Item response theory modeling with nonignorable missing data

This thesis discusses methods to detect nonignorable missing data and methods to adjust for the bias caused by nonignorable missing data, both by introducing a model for the missing data indicator using item response theory (IRT) models.

[1]  L. Wasserman,et al.  Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio , 1995 .

[2]  Appropriateness of IRT observed score equating , 1996 .

[3]  R. Little.  Models for Nonresponse in Sample Surveys , 1982 .

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

[5]  L. Shepard,et al.  Methods for Identifying Biased Test Items , 1994 .

[6]  Irini Moustaki,et al.  A Latent Variable Model for Ordinal Variables , 2000 .

[7]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

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

[9]  A. Béguin,et al.  MCMC estimation of multidimensional IRT models , 1998 .

[10]  N. D. Verhelst,et al.  Extensions of the partial credit model , 1989 .

[11]  G. Masters.  The Partial Credit Model , 2016 .

[12]  Cornelis A.W. Glas,et al.  Modification indices for the 2-PL and the nominal response model , 1999 .

[13]  Robert J. Mislevy.  Bayes modal estimation in item response models , 1986 .

[14]  E. Muraki,et al.  Full-Information Item Factor Analysis , 1988 .

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

[16]  Klaas Sijtsma,et al.  Methodology Review: Evaluating Person Fit , 2001 .

[17]  Nan M. Laird,et al.  Regression Analysis for Categorical Variables with Outcome Subject to Nonignorable Nonresponse , 1988 .

[18]  Terry Ackerman,et al.  Graphical Representation of Multidimensional Item Response Theory Analyses , 1996 .

[19]  Morton B. Brown,et al.  Log-linear models for a binary response with nonignorable nonresponse , 1997 .

[20]  G. J. Mellenbergh,et al.  A Unidimensional Latent Trait Model for Continuous Item Responses. , 1994, Multivariate behavioral research.

[21]  C. H. Coombs,et al.  Mathematical psychology : an elementary introduction , 1970 .

[22]  J. Dickey.  The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters , 1971 .

[23]  E. Muraki.  A GENERALIZED PARTIAL CREDIT MODEL: APPLICATION OF AN EM ALGORITHM , 1992 .

[24]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[25]  T. Cook,et al.  Quasi-experimentation: Design & analysis issues for field settings , 1979 .

[26]  Mark R. Conaway,et al.  The Analysis of Repeated Categorical Measurements Subject to Nonignorable Nonresponse , 1992 .

[27]  Eric T. Bradlow,et al.  A hierarchical latent variable model for ordinal data from a customer satisfaction survey with no answer responses , 1999 .

[28]  Francis Tuerlinckx,et al.  A Hierarchical IRT Model for Criterion-Referenced Measurement , 2000 .

[29]  Christine E. DeMars.  Incomplete Data and Item Parameter Estimates Under JMLE and MML Estimation , 2002 .

[30]  Cees A. W. Glas,et al.  Statistical tests for differential test functioning in Rasch's model for speed tests , 2001 .

[31]  J. Aitchison,et al.  Maximum-Likelihood Estimation of Parameters Subject to Restraints , 1958 .

[32]  Frederic M. Lord,et al.  Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability , 1983 .

[33]  Steven E. Rigdon,et al.  Parameter estimation in latent trait models , 1983 .

[34]  Klaas Sijtsma,et al.  Investigation and Treatment of Missing Item Scores in Test and Questionnaire Data , 2003, Multivariate behavioral research.

[35]  K Sijtsma,et al.  Influence of Imputation and EM Methods on Factor Analysis when Item Nonresponse in Questionnaire Data is Nonignorable , 2000, Multivariate behavioral research.

[36]  Raymond J. Adams,et al.  Multilevel Item Response Models: An Approach to Errors in Variables Regression , 1997 .

[37]  Erling B. Andersen,et al.  Conditional Inference and Models for Measuring , 1974 .

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

[39]  Ivo W. Molenaar,et al.  Estimation of Item Parameters , 1995 .

[40]  C. Glas.  Testing the generalized partial credit model , 1996 .

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

[42]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[43]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[44]  Mark Huisman,et al.  Item Nonresponse: Occurence, Causes, and Imputation of Missing Answers to Test Items , 1999 .

[45]  Jean-Paul Fox,et al.  Modelling response error in school effectiveness research , 2004 .

[46]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[47]  Brian W. Junker,et al.  Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses , 1999 .

[48]  J. Schafer,et al.  Missing data: our view of the state of the art. , 2002, Psychological methods.

[49]  Modeling variability in item parameters in educational measurement , 2005 .

[50]  Ivo W. Molenaar,et al.  Some improved diagnostics for failure of the Rasch model , 1983 .

[51]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[52]  Roderick P. McDonald,et al.  Normal-Ogive Multidimensional Model , 1997 .

[53]  Cornelis A.W. Glas,et al.  A Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model , 2003 .

[54]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[55]  Benjamin D. Wright,et al.  A Procedure for Sample-Free Item Analysis , 1969 .

[56]  Nancy L. Allen,et al.  Measuring the Benefits of Examinee-Selected Questions , 2005 .

[57]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[58]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[59]  Tom A. B. Snijders.  Asymptotic distribution of person fit statistics with estimated person parameters , 2001 .

[60]  D. Rubin,et al.  MULTIPLE IMPUTATIONS IN SAMPLE SURVEYS-A PHENOMENOLOGICAL BAYESIAN APPROACH TO NONRESPONSE , 2002 .

[61]  J. Hox,et al.  Prevention and treatment of item nonresponse. , 2003 .

[62]  Tests of fit for polytomous models , 1995 .

[63]  J. Gill.  Hierarchical Linear Models , 2005 .

[64]  Educational Evaluation.  Standards for Educational and Psychological Testing , 1999 .

[65]  Cornelis A.W. Glas,et al.  Educational Evaluation, Assessment and Monitoring: A Systematic Approach , 2003 .

[66]  C. A. W. Glas,et al.  The Rasch Model and Multistage Testing , 1988 .

[67]  Cornelis A.W. Glas,et al.  A dynamic generalization of the Rasch model , 1993 .

[68]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[69]  Cornelis A.W. Glas,et al.  A Steps Model to Analyze Partial Credit , 1997 .

[70]  M R Conaway.  Causal nonresponse models for repeated categorical measurements. , 1994, Biometrics.

[71]  R. P. McDonald,et al.  Nonlinear factor analysis. , 1967 .

[72]  D. Thissen,et al.  Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models , 2000 .

[73]  Mark Wilson,et al.  The partial credit model and null categories , 1993 .

[74]  Taesung Park,et al.  Models for Categorical Data with Nonignorable Nonresponse , 1994 .

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

[76]  Eric T. Bradlow,et al.  Item Response Theory Models Applied to Data Allowing Examinee Choice , 1998 .

[77]  M. Knott,et al.  Generalized latent trait models , 2000 .

[78]  Calyampudi R. Rao.  Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

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

[80]  E. Maris,et al.  A MCMC-method for models with continuous latent responses , 2002 .

[81]  Mark Huisman,et al.  Missing data in behavioral science research: Investigation of a collection of data sets , 1998 .

[82]  R. J. Mokken,et al.  A Theory and Procedure of Scale Analysis: With Applications in Political Research , 1971 .

[83]  Mark D. Reckase,et al.  The Difficulty of Test Items That Measure More Than One Ability , 1985 .

[84]  Henk Kelderman,et al.  Item bias detection using loglinear irt , 1989 .

[85]  R. Hambleton,et al.  Fundamentals of Item Response Theory , 1991 .

[86]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1969 .

[87]  I. W. Molenaar,et al.  Rasch models: foundations, recent developments and applications , 1995 .

[88]  Cees A. W. Glas,et al.  Dynamic Generalizations of the Rasch Model , 1995 .

[89]  G. Tutz.  Sequential item response models with an ordered response , 1990 .

[90]  R. Hambleton,et al.  Detecting potentially biased test items : Comparison of IRT area and Mantel-Haenszel methods , 1989 .

[91]  Gerardus Johannes Andre Fox.  Multilevel IRT: a Bayesian perspective on estimating parameters and testing statistical hypotheses , 2001 .

[92]  A. Buse.  The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note , 1982 .

[93]  Richard J. Patz,et al.  A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models , 1999 .

[94]  Rebecca Holman,et al.  Modelling non-ignorable missing-data mechanisms with item response theory models. , 2005, The British journal of mathematical and statistical psychology.

[95]  P. Green,et al.  A Bayesian Hierarchical Model for Categorical Data with Nonignorable Nonresponse , 2003, Biometrics.

[96]  Cornelis A.W. Glas,et al.  Modelling Measurement Error in Structural Multilevel Models , 2002 .

[97]  Karen Draney,et al.  Objective measurement : theory into practice , 1992 .

[98]  Frederic M. Lord,et al.  Small n justifies the Rasch model , 1983 .

[99]  Norman Verhelst,et al.  Maximum Likelihood Estimation in Generalized Rasch Models , 1986 .

[100]  Terry A. Ackerman.  Developments in Multidimensional Item Response Theory , 1996 .

[101]  Robert J. Mislevy,et al.  BILOG 3 : item analysis and test scoring with binary logistic models , 1990 .

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

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

[104]  Cees A. W. Glas,et al.  The derivation of some tests for the rasch model from the multinomial distribution , 1988 .

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

[106]  F. Baker,et al.  Item response theory : parameter estimation techniques , 1993 .

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

[108]  Cees A. W. Glas,et al.  DETECTION OF DIFFERENTIAL ITEM FUNCTIONING USING LAGRANGE MULTIPLIER TESTS , 1996 .

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

[110]  David Thissen,et al.  Marginal maximum likelihood estimation for the one-parameter logistic model , 1982 .

[111]  G. Barrie Wetherill,et al.  Sampling Inspection and Quality Control, 2nd Edition. , 1978 .

[112]  Robert J. Mislevy,et al.  The role of collateral information about examinees in item parameter estimation , 1989 .

[113]  W. H. Angoff,et al.  Perspectives on differential item functioning methodology. , 1993 .

[114]  Martin Knott,et al.  Weighting for item non‐response in attitude scales by using latent variable models with covariates , 2000 .

[115]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[116]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[117]  George A. Marcoulides,et al.  Latent variable and latent structure models , 2002 .

[118]  Kikumi K. Tatsuoka,et al.  Caution indices based on item response theory , 1984 .

[119]  Susan E. Embretson,et al.  Item Response Theory Models and Spurious Interaction Effects in Factorial ANOVA Designs , 1996 .

[120]  Ulrich Paquet.  Bayesian inference for latent variable models , 2007 .

[121]  R. Fay.  Causal Models for Patterns of Nonresponse , 1986 .

[122]  Cornelis A.W. Glas,et al.  Differential Item Functioning Depending on General Covariates , 2001 .

[123]  Klaas Sijtsma,et al.  Factor analysis of multidimensional polytomous item response data suffering from ignorable item nonresponse. , 1999 .

[124]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[125]  A. L. V. D. Wollenberg.  The Rasch model and time-limit tests: an application and some theoretical contributions , 1979 .

[126]  R. Darrell Bock,et al.  Multiple Group IRT , 1997 .

[127]  S. Embretson,et al.  Item response theory for psychologists , 2000 .

[128]  I. Moustaki,et al.  A one dimension latent trait model to infer attitude from nonresponse for nominal data , 2000 .

[129]  Eric T. Bradlow,et al.  A Bayesian random effects model for testlets , 1999 .

[130]  Gees A.W. Glas,et al.  Item Calibration and Parameter Drift , 2000 .

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

[132]  V. Linden,et al.  Classical Test Theory , 2005 .

[133]  Andrew Copas,et al.  Dealing with non‐ignorable non‐response by using an ‘enthusiasm‐to‐respond’ variable , 1998 .

[134]  J. Berger,et al.  [Testing Precise Hypotheses]: Rejoinder , 1987 .

[135]  A. Béguin,et al.  MCMC estimation and some model-fit analysis of multidimensional IRT models , 2001 .

[136]  Cees A. W. Glas,et al.  Testing the Rasch Model , 1995 .

[137]  Stan Lipovetsky,et al.  Latent Variable Models and Factor Analysis , 2001, Technometrics.

[138]  Howard Wainer,et al.  Testlet Response Theory: An Analog for the 3PL Model Useful in Testlet-Based Adaptive Testing , 2000 .

[139]  Pao-Kuei Wu,et al.  MISSING RESPONSES AND IRT ABILITY ESTIMATION: OMITS, CHOICE, TIME LIMITS, AND ADAPTIVE TESTING , 1996 .

[140]  Cees A. W. Glas.  Structural Item Response Models , 2005 .

[141]  Martin Abba Tanner,et al.  Tools for Statistical Inference: Observed Data and Data Augmentation Methods , 1993 .

[142]  Anton Beguin,et al.  Using Classical Test Theory in Combination with Item Response Theory , 2003 .

[143]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

[144]  Colm O'Muircheartaigh,et al.  Symmetric pattern models: a latent variable approach to item non‐response in attitude scales , 1999 .

[145]  Jim Albert,et al.  Ordinal Data Modeling , 2000 .

[146]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[147]  A. Winsor.  Sampling techniques. , 2000, Nursing times.

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

[149]  I. Klugkist.  Inequality Constrained Normal Linear Models , 1999 .

[150]  J. Kiefer,et al.  CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE PRESENCE OF INFINITELY MANY INCIDENTAL PARAMETERS , 1956 .

[151]  Jean-Paul Fox,et al.  Bayesian modeling of measurement error in predictor variables using item response theory , 2003 .

[152]  Tapabrata Maiti,et al.  Bayesian Data Analysis (2nd ed.) (Book) , 2004 .

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

[154]  Robert J. Mislevy,et al.  Does adaptive testing violate local independence? , 2000 .

[155]  I. Moustaki.  A latent trait and a latent class model for mixed observed variables , 1996 .

[156]  M. Jansen,et al.  The Rasch Model for Speed Tests and Some Extensions With Applications to Incomplete Designs , 1997 .

[157]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[158]  J. Fox,et al.  Bayesian estimation of a multilevel IRT model using gibbs sampling , 2001 .

[159]  Gerhard H. Fischer,et al.  Derivations of the Rasch Model , 1995 .

[160]  Herbert Hoijtink,et al.  On person parameter estimation in the dichotomous Rasch model , 1995 .

[161]  E. B. Andersen,et al.  A goodness of fit test for the rasch model , 1973 .

[162]  Arnold L. van den Wollenberg,et al.  Two new test statistics for the rasch model , 1982 .

[163]  M. Berger,et al.  Sequential sampling designs for the two-parameter item response theory model , 1992 .

[164]  C. Coombs.  A theory of data. , 1965, Psychology Review.

[165]  Mark D. Reckase,et al.  A Linear Logistic Multidimensional Model for Dichotomous Item Response Data , 1997 .

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

[167]  Frank B. Baker,et al.  An Investigation of the Item Parameter Recovery Characteristics of a Gibbs Sampling Procedure , 1998 .

[168]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[169]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .