Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory

REFERENCES

• Adams , R. J. , Wilson , M. R. and Wang , W. C. 1997 . The Multidimensional Random Coefficients Multinomial Logit Model . Applied Psychological Measurement , 21 : 1 – 23 .
   Web of Science ®Google Scholar
• Armitage , P. 1955 . Tests for Linear Trends in Proportions and Frequencies . Biometrics , 11 : 375 – 386 .
   Web of Science ®Google Scholar
• Baldwin , P. , Bernstein , J. and Wainer , H. 2009 . Hip Psychometrics . Statistics in Medicine , 28 : 2277 – 2292 .
   PubMedGoogle Scholar
• Berk , R. H. 1972 . Consistency and Asymptotic Normality of MLE's for Exponential Models . The Annals of Mathematical Statistics , 43 : 193 – 204 .
   Google Scholar
• Birch , M. W. 1964 . A New Proof of the Pearson-Fisher Theorem . Annals of Mathematical Statistics , 35 : 817 – 824 .
   Google Scholar
• Birnbaum , A. 1968 . “ Some Latent Trait Models and Their Use in Inferring an Examinee's Ability ” . In Statistical Theories of Mental Test Scores , Edited by: Lord , F. M. and Novick , M. R. 397 – 479 . Reading, MA : Addison-Wesley .
   Google Scholar
• Bock , R. D. 1997 . A Brief History of Item Response Theory . Educational Measurement: Issues and Practice , 16 : 21 – 33 .
   Google Scholar
• Bock , R. D. and Aitkin , M. 1981 . Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm . Psychometrika , 46 : 443 – 459 .
   Web of Science ®Google Scholar
• Bock , R. D. and Moustaki , I. 2007 . “ Item Response Theory in a General Framework ” . In Handbook of Statistics (Vol. 26) , Edited by: Rao , C. R. and Sinharay , S. 469 – 513 . Amsterdam : North-Holland .
   Google Scholar
• Boughton , K. , Larkin , K. and Yamamoto , K. 2004 . Modeling Differential Speededness Using a Hybrid Psychometric Approach . paper presented at the annual meeting of the American Educational Research Association, San Diego, CA
   Google Scholar
• Box , G. E. P. and Draper , N. R. 1987 . Empirical Model-Building and Response Surfaces , New York : Wiley .
   Google Scholar
• Cai , L. , du Toit , S. H. C. and Thissen , D. 2011 . IRTPRO: Flexible, Multidimensional, Multiple Categorical IRT Modeling , Chicago , IL : Scientific Software International .
   Google Scholar
• Chang , H. and Ying , Z. 2009 . Nonlinear Sequential Designs for Logistic Item Response Theory Models With Applications to Computerized Adaptive Tests . The Annals of Statistics , 37 : 1466 – 1488 .
   Google Scholar
• Chao , A. 1987 . Estimating the Population Size for Capture-Recapture Data With Unequal Catchability . Biometrics , 43 : 783 – 791 .
   PubMed Web of Science ®Google Scholar
• Cochran , W. G. 1954 . Some Methods for Strengthening the Common χ2 Tests . Biometrics , 10 : 417 – 451 .
   Web of Science ®Google Scholar
• Cochran , W. G. 1955 . A Test of a Linear Function of the Deviations Between Observed and Expected Numbers . Journal of the American Statistical Association , 50 : 377 – 397 .
   Google Scholar
• Cohen , J. and Jiang , T. 1999 . Comparison of Partially Measured Latent Traits Across Nominal Subgroups . Journal of the American Statistical Association , 94 : 1035 – 1044 .
   Google Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . “Maximum Likelihood From Incomplete Data via the EM Algorithm” (with discussion) . Journal of the Royal Statistical Society, Series B , 39 : 1 – 38 .
   Google Scholar
• Eaton , W. W. and Bohrnstedt , G. W. (eds.) . 1989 . Latent Variable Models for Dichotomous Outcomes: Analysis of Data From Epidemiological Catchment Area Program . Sociological Methods and Research , 18 : 3 – 182 .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1989 . Extensions of the Partial Credit Model . Psychometrika , 54 : 635 – 659 .
   Web of Science ®Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1995 . “ Testing the Rasch Model ” . In Rasch Models: Foundations, Recent Developments, and Applications , Edited by: Fischer , G. H. and Molenaar , I. W. 69 – 95 . New York : Springer .
   Google Scholar
• Haberman , S. J. 1976 . Generalized Residuals for Log-Linear Models . Proceedings of the Ninth International Biometrics Conference, vol. 1 , : 104 – 172 .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1977a . Log-Linear Models and Frequency Tables With Small Expected Cell Counts . The Annals of Statistics , 5 : 1148 – 1169 .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1977b . Maximum Likelihood Estimates in Exponential Response Models . The Annals of Statistics , 5 : 815 – 841 .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1978 . Analysis of Qualitative Data, Volume I: Introductory Topics , New York : Academic Press .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1979 . Analysis of Qualitative Data, Volume II: New Developments , New York : Academic Press .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 1988 . A Stabilized Newton-Raphson Algorithm for Log-Linear Models for Frequency Tables Derived by Indirect Observation . Sociological Methodology , 18 : 193 – 211 .
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 2004 . Joint and Conditional Maximum Likelihood Estimation for the Rasch Model for Binary Responses . Research Rep. No. RR-04-20, Princeton, NJ: ETS
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 2005 . Latent-Class Item Response Models . Research Rep. No. RR-05-28, Princeton, NJ: ETS
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 2006 . An Elementary Test of the Normal 2PL Model Against the Normal 3PL Alternative . ETS Research Rep. No. RR-06-14, Princeton, NJ: ETS
   Google Scholar
• Glas , C. A. W. and Verhelst , N. D. 2009 . Use of Generalized Residuals to Examine Goodness of Fit of Item Response Models . ETS Research Report No. RR-09-15, Princeton, NJ: ETS
   Google Scholar
• Haberman , S. J. , Sinharay , S. and Chon , K. H. 2013 . Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals From Estimated Item Response Functions . Psychometrika , 78 : 417 – 440 .
   PubMed Web of Science ®Google Scholar
• Haberman , S. J. , von Davier , M. and Lee , Y. 2008 . Comparison of Multidimensional Item Response Models: Multivariate Normal Ability Distributions Versus Multivariate Polytomous Distributions . ETS Research Rep. No. RR-08-45, Princeton, NJ: ETS
   Google Scholar
• Hambleton , R. K. and Han , N. 2005 . “ Assessing the Fit of IRT Models to Educational and Psychological Test Data: A Five Step Plan and Several Graphical Displays ” . In Advances in Health Outcomes Research Methods, Measurement, Statistical Analysis, and Clinical Applications , Edited by: Lenderking , W. R. and Revicki , D. 57 – 78 . Washington , DC : Degnon Associates .
   Google Scholar
• Hambleton , R. K. , Swaminathan , H. and Rogers , H. J. 1991 . Fundamentals of Item Response Theory , Newbury Park, CA : Sage .
   Google Scholar
• Hays , R. D. , Morales , L. S. and Reise , S. P. 2000 . Item Response Theory and Health Outcomes Measurement in the 21st Century . Medical Care , 38 : II28 – II42 .
   PubMed Web of Science ®Google Scholar
• Heinen , T. 1996 . Latent Class and Discrete Latent Trait Models , Thousand Oaks , CA : Sage .
   Google Scholar
• Holland , P. W. 1990 . The Dutch Identity: A New Tool for the Study of Item Response Models . Psychometrika , 55 : 5 – 18 .
   Google Scholar
• Holland , P. W. and Rosenbaum , P. 1986 . Conditional Association and Unidimensionality in Monotone Latent Variable Models . The Annals of Statistics , 14 : 1523 – 1543 .
   Web of Science ®Google Scholar
• Junker , B. W. 1993 . Conditional Association, Essential Independence and Monotone Unidimensional Item Response Models . The Annals of Statistics , 21 : 1359 – 1378 .
   Web of Science ®Google Scholar
• Lord , F. M. 1980 . Applications of Item Response Theory to Practical Testing Problems , Hillsdale , NJ : Erlbaum .
   Google Scholar
• Lord , F. M. and Wingersky , M. S. 1984 . Comparison of IRT True-Score and Equipercentile Observed-Score ‘Equatings’ . Applied Psychological Measurement , 8 : 453 – 461 .
   Web of Science ®Google Scholar
• Louis , T. 1982 . Finding the Observed Information Matrix When Using the EM Algorithm . Journal of the Royal Statistical Society, Series B , 44 : 226 – 233 .
   Web of Science ®Google Scholar
• Mantel , N. and Haenszel , W. 1959 . Statistical Aspects of the Analysis of Data From Retrospective Studies . Journal of the National Cancer Institute , 22 : 719 – 748 .
   PubMed Web of Science ®Google Scholar
• Muraki , E. 1997 . “ A Generalized Partial Credit Model ” . In Handbook of Modern Item Response Theory , Edited by: van der Linden , W. J. and Hambleton , R.K. New York : Springer-Verlag . chap. 9
   Google Scholar
• Muraki , E. and Bock , R. D. 2003 . PARSCALE 4: IRT Item Analysis and Test Scoring for Rating-Scale Data , Chicago , IL : Scientific Software .
   Google Scholar
• Naylor , A. F. M. and Smith , J. C. 1982 . Applications of a Method for the Efficient Computation of Posterior Distributions . Applied Statistics , 31 : 214 – 225 .
   Web of Science ®Google Scholar
• Orlando , M. and Thissen , D. 2000 . Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models . Applied Psychological Measurement , 24 : 50 – 64 .
   Web of Science ®Google Scholar
• Rao , C. R. 1973 . Linear Statistical Inference and Its Applications (2nd ed.) , New York : Wiley .
   Google Scholar
• Rasch , G. 1960 . Probabilistic Models for Some Intelligence and Attainment Tests , Copenhagen : Danish Institute for Educational Research .
   Google Scholar
• Reckase , M. D. 1997 . The Past and Future of Multidimensional Item Response Theory . Applied Psychological Measurement , 21 : 25 – 36 .
   Web of Science ®Google Scholar
• Reiser , M. 1996 . Analysis of Residual for the Multinomial Item Response Model . Psychometrika , 61 : 509 – 528 .
   Web of Science ®Google Scholar
• Rice , K. M. 2004 . Equivalence Between Conditional and Mixture Approaches to the Rasch Model and Matched Case-Control Studies, With Applications . Journal of the American Statistical Association , 99 : 510 – 522 .
   Web of Science ®Google Scholar
• Scott , S. L. and Ip , E. H. 2002 . Empirical Bayes and Item Clustering Effects in a Latent Variable Hierarchical Model: A Case Study From the National Assessment of Educational Progress . Journal of the American Statistical Association , 97 : 409 – 419 .
   Web of Science ®Google Scholar
• Sinharay , S. 2005 . Assessing Fit of Unidimensional Item Response Theory Models Using a Bayesian Approach . Journal of Educational Measurement , 42 : 375 – 394 .
   Web of Science ®Google Scholar
• Sinharay , S. 2006 . Model Diagnostics for Bayesian Networks . Journal of Educational and Behavioral Statistics , 31 : 1 – 33 .
   Web of Science ®Google Scholar
• Sinharay , S. , Johnson , M. S. and Stern , H. S. 2006 . Posterior Predictive Assessment of Item Response Theory Models . Applied Psychological Measurement , 30 : 298 – 321 .
   Web of Science ®Google Scholar
• Thissen , D. , Pommerich , M. , Billeaud , K. and Williams , V. 1995 . Item Response Theory for Scores on Tests Including Polytomous Items With Ordered Responses . Applied Psychological Measurement , 19 : 39 – 49 .
   Web of Science ®Google Scholar
• Tjur , T. 1982 . A Connection Between Rasch's Item Analysis Model and a Multiplicative Poisson Model . Scandinavian Journal of Statistics , 9 : 23 – 30 .
   Web of Science ®Google Scholar
• Yamamoto , K. 1989 . A Hybrid Model of IRT and Latent Class Models . ETS Research Rep. No. RR-89-41, Princeton, NJ: ETS
   Google Scholar
• Yates , F. 1948 . The Analysis of Contingency Tables With Groupings Based on Quantitative Characters . Biometrika , 35 : 176 – 181 .
   PubMed Web of Science ®Google Scholar
• Yen , W. 1993 . Scaling Performance Assessments: Strategies for Managing Local Item Dependence . Journal of Educational Measurement , 30 : 187 – 213 .
   Web of Science ®Google Scholar
• Ziegler , A. 2011 . Generalized Estimating Equations , New York : Springer .
   Google Scholar