Keywords
Teoría de respuesta al ítem
modelos de mezcla
clases latentes
Escala de depresión geriátrica.
Psychometrics
Item Response Theory
mixture models
latent classes
Geriatric Depression Scale.
How to Cite
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.
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.
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.
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.
Borsboom, D., Mellenbergh, G., & Heerden, J. (2004). The Concept of Validity. Psychological Review, 111(4), 1061-1071.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Eid, M., & Rauber, M. (2000). Detecting Measurement Invariance in Organizational Surveys. European Journal of Psychological Assessment, 16(1), 20-30.
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.
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.
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.
Gollwitzer, M., Eid, M., & Jürgensen, R. (2005). Response Styles in the Assessment of Anger Expression. Psychological Assessment, 17(1), 56-59.
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.
Holmes, W., & Pierson, E. (2011). A Mixture IRT Analysis of Risky Youth Behavior. Frontiers in Psychology, 2, 1-10.
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.
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.
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.
Li, F., Cohen, A., Kim, S., & Cho, S. (2009). Model Selection Methods for Mixture Dichotomous IRT Models. Applied Psychological Measurement, 33(5), 353-373.
Lubke, G., & Muthen, B. (2005). Investigating Population Heterogeneity with Factor Mixture Models. Psychological Methods, 10(1), 21-39.
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.
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.
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.
Meiser, T., & Machunsky, M. (2008). The Personal Structure of Personal Need for Structure. European Journal of Psychological Assessment, 24(1), 27-34.
Meyer, J. (2010). A Mixture Rasch Model with Item Response Time Components. Applied Psychological Measurement, 34(7), 521-538.
Mislevy, R., & Verhelst, N. (1990). Modeling Item Responses When Different Subjects Employ Different Solution Strategies. Psychometrika, 55(2), 195-215.
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.
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.
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.
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.
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.
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.
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.
Preinerstorfer, D., & Formann, A. (2011). Parameter Recovery and Model Selection in Mixed Rasch Models. British Journal of Mathematical and Statistical Psychology, 65, 251-262.
Raykov, T., & Marcoulides, G. (2011). Introduction to Psychometric Theory. Estados Unidos: Routledge.
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.
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.
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.
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.
Sterba, S. (2013). Understanding Linkages Among Mixture Models. Multivariate Behavioral Research, 48, 775-815.
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.
Tueller, S., & Lubke, G. (2010). Evaluation of Structural Equation Mixture Models: Parameter Estimates and Correct Class Assignment. Structural Equation Modeling, 17, 165-192.
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.
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.
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.
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.
Willse, J. (2011). Mixture Rasch Models with Joint Maximum Likelihood Estimation. Educational and Psychological Measurement, 71(1), 5-19.
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.