Los modelos mixtos de teoría de respuesta al ítem

Brizuela, Armel

doi:10.15517/ap.v29i119.18728

Authors

Armel Brizuela Instituto de Investigaciones Psicológicas, Universidad de Costa Rica Author

DOI:

https://doi.org/10.15517/ap.v29i119.18728

Keywords:

Psychometrics, Item Response Theory, mixture models, latent classes, Geriatric Depression Scale.

Abstract

The Item Response Theory mixture models and how these can be used to identify unobserved sub-groups of examinees, known as latent classes, are presented. The usefulness of the two-parameter mixture model parameters is exemplified by detecting the presence of items in a depression scale that measure the examinees differently in comparison with the rest of items. Finally, some general recommendations regarding the complementarity that should exist between the substantive theory underlying the development of a scale and the use of these models are given.

Downloads

Download data is not yet available.

Author Biography

Armel Brizuela, Instituto de Investigaciones Psicológicas, Universidad de Costa Rica

Programa Prueba de Aptitud Académica. Escuela de Psicología, Universidad de Costa Rica.

References

AERA, APA, & NCME (2014). Standards for Educational and Psychological Testing. Washington, Estados Unidos: American Educational Research Association.

Alexeev, N., Templin, J., & Cohen, A. (2011). Spurious Latent Classes in the Mixture Rasch Model. Journal of Educational Measurement, 48(3), 313-332. DOI: https://doi.org/10.1111/j.1745-3984.2011.00146.x

Asparouhov, T., & Muthen, B. (2012). Using Mplus TECH11 and TECH14 to test the number of latent classes. Recuperado de https://www.statmodel. com/examples/webnotes/webnote14.pdf

Asparouhov, T., & Muthen, B. (2014). Variable-Specific Entropy Contribution. Recuperado de http://www.statmodel.com/download/UnivariateEntropy.pdf

Baghaei, P., & Carstensen, C. (2013). Fitting the Mixed Rasch Model to a Reading Comprehension Test: Identifying Reader Types. Practical Assessment, Research & Evaluation, 18(5). Recuperado de http:// pareonline.net

Bolt, D., Cohen, A., & Wollackm J. (2001). A Mixture Item Response Model for Multiple-Choice Data. Journal of Educational and Behavioral Statistics, 26(4), 381-409. DOI: https://doi.org/10.3102/10769986026004381

Bolt, D., Cohen, A., & Wollack, J. (2002). Item Parameter Estimation Under Conditions of Test Speededness: Application of a Mixture Rasch Model With Ordinal Constraints. Journal of Educational Measurement, 39(4), 331-348. DOI: https://doi.org/10.1111/j.1745-3984.2002.tb01146.x

Borsboom, D., Mellenbergh, G., & Heerden, J. (2004). The Concept of Validity. Psychological Review, 111(4), 1061-1071. DOI: https://doi.org/10.1037/0033-295X.111.4.1061

Brown, L. M., & Schinka, J. A. (2005). Development and initial validation of a 15- item informant version of the Geriatric Depression Scale. International journal of geriatric psychiatry, 20(10), 911-918. DOI: https://doi.org/10.1002/gps.1375

Carter, N., Dalal, D., Lake, C., Lin, B., & Zickar, M. (2011). Using Mixed-Model Item Response Theory to Analyze Organizational Survey Responses: An Illustration Using the Job Descriptive Index. Organizational Research Methods, 14(1), 116 - 146. DOI: https://doi.org/10.1177/1094428110363309

Chen, Y., & Jiao, H. (2013). Does Model Misspecification Lead to Spurious Latent Classes? An Evaluation of Model Comparison Indices. En R. Millsap, L. van der Ark, D. Bolt & C. Woods (Eds.), New Developments in Quantitative Psychology. Presentations from the 77th Annual Psychometric Society Meeting (pp. 345-355). Estados Unidos: Springer. DOI: https://doi.org/10.1007/978-1-4614-9348-8_22

Cho, S., & Cohen, A. (2010). A Multilevel Mixture IRT Model With an Application to DIF. Journal of Educational and Behavioral Statistics, 35(3), 336-370. DOI: https://doi.org/10.3102/1076998609353111

Choi, Y., Alexeev, N., & Cohen, A. (2014). DIF Analysis using a Mixture 3PL Model with a Covariate on the TIMSS 2007 Mathematics Test. KAERA Research Forum, 1(1), 4-14. Recuperado de http://www.k- aera.org/research-forum/

Cohen, A., & Bolt, D. (2005). A Mixture Model Actualidades en Psicología, 29(119), 2015, 79-90 Analysis of Differential Item Functioning. Journalof Educational Measurement, 42(2), 133-148. Collins, L., & Lanza, S. (2010). Latent Class and Latent Transition Analysis. Estados Unidos: WILEY. DOI: https://doi.org/10.1111/j.1745-3984.2005.00007

Dai, Y. (2013). A Mixture Rasch Model With a Covariate: A Simulation Study via Bayesian Markov Chain Monte Carlo Estimation. Applied Psychological Measurement, 37(5), 375-396. DOI: https://doi.org/10.1177/0146621612475076

De Ayala, R. (2009). The Theory and Practice of Item Response Theory. Estados Unidos: The Guilford Press.

De Boeck, P., & Rijmen, F. (2003). A Latent Class Model for Individual Differences in the Interpretation of Conditionals. Psychological Research, 67, 219-231. DOI: https://doi.org/10.1007/s00426-002-0092-7

DeMars, C., & Lau, A. (2011). Differential Item Functioning Detection with Latent Classes: How Accurately Can We Detect Who Is Responding Differentially? Educational and Psychological Measurement, 71(4), 597-616. DOI: https://doi.org/10.1177/0013164411404221

Egberink, I., Meijer, R., & Veldkamp, B. (2010). Conscientiousness in the Workplace: Applying Mixture IRT to Investigate Scalability and Predictive Validity. Journal of Research in Personality, 44, 232- 244. DOI: https://doi.org/10.1016/j.jrp.2010.01.007

Eid, M., & Rauber, M. (2000). Detecting Measurement Invariance in Organizational Surveys. European Journal of Psychological Assessment, 16(1), 20-30. DOI: https://doi.org/10.1027//1015-5759.16.1.20

Elosúa, P. & López, A. (2006). Clases latentes y funcionamiento diferencial del ítem. Psicothema, 17(3), 516-521.

Embretson, S. (2007). Mixed Rasch Models for Measurement in Cognitive Psychology. En M. von Davier & C. Carstensen (Eds.), Multivariate and Mixture Distribution Rasch Models: Extensions and Applications (pp. 235-253). Estados Unidos: Springer. DOI: https://doi.org/10.1007/978-0-387-49839-3_15

Formann, A., & Kohlmann, T. (2002). Three- Parameter Linear Logistic Latent Class Analysis. En J. Hagenaars & A. McCutcheon (Eds.), Applied Latent Class Analysis (pp. 183 - 210). Estados Unidos: Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511499531.008

Frick, H., Strobl, C., & Zeileis, A. (en prensa). Rasch Mixture Models for DIF Detection: A Comparison of Old and New Score Specifications. Educational and Psychological Measurement. Recuperado de http:// epm.sagepub.com

Friedman, B., Heisel, M. J., & Delavan, R. L. (2005). Psychometric properties of the 15-item geriatric depression scale in functionally impaired, cognitively intact, community-dwelling elderly primary care patients. Journal of the American Geriatrics Society, 53(9), 1570-1576. DOI: https://doi.org/10.1111/j.1532-5415.2005.53461.x

Gollwitzer, M., Eid, M., & Jürgensen, R. (2005). Response Styles in the Assessment of Anger Expression. Psychological Assessment, 17(1), 56-59. DOI: https://doi.org/10.1037/1040-3590.17.1.56

Hambleton, R., Swaminathan, H., & Rogers, H. (1991). Fundamentals of Item Response Theory. Estados Unidos: Sage.

Holden, R., & Book, A. (2009). Using Hybrid Rasch- Latent Class Modeling to Improve the Detection of Fakers on a Personality Inventory. Personality and Individual Differences, 47, 185-190. DOI: https://doi.org/10.1016/j.paid.2009.02.024

Holmes, W., & Pierson, E. (2011). A Mixture IRT Analysis of Risky Youth Behavior. Frontiers in Psychology, 2, 1-10. DOI: https://doi.org/10.3389/fpsyg.2011.00098

Hong, S., & Min, S. (2007). Mixed Rasch Modeling of the Self-Rating Depression Scale: Incorporating Latent Class and Rasch Rating Scale Models. Educational and Psychological Measurement, 67(2), 280-299. DOI: https://doi.org/10.1177/0013164406292072

Jiao, H., Lissitz, R., Macready, G., Wang, S., & Liang, S. (2011). Exploring Levels of Performance Using the Mixture Rasch Model for Standard Setting. Psychological Test and Assessment Modeling, 53(4), 499-522.

Jongenelis, K., Pot, A. M., Eisses, A. M. H., Gerritsen, D. L., Derksen, M., Beekman, A. T. F & Ribbe, M. W. (2005). Diagnostic accuracy of the original 30-item and shortened versions of the Geriatric Depression Scale in nursing home patients. International journal of geriatric psychiatry, 20(11), 1067-1074. DOI: https://doi.org/10.1002/gps.1398

Lee, H. & Beretvas, S. (2014). Evaluation of Two Types of Differential Item Functioning in Factor Mixture Models With Binary Outcomes. Educational and Psychological Measurement, 74(5), 831-858. DOI: https://doi.org/10.1177/0013164414526881

Li, F., Cohen, A., Kim, S., & Cho, S. (2009). Model Selection Methods for Mixture Dichotomous IRT Models. Applied Psychological Measurement, 33(5), 353-373. DOI: https://doi.org/10.1177/0146621608326422

Lubke, G., & Muthen, B. (2005). Investigating Population Heterogeneity with Factor Mixture Models. Psychological Methods, 10(1), 21-39. DOI: https://doi.org/10.1037/1082-989X.10.1.21

Masyn, K. (2013). Latent Class Analysis and Finite Mixture Modeling. En T. Little (Ed.), The Oxford Handbook of Quantitative Methods in Psychology: Volumen 2 (pp. 551 - 611). Estados Unidos: Oxford University Press. DOI: https://doi.org/10.1093/oxfordhb/9780199934898.013.0025

Meij, A., Kelderman, H., & Flier, H. (2008). Fitting a Mixture Item Response Theory Model to Personality Questionnaire Data: Characterizing Latent Classes and Investigating Possibilities for Improving Prediction. Applied Psychological Measurement, 32(8), 611-631. DOI: https://doi.org/10.1177/0146621607312613

Meij, A., Kelderman, H., & Flier, H. (2010). Improvement in Detection of Differential Item Functioning Using a Mixture Item Response Theory Model. Multivariate Behavioral Research, 45, 975 - 999. DOI: https://doi.org/10.1080/00273171.2010.533047

Meiser, T., & Machunsky, M. (2008). The Personal Structure of Personal Need for Structure. European Journal of Psychological Assessment, 24(1), 27-34. DOI: https://doi.org/10.1027/1015-5759.24.1.27

Meyer, J. (2010). A Mixture Rasch Model with Item Response Time Components. Applied Psychological Measurement, 34(7), 521-538. DOI: https://doi.org/10.1177/0146621609355451

Mislevy, R., & Verhelst, N. (1990). Modeling Item Responses When Different Subjects Employ Different Solution Strategies. Psychometrika, 55(2), 195-215. DOI: https://doi.org/10.1007/BF02295283

Mittelhaëuser, M., Béguin, A., & Sijtsma, K. (2013). Modeling Differences in Test-Taking Motivation: Exploring the Usefulness of the Mixture Rasch Model and Person-Fit Statistics. En R. Millsap, L. van der Ark, D. Bolt & C. Woods (Eds.), New Developments in Quantitative Psychology. Presentations from the 77th Annual Psychometric Society Meeting (pp. 345-355). Estados Unidos: Springer. DOI: https://doi.org/10.1007/978-1-4614-9348-8_23

Mneimneh, Z., Heeringa, S., Tourangeau, R., & Elliott, M. (2014). Bringing Psychometrics and Survey Methodology: Can Mixed Rasch Models Identify Socially Desirable Reporting Behavior? Journal of Survey Statistics and Methodology, 2, 257-282. DOI: https://doi.org/10.1093/jssam/smu008

MPLUS (Versión 7.3) [Software de computación]. Los Ángeles, CA: Muthen & Muthen.

Muthen, B., & Asparouhov, T. (2006). Item Response Mixture Modeling: Application to Tobacco Dependence Criteria. Addictive Behaviors, 31, 1050- 1066. DOI: https://doi.org/10.1016/j.addbeh.2006.03.026

Muthen, B., & Lubke, G. (2007). Performance of Factor Mixture Models as a Function of Model Size, Covariate Effects, and Class-Specific Parameters. Structural Equation Modeling, 14(1), 26-47. DOI: https://doi.org/10.1080/10705510709336735

Nylund, K., Asparouhov, T., & Muthen, B. (2007). Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study. Structural Equation Modeling, 14(4), 535-569. DOI: https://doi.org/10.1080/10705510701575396

Oliveri, M., Ercikan, K., Zumbo, B., & Lawless, R. (2014). Uncovering Substantive Patterns in Student Responses in International Large-Scale Assessments? Comparing a Latent Class to a Manifest DIF Approach. International Journal of Testing, 14, 265-287. DOI: https://doi.org/10.1080/15305058.2014.891223

Paek, I., & Cho, S. (2015). A Note on Parameter Estimate Comparability: Across Latent Classes in Mixture IRT Modeling. Applied Psychological Measurement, 39(2), 135-143. DOI: https://doi.org/10.1177/0146621614549651

Preinerstorfer, D., & Formann, A. (2011). Parameter Recovery and Model Selection in Mixed Rasch Models. British Journal of Mathematical and Statistical Psychology, 65, 251-262. DOI: https://doi.org/10.1111/j.2044-8317.2011.02020.x

Raykov, T., & Marcoulides, G. (2011). Introduction to Psychometric Theory. Estados Unidos: Routledge. DOI: https://doi.org/10.4324/9780203841624

Raykov, T., Marcoulides, G., Lee, C., & Chang, C. (2013). Studying Differential Item Functioning via Latent Variable Modeling: A Note on a Multiple- Testing Procedure. Educational and Psychological Measurement, 73(5), 898-908. DOI: https://doi.org/10.1177/0013164413478165

Rosero, L., Fernández, X., & Dow, W. (2005). CRELES: Costa Rican Longevity and Healthy Aging Study (Costa Rica Estudio de Longevidad y Envejecimiento Saludable). ICPSR26681-v2. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [Distribuidor]. Recuperado de http://doi.org/10.3886/ ICPSR26681.v2

Rost, J. (1990). Rasch Models in Latent Classes: An Integration of Two Approaches to Item Analysis. Applied Psychological Measurement, 14(3), 271-282. DOI: https://doi.org/10.1177/014662169001400305

Sawatzky, R., Ratner, P., Kopec, J., & Zumbo, B. (2012). Latent Variable Mixture Models: A Promising Approach for the Validation of Patient Reported Outcomes. Quality of Life Research, 21, 637-650. DOI: https://doi.org/10.1007/s11136-011-9976-6

Schmiege, S., Meek, P., Bryan, A., & Petersen, H. (2012). Latent Variable Mixture Modeling: A Flexible Statistical Approach for Identifying and Classifying Heterogeneity. Nursing Research, 61(3), 204-212. DOI: https://doi.org/10.1097/NNR.0b013e3182539f4c

Sterba, S. (2013). Understanding Linkages Among Mixture Models. Multivariate Behavioral Research, 48, 775-815. DOI: https://doi.org/10.1080/00273171.2013.827564

Smit, A., Kelderman, H., & van der Flier, H. (1999). Collateral Information and Mixed Rasch Models. Methods of Psychological Research, 4(3). Recuperado de http://dare.ubvu.vu.nl/handle/1871/18667

Smit, A., Kelderman, H., & van der Flier, H. (2000). The Mixed Birnbaum Model: Estimation Using Collateral Information. Methods of Psychological Research, 5(4). Recuperado de http://dare.ubvu. vu.nl/handle/1871/18670

Tay, L., Newman, D., & Vermunt, J. (2011). Using Mixed-Measurement Item Response Theory With Covariates (MM-IRT-C) to Ascertain Observed and Unobserved Measurement Equivalence. Organizational Research Methods, 14(1), 147-176. DOI: https://doi.org/10.1177/1094428110366037

Tueller, S., & Lubke, G. (2010). Evaluation of Structural Equation Mixture Models: Parameter Estimates and Correct Class Assignment. Structural Equation Modeling, 17, 165-192. DOI: https://doi.org/10.1080/10705511003659318

Vermunt, J. (2014). Latent Class Model. En A. Michalos (Ed.), Encyclopedia of Quality of Life and Well-Being Research (pp. 3509 - 3515). Estados Unidos: Springer. DOI: https://doi.org/10.1007/978-94-007-0753-5_1604

Von Davier, M., & Molenaar, I. (2003). A Person- Fit Index for Polytomous Rasch Models, Latent Class Models, and their Mixture Generalizations. Psychometrika, 68(2), 213-228. DOI: https://doi.org/10.1007/BF02294798

Von Davier, M., & Yamamoto, K. (2007). Mixture- Distribution and HYBRID Rasch Models. En M. von Davier & C. Carstensen (Eds.), Multivariate and Mixture Distribution Rasch Models: Extensions and Applications (pp. 99-115). Estados Unidos: Springer. DOI: https://doi.org/10.1007/978-0-387-49839-3_6

Von Davier, M. (2010). Mixture Distribution Item Response Theory, Latent Class Analysis, and Diagnostic Mixture Models. En S. Embretson (Ed.), Measuring Psychological Constructs: Advances in Model-Based Approaches (pp. 11-34). Estados Unidos: American Psychological Association. DOI: https://doi.org/10.1037/12074-002

Willse, J. (2011). Mixture Rasch Models with Joint Maximum Likelihood Estimation. Educational and Psychological Measurement, 71(1), 5-19. DOI: https://doi.org/10.1177/0013164410387335

Zickar, M., Gibby, R., & Robie, C. (2004). Uncovering Faking Samples in Applicant, Incumbent, and Experimental Data Sets: An Application of Mixed- Model Item Response Theory. Organizational Research Methods, 7(2), 168-190. DOI: https://doi.org/10.1177/1094428104263674