairs Using Item Response Theory , 1997 .

[56]  Frederic M. Lord,et al.  An Upper Asymptote for the Three-Parameter Logistic Item-Response Model. , 1981 .

[57]  P. Boeck,et al.  Explanatory item response models : a generalized linear and nonlinear approach , 2004 .

[58]  William Stout,et al.  A nonparametric approach for assessing latent trait unidimensionality , 1987 .

[59]  Robert J. Mislevy,et al.  Bayes modal estimation in item response models , 1986 .

[60]  John Hattie,et al.  An Empirical Study of Various Indices for Determining Unidimensionality. , 1984, Multivariate behavioral research.

[61]  H. Jeffreys,et al.  Theory of probability , 1896 .

[62]  Francis Tuerlinckx,et al.  Copula Functions for Residual Dependency , 2007 .

[63]  Wim J. van der Linden,et al.  IRT Parameter Estimation With Response Times as Collateral Information , 2010 .

[64]  Gregory Camilli,et al.  5 Differential Item Functioning and Item Bias , 2006 .

[65]  Robert J. Mislevy,et al.  Biweight Estimates of Latent Ability , 1982 .

[66]  David Thissen,et al.  A taxonomy of item response models , 1986 .

[67]  R. Hambleton,et al.  Item Response Theory: Principles and Applications , 1984 .

[68]  Allan Birnbaum,et al.  STATISTICAL THEORY FOR LOGISTIC MENTAL TEST MODELS WITH A PRIOR DISTRIBUTION OF ABILITY , 1967 .

[69]  G. Masters,et al.  Rating scale analysis , 1982 .

[70]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[71]  E. B. Andersen,et al.  Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[72]  R. Hambleton,et al.  Item Response Theory , 1984, The History of Educational Measurement.

[73]  Tomokazu Haebara,et al.  EQUATING LOGISTIC ABILITY SCALES BY A WEIGHTED LEAST SQUARES METHOD , 1980 .

[74]  Eiji Muraki,et al.  Fitting a Polytomous Item Response Model to Likert-Type Data , 1990 .

[75]  Wendy M. Yen,et al.  Scaling Performance Assessments: Strategies for Managing Local Item Dependence , 1993 .

[76]  D. Magis.  On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models. , 2014, The British journal of mathematical and statistical psychology.

[77]  David Magis,et al.  A Note on the Equivalence Between Observed and Expected Information Functions With Polytomous IRT Models , 2015 .

[78]  R. Darrell Bock,et al.  Fitting a response model forn dichotomously scored items , 1970 .