Local response dependence and the Rasch factor model
|
|
- Pauline Natalie Freeman
- 5 years ago
- Views:
Transcription
1 Local response dependence and the Rasch factor model Dept. of Biostatistics, Univ. of Copenhagen Rasch6 Cape Town
2 Uni-dimensional latent variable model X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items. Monotone relationships. [Holland and Rosenbaum, 1986]
3 Uni-dimensional latent variable model - Rasch model X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items. Monotone relationships. Rasch: invariance, sufficiency
4 Rasch model for item response X i Item parameters β i = (β i0, β i1, β i2,...) P(X i = x Θ = θ) = exp(xθ + β ix )K i (θ) 1 (1) for x = 0, 1,..., m i. β i0 = 0 for convenience and K i (θ) = m i h=0 exp(hθ + β ih)
5 Assumption of local independence Response vector X = (X i ) i I P( X = x Θ = θ) = i I P(X i = x Θ = θ) yielding P( X = x Θ = θ) = exp ( Rθ + i I β ixi ) K(θ) 1 (2) where K(θ) = i I K i(θ) R = i I X i sufficient.
6 Marginal probability P( X = x) = P( X = x Θ = θ)ϕ(θ)dθ ( ) = exp β ixi exp(rθ)k(θ) 1 ϕ σ (θ)dθ i I
7 Conditional probability P( X = x R = r) = exp ( i I β ix i ) γ R ( β) (3) β = ( β i ) i I, (3) independent of θ
8 Likelihood functions, inference MML l MML ( β, σ) = v i I β ixi + log exp(rθ)k(θ) 1 ϕ σ (θ)dθ (4) CML (complete cases) l CML ( β) = v Pairwise conditional l PW ( β) = v β ixvi log γ Rv ( β) (5) i I β ixvi log γ R (i,i ) i i v ( β) (6) Implementation: ConQuest [Wu et al., 2007], DIGRAM [Kreiner, 2003], RUMM [Andrich et al., 2010]. Standard software [Christensen, 2006].
9 Uni-dimensional latent variable model X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items. Monotone relationships. [Holland and Rosenbaum, 1986]
10 Uni-dimensional latent variable model, local dependence X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items. Monotone relationships. [Andrich, 1991]
11 Uni-dimensional latent variable model, local dependence X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items. Monotone relationships. Rasch: invariance, sufficiency. [Kreiner and Christensen, 2007]
12 Testing LD 1 Generalized Tjur test [Tjur, 1982] 2 Include interaction term in (9), i.e. loglinear Rasch model [Kelderman, 1984] 3 Item splitting [for dichotomous items] 4 Correlation structure in residuals
13 Testing LD 1 Generalized Tjur test Result for three dichotomous Rasch items [Tjur, 1982]: X 1 X 2 X 1 + X 3 generalization [Kreiner and Christensen, 2004]: X 1 X 2 R (1) and X 1 X 2 R (2) where R (1) = i 1 X i and R (2) = i 2 X i are rest scores. (Note: two p-values, need to control type I error rate). 1 Implementation: Standard software or the item screening in DIGRAM
14 Testing LD 2 Loglinear Rasch model Rasch model (9): ( P( X = x Θ = θ) = exp Rθ + i I β ixi ) K(θ) 1 include interaction term [Kelderman, 1984]: ( ) P( X = x Θ = θ) = exp Rθ + β ixi + δ(x 1, x 2 ) i I K(θ) 1 (7) compare (9) and (7) using likelihood ratio test. 2 Implementation: DIGRAM
15 Testing LD 3 Item splitting Splitting dependent item X 2 into Xi2 [Andrich and Kreiner, 2010] Illustration (dichotomous items) (0) and X i2 (1). ID X 1 X ID X 1 X2 (0) X 2 (1) Fit model for items X 2 (0), X 2 (1), X 3,... compare item parameters ( DIF test). Need asymptotic (co)variance for formal test. 3 Implementation: RUMM, DIGRAM
16 Item splitting X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4
17 Item splitting X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4
18 Testing LD 4 Residuals Local dependence for (X 1, X 2 ). [Yen, 1984, Q3] Observe (X 1v, X 2v ) v=1,...,n Estimate (θ v ) v=1,...,n Compute standardized residuals R iv = X iv E(X i ˆθ v ) V (X i ˆθ v ) and ρ OBS = corr(r 1, R 2 ) Test LD: Is observed value of ρ OBS due to random variation 4 Implementation: RUMM
19 Testing LD using residuals Local dependence for (X 1, X 2 ). [Yen, 1984, Q3] Observe (X 1v, X 2v ) v=1,...,n Estimate (θ v ) v=1,...,n Compute residuals R iv = X iv E(X i ˆθ v ) and ρ OBS = corr(r 1, R 2 ) Test LD: Is observed value of ρ OBS due to random variation But we don t know the null distribution of ρ...
20 Testing LD using residuals Local dependence for (X 1, X 2 ). [Yen, 1984, Q3] Observe (X 1v, X 2v ) v=1,...,n Estimate (θ v ) v=1,...,n Compute residuals R iv = X iv E(X i ˆθ v ) and ρ OBS = corr(r 1, R 2 ) Test LD: Is observed value of ρ OBS due to random variation But we don t know the null distribution of ρ... No formal test, rule-of-thumb ρ OBS > ρ 0, ρ 0 = 0.2, 0.3, 0.6,...
21 The problem with residuals we don t know the distribution of ˆθ ˆθ is a biased estimate of θ R iv can only take m i + 1 different values under the Rasch model corr(r 1, R 2 ) < [Kreiner and Christensen, 2011a]
22 Data example (9 items from the SF36, acute leukemia) How much of the time during the past 4 weeks Did you feel full of pep? Have you been a very nervous person? Have you felt so down in the dumps that nothing could cheer you up? Have you felt calm and peaceful? Did you have a lot of energy? Have you felt downhearted and blue? Did you feel worn out? Have you been a happy person? Did you feel tired? Response options: All of the Time, Most of the Time, A Good Bit of the Time, Some of the Time, A Little of the Time, None of the Time
23 Generalized Tjur test X 9 X 8 X 7 X 6 Θ X 5 X 4 X 1 X 2 X 3 Latent variable Θ, X 1,..., X 9 items. Results from item screening [Kreiner and Christensen, 2011b]
24 Log linear Rasch model X 9 X 8 X 7 X 6 Θ X 5 X 4 X 1 X 2 X 3 Latent variable Θ, X 1,..., X 9 items. Same as Tjur + five additional (neg. LD also found, not shown)
25 Correlation matrix of observed residuals
26 Correlation matrix of observed residuals
27 LD summary Generalized Tjur tests and residuals disagree x x x x x x x x x x x All models incorrect. Agreement about the most highly significant pair type I error known for Tjur tests. need to know the (multivariate) distribution of the correlation matrix (or the distribution of residuals) under the Rasch model.
28 Rasch measurement X 1 TREATMENT δ T X 2 AGE δ A Θ X 3 X 4 Latent variable Θ, X 1,..., X 4 items.
29 Rasch measurement, multidimensionality X 1 TREATMENT δ 1,A δ 1,T Θ 1 X 2 AGE δ 2,T δ 2,A Θ 2 X 3 X 4 Latent variable Θ, X 1,..., X 4 items.
30 Two-dimensional model Set of items split into d disjoint sets. For d = 2: θ = [ θ1 θ 2 I = I 1 I 2, (8) with items in I 1 and I 2 measuring latent variables θ 1 and θ 2 respectively. P(X = x Θ = θ) = exp ( R 1 θ 1 + R 2 θ 2 + i I η ) ix i K( θ) = exp ( d R dθ d + i I η ) ix i where R d = i I d x i and K( θ) = d K( θ) i I d K i (θ d ) ]
31 Marginal probability ( ) ( ) P( X = x) = exp β ixi exp R d θ d K(θ) 1 ϕ Σ ( θ)d θ i I can write d dim. marginal likelihood function. Unidim. likelihood function (4) nested within, but singular. can t compare nested models using LRT [Christensen et al., 2002, Harrell-Williams and Wolfe, 2014] d
32 Conditional probability P( X = x R = r) = exp ( i I β ix i ) d γ(d) r d (( β i ) i Id ) d dim. conditional likelihood function is the sum l CML ( β (d) ). Unidim. likelihood function (4) nested within? d
33 Rasch measurement, multidimensionality Patterns in residuals t-test observed vs. expected sub score correlationn Rasch factor model Summary of tests and diagnostics by Horton et al [Horton et al., 2013]
34 Patterns in residuals
35 Patterns in residuals
36 Tests currently avaliable Use patterns in residuals or Tjur tests to provide hypothetises beware of circular logic I 1 I 2 t-test, observed vs. expected sub score correlation and other tests are significant for many hypothetical I = I 1 I 2 Lack of overview, many tests, risk of type I error.. (still) need to know the (multivariate) distribution of the matrix of residuals under the Rasch model.
37 Rasch factor model Use P( X = x θ) = P( X = x R = r) P( R = r θ) }{{} ν to write extended likelihood l EML ( β, ν) = d l CML ( β (d) ) + v log ν v with the probabilities of the marginal sub score vector distribution as unrestricted parameters ν. Compare nested models using LRT [Christensen et al., 2002]
38 Factor models (1, 5, 8) + (2, 6) + (3, 4) + (7, 9) (1, 2, 5, 6, 8) + (3, 4) + (7, 9) (1, 3, 4, 5, 8) + (2, 6) + (7, 9) (1, 5, 8) + (2, 6) + (3, 4, 7, 9) (1, 2, 5, 6, 8) + (3, 4, 7, 9) (1, 3, 4, 5, 8) + (2, 6, 7, 9) (1, 2,..., 9) Compare nested models using LRT (or use BIC [Schwarz, 1978])
39 Factor models l =..., NPAR = 205 l =..., NPAR = 184 l =..., NPAR = 194 l =..., NPAR = 190 l =..., NPAR = 141 l =..., NPAR = 159 l =..., NPAR = (45 1) + (45 1) = 88 Compare nested models using LRT (or use BIC [Schwarz, 1978])
40 Andrich, D. (1991). Book review: Langeheine and Rost Latent Trait and Latent Class Models. Psychometrika, 56(1): Andrich, D. and Kreiner, S. (2010). Quantifying response dependence between two dichotomous items using the rasch model. Applied Psychological Measurement, 34(3): Andrich, D., Sheridan, B., and Luo, G. (2010). RUMM2030 [Computer software and manual]. RUMM Laboratory, Perth, Australia. Christensen, K. B. (2006). Fitting polytomous Rasch models in SAS. Journal of applied measurement, 7(4):
41 Christensen, K. B., Bjorner, J. B., S., K., and Petersen, J. H. (2002). Testing unidimensionality in polytomous Rasch models. Psychometrika, 67: Harrell-Williams, L. and Wolfe, E. (2014). Performance of the likelihood ratio difference (g2 diff) test for detecting unidimensionality in applications of the multidimensional rasch model. Journal of applied measurement, 15(3): Holland, P. W. and Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 14(4): Horton, M., Marais, I., and Christensen, K. B. (2013). Dimensionality, pages
42 John Wiley & Sons, Inc. Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49: Kreiner, S. (2003). Introduction to digram. Research Report 10, Department of Statistics, University of Copenhagen. Kreiner, S. and Christensen, K. B. (2004). Analysis of local dependence and multidimensionality in graphical loglinear rasch models. Communications in Statistics - Theory and Methods, 33: Kreiner, S. and Christensen, K. B. (2007). Validity and objectivity in health-related scales: Analysis by graphical loglinear rasch models.
43 In Multivariate and Mixture Distribution Rasch Models, Statistics for Social and Behavioral Sciences, pages Springer New York. Kreiner, S. and Christensen, K. B. (2011a). Exact evaluation of bias in Rasch model residuals. In Baswell, editor, Advances in Mathematics Research vol.12, pages Nova publishers. Kreiner, S. and Christensen, K. B. (2011b). Item screening in graphical loglinear rasch models. Psychometrika, 76(2): Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics, 6: Tjur, T. (1982). A connection between Rasch s item analysis model and a multiplicative poisson model.
44 Scandinavian Journal of Statistics, 9: Wu, M. L., Adams, R. J., Wilson, M. R., and Haldane, S. A. (2007). ACER ConQuest Version 2: Generalised item response modelling software. Australian Council for Educational Research, Camberwell. Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8(2):
Conditional maximum likelihood estimation in polytomous Rasch models using SAS
Conditional maximum likelihood estimation in polytomous Rasch models using SAS Karl Bang Christensen kach@sund.ku.dk Department of Biostatistics, University of Copenhagen November 29, 2012 Abstract IRT
More informationUsing modern statistical methodology for validating and reporti. Outcomes
Using modern statistical methodology for validating and reporting Patient Reported Outcomes Dept. of Biostatistics, Univ. of Copenhagen joint DSBS/FMS Meeting October 2, 2014, Copenhagen Agenda 1 Indirect
More informationA Note on Item Restscore Association in Rasch Models
Brief Report A Note on Item Restscore Association in Rasch Models Applied Psychological Measurement 35(7) 557 561 ª The Author(s) 2011 Reprints and permission: sagepub.com/journalspermissions.nav DOI:
More informationStudies on the effect of violations of local independence on scale in Rasch models: The Dichotomous Rasch model
Studies on the effect of violations of local independence on scale in Rasch models Studies on the effect of violations of local independence on scale in Rasch models: The Dichotomous Rasch model Ida Marais
More informationMonte Carlo Simulations for Rasch Model Tests
Monte Carlo Simulations for Rasch Model Tests Patrick Mair Vienna University of Economics Thomas Ledl University of Vienna Abstract: Sources of deviation from model fit in Rasch models can be lack of unidimensionality,
More informationRater agreement - ordinal ratings. Karl Bang Christensen Dept. of Biostatistics, Univ. of Copenhagen NORDSTAT,
Rater agreement - ordinal ratings Karl Bang Christensen Dept. of Biostatistics, Univ. of Copenhagen NORDSTAT, 2012 http://biostat.ku.dk/~kach/ 1 Rater agreement - ordinal ratings Methods for analyzing
More informationComparison between conditional and marginal maximum likelihood for a class of item response models
(1/24) Comparison between conditional and marginal maximum likelihood for a class of item response models Francesco Bartolucci, University of Perugia (IT) Silvia Bacci, University of Perugia (IT) Claudia
More informationWhat is an Ordinal Latent Trait Model?
What is an Ordinal Latent Trait Model? Gerhard Tutz Ludwig-Maximilians-Universität München Akademiestraße 1, 80799 München February 19, 2019 arxiv:1902.06303v1 [stat.me] 17 Feb 2019 Abstract Although various
More informationPIRLS 2016 Achievement Scaling Methodology 1
CHAPTER 11 PIRLS 2016 Achievement Scaling Methodology 1 The PIRLS approach to scaling the achievement data, based on item response theory (IRT) scaling with marginal estimation, was developed originally
More informationLesson 7: Item response theory models (part 2)
Lesson 7: Item response theory models (part 2) Patrícia Martinková Department of Statistical Modelling Institute of Computer Science, Czech Academy of Sciences Institute for Research and Development of
More informationPairwise Parameter Estimation in Rasch Models
Pairwise Parameter Estimation in Rasch Models Aeilko H. Zwinderman University of Leiden Rasch model item parameters can be estimated consistently with a pseudo-likelihood method based on comparing responses
More informationA Marginal Maximum Likelihood Procedure for an IRT Model with Single-Peaked Response Functions
A Marginal Maximum Likelihood Procedure for an IRT Model with Single-Peaked Response Functions Cees A.W. Glas Oksana B. Korobko University of Twente, the Netherlands OMD Progress Report 07-01. Cees A.W.
More informationEstimating the Hausman test for multilevel Rasch model. Kingsley E. Agho School of Public health Faculty of Medicine The University of Sydney
Estimating the Hausman test for multilevel Rasch model Kingsley E. Agho School of Public health Faculty of Medicine The University of Sydney James A. Athanasou Faculty of Education University of Technology,
More informationOverview. Multidimensional Item Response Theory. Lecture #12 ICPSR Item Response Theory Workshop. Basics of MIRT Assumptions Models Applications
Multidimensional Item Response Theory Lecture #12 ICPSR Item Response Theory Workshop Lecture #12: 1of 33 Overview Basics of MIRT Assumptions Models Applications Guidance about estimating MIRT Lecture
More informationBasic IRT Concepts, Models, and Assumptions
Basic IRT Concepts, Models, and Assumptions Lecture #2 ICPSR Item Response Theory Workshop Lecture #2: 1of 64 Lecture #2 Overview Background of IRT and how it differs from CFA Creating a scale An introduction
More informationFitting Multidimensional Latent Variable Models using an Efficient Laplace Approximation
Fitting Multidimensional Latent Variable Models using an Efficient Laplace Approximation Dimitris Rizopoulos Department of Biostatistics, Erasmus University Medical Center, the Netherlands d.rizopoulos@erasmusmc.nl
More informationLog-linear multidimensional Rasch model for capture-recapture
Log-linear multidimensional Rasch model for capture-recapture Elvira Pelle, University of Milano-Bicocca, e.pelle@campus.unimib.it David J. Hessen, Utrecht University, D.J.Hessen@uu.nl Peter G.M. Van der
More informationContributions to latent variable modeling in educational measurement Zwitser, R.J.
UvA-DARE (Digital Academic Repository) Contributions to latent variable modeling in educational measurement Zwitser, R.J. Link to publication Citation for published version (APA): Zwitser, R. J. (2015).
More informationOn the Construction of Adjacent Categories Latent Trait Models from Binary Variables, Motivating Processes and the Interpretation of Parameters
Gerhard Tutz On the Construction of Adjacent Categories Latent Trait Models from Binary Variables, Motivating Processes and the Interpretation of Parameters Technical Report Number 218, 2018 Department
More informationA Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model
A Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model Cees A. W. Glas, University of Twente, the Netherlands Juan Carlos Suárez Falcón, Universidad Nacional de Educacion a Distancia,
More informationLinks Between Binary and Multi-Category Logit Item Response Models and Quasi-Symmetric Loglinear Models
Links Between Binary and Multi-Category Logit Item Response Models and Quasi-Symmetric Loglinear Models Alan Agresti Department of Statistics University of Florida Gainesville, Florida 32611-8545 July
More informationAn Equivalency Test for Model Fit. Craig S. Wells. University of Massachusetts Amherst. James. A. Wollack. Ronald C. Serlin
Equivalency Test for Model Fit 1 Running head: EQUIVALENCY TEST FOR MODEL FIT An Equivalency Test for Model Fit Craig S. Wells University of Massachusetts Amherst James. A. Wollack Ronald C. Serlin University
More informationDoctor of Philosophy
MAINTAINING A COMMON ARBITRARY UNIT IN SOCIAL MEASUREMENT STEPHEN HUMPHRY 2005 Submitted in fulfillment of the requirements of the degree of Doctor of Philosophy School of Education, Murdoch University,
More informationWhats beyond Concerto: An introduction to the R package catr. Session 4: Overview of polytomous IRT models
Whats beyond Concerto: An introduction to the R package catr Session 4: Overview of polytomous IRT models The Psychometrics Centre, Cambridge, June 10th, 2014 2 Outline: 1. Introduction 2. General notations
More informationConfirmatory Factor Analysis: Model comparison, respecification, and more. Psychology 588: Covariance structure and factor models
Confirmatory Factor Analysis: Model comparison, respecification, and more Psychology 588: Covariance structure and factor models Model comparison 2 Essentially all goodness of fit indices are descriptive,
More informationThe Covariate-Adjusted Frequency Plot for the Rasch Poisson Counts Model
Thailand Statistician 2015; 13(1): 67-78 http://statassoc.or.th Contributed paper The Covariate-Adjusted Frequency Plot for the Rasch Poisson Counts Model Heinz Holling [a], Walailuck Böhning [a] and Dankmar
More informationAnders Skrondal. Norwegian Institute of Public Health London School of Hygiene and Tropical Medicine. Based on joint work with Sophia Rabe-Hesketh
Constructing Latent Variable Models using Composite Links Anders Skrondal Norwegian Institute of Public Health London School of Hygiene and Tropical Medicine Based on joint work with Sophia Rabe-Hesketh
More informationComputationally Efficient Estimation of Multilevel High-Dimensional Latent Variable Models
Computationally Efficient Estimation of Multilevel High-Dimensional Latent Variable Models Tihomir Asparouhov 1, Bengt Muthen 2 Muthen & Muthen 1 UCLA 2 Abstract Multilevel analysis often leads to modeling
More informationABSTRACT. Yunyun Dai, Doctor of Philosophy, Mixtures of item response theory models have been proposed as a technique to explore
ABSTRACT Title of Document: A MIXTURE RASCH MODEL WITH A COVARIATE: A SIMULATION STUDY VIA BAYESIAN MARKOV CHAIN MONTE CARLO ESTIMATION Yunyun Dai, Doctor of Philosophy, 2009 Directed By: Professor, Robert
More informationMeiser et. al.: Latent Change in Discrete Data 76 as new perspectives in the application of test models to social science issues (e.g., Fischer & Mole
Methods of Psychological Research Online 1998, Vol.3, No.2 Internet: http://www.pabst-publishers.de/mpr/ Latent Change in Discrete Data: Unidimensional, Multidimensional, and Mixture Distribution Rasch
More informationItem-Focussed Trees for the Detection of Differential Item Functioning in Partial Credit Models
arxiv:1609.08970v1 [stat.me] 8 Sep 016 Item-Focussed Trees for the Detection of Differential Item Functioning in Partial Credit Models Stella Bollmann, Moritz Berger & Gerhard Tutz Ludwig-Maximilians-Universität
More informationWalkthrough for Illustrations. Illustration 1
Tay, L., Meade, A. W., & Cao, M. (in press). An overview and practical guide to IRT measurement equivalence analysis. Organizational Research Methods. doi: 10.1177/1094428114553062 Walkthrough for Illustrations
More informationCreating and Interpreting the TIMSS Advanced 2015 Context Questionnaire Scales
CHAPTER 15 Creating and Interpreting the TIMSS Advanced 2015 Context Questionnaire Scales Michael O. Martin Ina V.S. Mullis Martin Hooper Liqun Yin Pierre Foy Lauren Palazzo Overview As described in Chapter
More informationTesting Algebraic Hypotheses
Testing Algebraic Hypotheses Mathias Drton Department of Statistics University of Chicago 1 / 18 Example: Factor analysis Multivariate normal model based on conditional independence given hidden variable:
More informationSummer School in Applied Psychometric Principles. Peterhouse College 13 th to 17 th September 2010
Summer School in Applied Psychometric Principles Peterhouse College 13 th to 17 th September 2010 1 Two- and three-parameter IRT models. Introducing models for polytomous data. Test information in IRT
More informationIntroduction to Structural Equation Modeling
Introduction to Structural Equation Modeling Notes Prepared by: Lisa Lix, PhD Manitoba Centre for Health Policy Topics Section I: Introduction Section II: Review of Statistical Concepts and Regression
More informationItem Response Theory (IRT) Analysis of Item Sets
University of Connecticut DigitalCommons@UConn NERA Conference Proceedings 2011 Northeastern Educational Research Association (NERA) Annual Conference Fall 10-21-2011 Item Response Theory (IRT) Analysis
More informationItem Response Theory (IRT) an introduction. Norman Verhelst Eurometrics Tiel, The Netherlands
Item Response Theory (IRT) an introduction Norman Verhelst Eurometrics Tiel, The Netherlands Installation of the program Copy the folder OPLM from the USB stick Example: c:\oplm Double-click the program
More informationSequential Analysis of Quality of Life Measurements Using Mixed Rasch Models
1 Sequential Analysis of Quality of Life Measurements Using Mixed Rasch Models Véronique Sébille 1, Jean-Benoit Hardouin 1 and Mounir Mesbah 2 1. Laboratoire de Biostatistique, Faculté de Pharmacie, Université
More informationParametric Modelling of Over-dispersed Count Data. Part III / MMath (Applied Statistics) 1
Parametric Modelling of Over-dispersed Count Data Part III / MMath (Applied Statistics) 1 Introduction Poisson regression is the de facto approach for handling count data What happens then when Poisson
More informationA Very Brief Summary of Statistical Inference, and Examples
A Very Brief Summary of Statistical Inference, and Examples Trinity Term 2008 Prof. Gesine Reinert 1 Data x = x 1, x 2,..., x n, realisations of random variables X 1, X 2,..., X n with distribution (model)
More informationNew Developments for Extended Rasch Modeling in R
New Developments for Extended Rasch Modeling in R Patrick Mair, Reinhold Hatzinger Institute for Statistics and Mathematics WU Vienna University of Economics and Business Content Rasch models: Theory,
More informationMixtures of Rasch Models
Mixtures of Rasch Models Hannah Frick, Friedrich Leisch, Achim Zeileis, Carolin Strobl http://www.uibk.ac.at/statistics/ Introduction Rasch model for measuring latent traits Model assumption: Item parameters
More informationAn Overview of Item Response Theory. Michael C. Edwards, PhD
An Overview of Item Response Theory Michael C. Edwards, PhD Overview General overview of psychometrics Reliability and validity Different models and approaches Item response theory (IRT) Conceptual framework
More informationDimensionality Assessment: Additional Methods
Dimensionality Assessment: Additional Methods In Chapter 3 we use a nonlinear factor analytic model for assessing dimensionality. In this appendix two additional approaches are presented. The first strategy
More informationCorrelations with Categorical Data
Maximum Likelihood Estimation of Multiple Correlations and Canonical Correlations with Categorical Data Sik-Yum Lee The Chinese University of Hong Kong Wal-Yin Poon University of California, Los Angeles
More informationThe application and empirical comparison of item. parameters of Classical Test Theory and Partial Credit. Model of Rasch in performance assessments
The application and empirical comparison of item parameters of Classical Test Theory and Partial Credit Model of Rasch in performance assessments by Paul Moloantoa Mokilane Student no: 31388248 Dissertation
More information36-720: The Rasch Model
36-720: The Rasch Model Brian Junker October 15, 2007 Multivariate Binary Response Data Rasch Model Rasch Marginal Likelihood as a GLMM Rasch Marginal Likelihood as a Log-Linear Model Example For more
More informationLSAC RESEARCH REPORT SERIES. Law School Admission Council Research Report March 2008
LSAC RESEARCH REPORT SERIES Structural Modeling Using Two-Step MML Procedures Cees A. W. Glas University of Twente, Enschede, The Netherlands Law School Admission Council Research Report 08-07 March 2008
More informationA Note on a Tucker-Lewis-Index for Item Response Theory Models. Taehun Lee, Li Cai University of California, Los Angeles
A Note on a Tucker-Lewis-Index for Item Response Theory Models Taehun Lee, Li Cai University of California, Los Angeles 1 Item Response Theory (IRT) Models IRT is a family of statistical models used to
More informationMARGINAL HOMOGENEITY MODEL FOR ORDERED CATEGORIES WITH OPEN ENDS IN SQUARE CONTINGENCY TABLES
REVSTAT Statistical Journal Volume 13, Number 3, November 2015, 233 243 MARGINAL HOMOGENEITY MODEL FOR ORDERED CATEGORIES WITH OPEN ENDS IN SQUARE CONTINGENCY TABLES Authors: Serpil Aktas Department of
More informationContents. 3 Evaluating Manifest Monotonicity Using Bayes Factors Introduction... 44
Contents 1 Introduction 4 1.1 Measuring Latent Attributes................. 4 1.2 Assumptions in Item Response Theory............ 6 1.2.1 Local Independence.................. 6 1.2.2 Unidimensionality...................
More informationEnsemble Rasch Models
Ensemble Rasch Models Steven M. Lattanzio II Metamatrics Inc., Durham, NC 27713 email: slattanzio@lexile.com Donald S. Burdick Metamatrics Inc., Durham, NC 27713 email: dburdick@lexile.com A. Jackson Stenner
More informationModel comparison and selection
BS2 Statistical Inference, Lectures 9 and 10, Hilary Term 2008 March 2, 2008 Hypothesis testing Consider two alternative models M 1 = {f (x; θ), θ Θ 1 } and M 2 = {f (x; θ), θ Θ 2 } for a sample (X = x)
More informationMeasurement Invariance (MI) in CFA and Differential Item Functioning (DIF) in IRT/IFA
Topics: Measurement Invariance (MI) in CFA and Differential Item Functioning (DIF) in IRT/IFA What are MI and DIF? Testing measurement invariance in CFA Testing differential item functioning in IRT/IFA
More informationPreliminary Manual of the software program Multidimensional Item Response Theory (MIRT)
Preliminary Manual of the software program Multidimensional Item Response Theory (MIRT) July 7 th, 2010 Cees A. W. Glas Department of Research Methodology, Measurement, and Data Analysis Faculty of Behavioural
More informationOn the Use of Nonparametric ICC Estimation Techniques For Checking Parametric Model Fit
On the Use of Nonparametric ICC Estimation Techniques For Checking Parametric Model Fit March 27, 2004 Young-Sun Lee Teachers College, Columbia University James A.Wollack University of Wisconsin Madison
More informationNonparametric tests for the Rasch model: explanation, development, and application of quasi-exact tests for small samples
Nonparametric tests for the Rasch model: explanation, development, and application of quasi-exact tests for small samples Ingrid Koller 1* & Reinhold Hatzinger 2 1 Department of Psychological Basic Research
More informationJoint Modeling of Longitudinal Item Response Data and Survival
Joint Modeling of Longitudinal Item Response Data and Survival Jean-Paul Fox University of Twente Department of Research Methodology, Measurement and Data Analysis Faculty of Behavioural Sciences Enschede,
More informationANALYSIS OF ORDINAL SURVEY RESPONSES WITH DON T KNOW
SSC Annual Meeting, June 2015 Proceedings of the Survey Methods Section ANALYSIS OF ORDINAL SURVEY RESPONSES WITH DON T KNOW Xichen She and Changbao Wu 1 ABSTRACT Ordinal responses are frequently involved
More informationCenter for Advanced Studies in Measurement and Assessment. CASMA Research Report
Center for Advanced Studies in Measurement and Assessment CASMA Research Report Number 41 A Comparative Study of Item Response Theory Item Calibration Methods for the Two Parameter Logistic Model Kyung
More informationPolytomous Item Explanatory IRT Models with Random Item Effects: An Application to Carbon Cycle Assessment Data
Polytomous Item Explanatory IRT Models with Random Item Effects: An Application to Carbon Cycle Assessment Data Jinho Kim and Mark Wilson University of California, Berkeley Presented on April 11, 2018
More informationComparison of parametric and nonparametric item response techniques in determining differential item functioning in polytomous scale
American Journal of Theoretical and Applied Statistics 2014; 3(2): 31-38 Published online March 20, 2014 (http://www.sciencepublishinggroup.com/j/ajtas) doi: 10.11648/j.ajtas.20140302.11 Comparison of
More informationComparing Multi-dimensional and Uni-dimensional Computer Adaptive Strategies in Psychological and Health Assessment. Jingyu Liu
Comparing Multi-dimensional and Uni-dimensional Computer Adaptive Strategies in Psychological and Health Assessment by Jingyu Liu BS, Beijing Institute of Technology, 1994 MS, University of Texas at San
More informationA Goodness-of-Fit Measure for the Mokken Double Monotonicity Model that Takes into Account the Size of Deviations
Methods of Psychological Research Online 2003, Vol.8, No.1, pp. 81-101 Department of Psychology Internet: http://www.mpr-online.de 2003 University of Koblenz-Landau A Goodness-of-Fit Measure for the Mokken
More informationGrowth Mixture Model
Growth Mixture Model Latent Variable Modeling and Measurement Biostatistics Program Harvard Catalyst The Harvard Clinical & Translational Science Center Short course, October 28, 2016 Slides contributed
More informationStructural Equation Modeling and Confirmatory Factor Analysis. Types of Variables
/4/04 Structural Equation Modeling and Confirmatory Factor Analysis Advanced Statistics for Researchers Session 3 Dr. Chris Rakes Website: http://csrakes.yolasite.com Email: Rakes@umbc.edu Twitter: @RakesChris
More informationApplied Psychological Measurement 2001; 25; 283
Applied Psychological Measurement http://apm.sagepub.com The Use of Restricted Latent Class Models for Defining and Testing Nonparametric and Parametric Item Response Theory Models Jeroen K. Vermunt Applied
More informationItem Response Theory and Computerized Adaptive Testing
Item Response Theory and Computerized Adaptive Testing Richard C. Gershon, PhD Department of Medical Social Sciences Feinberg School of Medicine Northwestern University gershon@northwestern.edu May 20,
More informationStandard Error of Technical Cost Incorporating Parameter Uncertainty
Standard Error of Technical Cost Incorporating Parameter Uncertainty Christopher Morton Insurance Australia Group This presentation has been prepared for the Actuaries Institute 2012 General Insurance
More informationLikelihood-Based Methods
Likelihood-Based Methods Handbook of Spatial Statistics, Chapter 4 Susheela Singh September 22, 2016 OVERVIEW INTRODUCTION MAXIMUM LIKELIHOOD ESTIMATION (ML) RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION (REML)
More information1 if response to item i is in category j 0 otherwise (1)
7 Scaling Methodology and Procedures for the Mathematics and Science Literacy, Advanced Mathematics, and Physics Scales Greg Macaskill Raymond J. Adams Margaret L. Wu Australian Council for Educational
More informationGENERALIZED LATENT TRAIT MODELS. 1. Introduction
PSYCHOMETRIKA VOL. 65, NO. 3, 391 411 SEPTEMBER 2000 GENERALIZED LATENT TRAIT MODELS IRINI MOUSTAKI AND MARTIN KNOTT LONDON SCHOOL OF ECONOMICS AND POLITICAL SCIENCE In this paper we discuss a general
More informationLOG-MULTIPLICATIVE ASSOCIATION MODELS AS LATENT VARIABLE MODELS FOR NOMINAL AND0OR ORDINAL DATA. Carolyn J. Anderson* Jeroen K.
3 LOG-MULTIPLICATIVE ASSOCIATION MODELS AS LATENT VARIABLE MODELS FOR NOMINAL AND0OR ORDINAL DATA Carolyn J. Anderson* Jeroen K. Vermunt Associations between multiple discrete measures are often due to
More informationSeminar über Statistik FS2008: Model Selection
Seminar über Statistik FS2008: Model Selection Alessia Fenaroli, Ghazale Jazayeri Monday, April 2, 2008 Introduction Model Choice deals with the comparison of models and the selection of a model. It can
More informationFor more information about how to cite these materials visit
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http://creativecommons.org/licenses/by-sa/3.0/
More informationComparing IRT with Other Models
Comparing IRT with Other Models Lecture #14 ICPSR Item Response Theory Workshop Lecture #14: 1of 45 Lecture Overview The final set of slides will describe a parallel between IRT and another commonly used
More informationTitle: Testing for Measurement Invariance with Latent Class Analysis. Abstract
1 Title: Testing for Measurement Invariance with Latent Class Analysis Authors: Miloš Kankaraš*, Guy Moors*, and Jeroen K. Vermunt Abstract Testing for measurement invariance can be done within the context
More informationExtensions and Applications of Item Explanatory Models to Polytomous Data in Item Response Theory. Jinho Kim
Extensions and Applications of Item Explanatory Models to Polytomous Data in Item Response Theory by Jinho Kim A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor
More informationSTAT 461/561- Assignments, Year 2015
STAT 461/561- Assignments, Year 2015 This is the second set of assignment problems. When you hand in any problem, include the problem itself and its number. pdf are welcome. If so, use large fonts and
More informationRANDOM INTERCEPT ITEM FACTOR ANALYSIS. IE Working Paper MK8-102-I 02 / 04 / Alberto Maydeu Olivares
RANDOM INTERCEPT ITEM FACTOR ANALYSIS IE Working Paper MK8-102-I 02 / 04 / 2003 Alberto Maydeu Olivares Instituto de Empresa Marketing Dept. C / María de Molina 11-15, 28006 Madrid España Alberto.Maydeu@ie.edu
More informationThe Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations
The Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations John R. Michael, Significance, Inc. and William R. Schucany, Southern Methodist University The mixture
More informationLocal Dependence Diagnostics in IRT Modeling of Binary Data
Local Dependence Diagnostics in IRT Modeling of Binary Data Educational and Psychological Measurement 73(2) 254 274 Ó The Author(s) 2012 Reprints and permission: sagepub.com/journalspermissions.nav DOI:
More informationA DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY. Yu-Feng Chang
A Restricted Bi-factor Model of Subdomain Relative Strengths and Weaknesses A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Yu-Feng Chang IN PARTIAL FULFILLMENT
More informationIRT Model Selection Methods for Polytomous Items
IRT Model Selection Methods for Polytomous Items Taehoon Kang University of Wisconsin-Madison Allan S. Cohen University of Georgia Hyun Jung Sung University of Wisconsin-Madison March 11, 2005 Running
More informationA Nonlinear Mixed Model Framework for Item Response Theory
Psychological Methods Copyright 2003 by the American Psychological Association, Inc. 2003, Vol. 8, No. 2, 185 205 1082-989X/03/$12.00 DOI: 10.1037/1082-989X.8.2.185 A Nonlinear Mixed Model Framework for
More informationAn Introduction to Causal Mediation Analysis. Xu Qin University of Chicago Presented at the Central Iowa R User Group Meetup Aug 10, 2016
An Introduction to Causal Mediation Analysis Xu Qin University of Chicago Presented at the Central Iowa R User Group Meetup Aug 10, 2016 1 Causality In the applications of statistics, many central questions
More informationAnalysis of Multinomial Response Data: a Measure for Evaluating Knowledge Structures
Analysis of Multinomial Response Data: a Measure for Evaluating Knowledge Structures Department of Psychology University of Graz Universitätsplatz 2/III A-8010 Graz, Austria (e-mail: ali.uenlue@uni-graz.at)
More informationDiagnostic Classification Models: Psychometric Issues and Statistical Challenges
Diagnostic Classification Models: Psychometric Issues and Statistical Challenges Jonathan Templin Department of Educational Psychology The University of Georgia University of South Carolina Talk Talk Overview
More informationSELECTION OF ITEMS FITTING A RASCH MODEL
SELECTION OF ITEMS FITTING A RASCH MODEL ABSTRACT In a preceeding paper, the authors propose a procedure based on the Multidimensional Marginaly Sufficient Rasch Model (MMSRM) to select items in scales
More informationWU Weiterbildung. Linear Mixed Models
Linear Mixed Effects Models WU Weiterbildung SLIDE 1 Outline 1 Estimation: ML vs. REML 2 Special Models On Two Levels Mixed ANOVA Or Random ANOVA Random Intercept Model Random Coefficients Model Intercept-and-Slopes-as-Outcomes
More informationA class of latent marginal models for capture-recapture data with continuous covariates
A class of latent marginal models for capture-recapture data with continuous covariates F Bartolucci A Forcina Università di Urbino Università di Perugia FrancescoBartolucci@uniurbit forcina@statunipgit
More informationNESTED LOGIT MODELS FOR MULTIPLE-CHOICE ITEM RESPONSE DATA UNIVERSITY OF TEXAS AT AUSTIN UNIVERSITY OF WISCONSIN-MADISON
PSYCHOMETRIKA VOL. 75, NO. 3, 454 473 SEPTEMBER 2010 DOI: 10.1007/S11336-010-9163-7 NESTED LOGIT MODELS FOR MULTIPLE-CHOICE ITEM RESPONSE DATA YOUNGSUK SUH UNIVERSITY OF TEXAS AT AUSTIN DANIEL M. BOLT
More informationDefinition 3.1 A statistical hypothesis is a statement about the unknown values of the parameters of the population distribution.
Hypothesis Testing Definition 3.1 A statistical hypothesis is a statement about the unknown values of the parameters of the population distribution. Suppose the family of population distributions is indexed
More informationFACTOR ANALYSIS AND MULTIDIMENSIONAL SCALING
FACTOR ANALYSIS AND MULTIDIMENSIONAL SCALING Vishwanath Mantha Department for Electrical and Computer Engineering Mississippi State University, Mississippi State, MS 39762 mantha@isip.msstate.edu ABSTRACT
More informationDETECTION OF DIFFERENTIAL ITEM FUNCTIONING USING LAGRANGE MULTIPLIER TESTS
Statistica Sinica 8(1998), 647-667 DETECTION OF DIFFERENTIAL ITEM FUNCTIONING USING LAGRANGE MULTIPLIER TESTS C. A. W. Glas University of Twente, Enschede, the Netherlands Abstract: In the present paper
More informationThe SAS Macro-Program %AnaQol to Estimate the Parameters of Item Responses Theory Models
Communications in Statistics Simulation and Computation, 36: 437 453, 2007 Copyright Taylor & Francis Group, LLC ISSN: 0361-0918 print/1532-4141 online DOI: 10.1080/03610910601158351 Computational Statistics
More information1. Fisher Information
1. Fisher Information Let f(x θ) be a density function with the property that log f(x θ) is differentiable in θ throughout the open p-dimensional parameter set Θ R p ; then the score statistic (or score
More informationMultiple Linear Regression for the Supervisor Data
for the Supervisor Data Rating 40 50 60 70 80 90 40 50 60 70 50 60 70 80 90 40 60 80 40 60 80 Complaints Privileges 30 50 70 40 60 Learn Raises 50 70 50 70 90 Critical 40 50 60 70 80 30 40 50 60 70 80
More informationGeneralized Linear Latent and Mixed Models with Composite Links and Exploded
Generalized Linear Latent and Mixed Models with Composite Links and Exploded Likelihoods Anders Skrondal 1 and Sophia Rabe-Hesketh 2 1 Norwegian Institute of Public Health, Oslo (anders.skrondal@fhi.no)
More information