Abstract
In many ways, Chap. 5 is an extension of the methods and techniques used to gather evidence based on the internal structure of the instrument and continues to describe the latent variable approach to instrument development. In this chapter, we introduce two common instrument development situations where discrete mathematical structures are encountered: latent class analysis (LCA) and item response theory (IRT). In LCA, both the latent variable and the indicator variable are best represented by a categorical structure. In IRT, the latent trait is continuous, but the items are the items are categorical. IRT has historically been used in educational achievement applications, however, it is gaining popularity in some affective characteristic measurement scenarios. The last section of the chapter is devoted to the topic of measurement invariance and the analytic techniques that allow instrument developers to explore whether the scale functions in the same manner (exhibits the same internal structure) across subgroups. If the items that reflect their latent constructs and the connections between the constructs operate in a fundamentally different way depending on group membership, cross group comparisons become difficult, if not impossible. This chapter discusses the most common statistical techniques (along with examples) for establishing invariance for both scenarios where the indicators are either continuous or categorical.
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Notes
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Material from Gable et al. (2011) included with permission from Sage Publications.
References
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52(3), 317–332.
American Educational Research Association (AERA), American Psychological Association (APA), & National Council on Measurement in Education (NCME). (1999). The standards for educational and psychological testing. Washington, DC: American Educational Research Association.
Andrich, D. (1978a). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement, 2, 581–594.
Andrich, D. (1978b). Rating formulation for ordered response categories. Psychometrika, 43, 561–573.
Andrich, D. (1978c). Scaling attitude items constructed and scored in the Likert tradition. Educational and Psychological Measurement, 38, 665–680.
Beck, C. T., & Gable, R. K. (2001). Further validation of the postpartum depression screening scale. Nursing Research, 50, 155–164.
Boscardin, C. (2012). Profiling students for remediation using latent class analysis. Advances in Health Sciences, 17, 56–63.
Boscardin, C. K., Muthen, B., Francis, D. J., & Baker, E. L. (2008). Early identification of reading difficulties using heterogeneous developmental trajectories. Journal of Educational Psychology, 100(1), 192–208.
Bozdogan, H. (1987). Model selection and Akaike’s information criteria (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345–370.
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: The Guilford Press.
Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis with applications in the social, behavioral, and health sciences. Hoboken, NJ: Wiley.
Dias, J. G., & Vermunt, J. K. (2006). Bootstrap methods for measuring classification uncertainty in latent class analysis. In A. Rizzi & M. Vichi (Eds.), Proceedings in computational statistics (pp. 31–41). Heidelberg: Springer.
Dimitrov, D. M. (2010). Testing factorial invariance in the context of construct validation. Measurement and Evaluation in Counseling and Development, 43(2), 121–149.
Embretson, S. E. (1999). Issues in the measurement of cognitive abilities. In S. Embretson & S. Hershberger (Eds.), The new rules of measurement: What every psychologist and educator should know (pp. 1–15). Mahwah, NJ: Lawrence Erlbaum Associates.
French, B. F., & Finch, W. H. (2008). Multigroup confirmatory factor analysis: Locating the invariant reference sets. Structural Equation Modeling: A Multidisciplinary Journal, 15, 96–113.
Finch, W. H., & Bronk, K. C. (2011). Conducting confirmatory latent class analysis using Mplus. Structural Equation Modeling: A Multidisciplinary Journal, 18(1), 132–151.
Franek, M. (2005/2006). Foiling cyberbullies in the new Wild West. Educational Leadership, 63, 39–43.
Gable, R. K., Ludlow, L. H., Kite, S. L., McCoach, D. B., & Filippelli, L. P. (2009, April). Development and validation of the survey of knowledge of internet risk and internet behavior. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.
Gable, R. K., Ludlow, L. H., McCoach, D. B., & Kite, S. L. (2010, October). Construct invariance of the survey of knowledge of internet risk and internet behavior. Paper presented at the Annual Conference of the Northeastern Educational Research Association, Rocky Hill, CT.
Gable, R. K., Ludlow, L. H., McCoach, D. B., & Kite, S. L. (2011). Validation of the survey of knowledge of internet risk and internet behavior. Educational and Psychological Measurement, 71(1), 217–230.
Gable, R. K., Ludlow, L. H., & Wolf, M. B. (1990). The use of classical and Rasch latent trait models to enhance the validity of affective measures. Educational and Psychological Measurement, 50(4), 869–878.
Gable, R. K., & Wolf, M. B. (1993). Instrument development in the affective domain: Measuring attitudes and values in corporate and school settings (2nd ed.). Boston: Kluwer-Nijhoff.
Hadzi-Pavlovic, D. (2009). Finding patterns and groupings: I. Introduction to latent class analysis. Acta Neuropsychiatrica, 21(6), 312–313.
Hagenaars, J. A., & McCutcheon, A. L. (2002). Applied latent class analysis. Cambridge: Cambridge University Press.
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage.
Hattie, J., Jaeger, R. M., & Bond, L. (1999). Persistent methodological questions in educational testing. Review of Research in Education, 24, 393–446.
Helms, B. J., & Gable, R. K. (1989). School situation survey manual. Palo Alto: Consulting Psychologists Press/The Mind Garden.
Holland, W., & Wainer, H. (1993). Differential item functioning. Mahwah, NJ: Lawrence Erlbaum Associates.
Henson, J. M., Reise, S. P., & Kim, K. H. (2007). Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling: A Multidisciplinary Journal, 14(2), 202–226.
Johnson, W. J., Dixon, P. N., & Ryan, J. M. (1991, April). Factorial and Rasch analysis of the Charles F. Kettering Ltd. school climate profile. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.
Kite, S. L., Gable, R. K., & Filippelli, L. P. (2010a). Assessment of students’ knowledge of Internet risk and Internet behaviors: Potential threat to bullying and contact by InternetpPredators. Paper presented at the Annual Meeting of the Northeastern Educational Research Association, Rocky Hill, CT.
Kite, S. L., Gable, R. K., & Filippelli, L. (2010b). Assessing middle school students’ knowledge of conduct/consequences and their behaviors regarding the use of social networking sites. The Clearing House, 1939-912X, 83, 158–163.
Lin, T. H., & Dayton, C. M. (1997). Model selection information criteria for non-nested latent class models. Journal of Educational and Behavioral Statistics, 22(3), 249–264.
Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767–778.
Ludlow, L. H., Enterline, S., & Cochran-Smith, M. (2008). Learning to teach for social justice-beliefs scale: An application of Rasch measurement principles. Measurement and Evaluation in Counseling and Development, 20, 194–214.
Ludlow, L. H., & Haley, S. M. (1995). Rasch model logits: Interpretation, use, and transformation. Educational and Psychological Measurement, 55, 967–975.
Magidson, J., & Vermunt, J. K. (2004). Latent class models. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 175–198). Thousand Oaks, CA: Sage.
Masters, G. N. (1980). A Rasch model for rating scales (Unpublished doctoral dissertation). Chicago, IL: University of Chicago.
Masters, G. N., & Hyde, N. H. (1984). Measuring attitude to school with a latent trait model. Applied Psychological Measurement, 8(1), 39–48.
McCoach, D. B. (2002). A validity study of the school attitude assessment survey (SAAS). Measurement and Evaluation in Counseling and Development, 35, 66–77.
McCoach, D. B., & Siegle, D. (2003a). The SAAS-R: A new instrument to identify academically able students who underachieve. Educational and Psychological Measurement, 63, 414–429.
McCoach, D. B., & Siegle, D. (2003b). The structure and function of academic self-concept in gifted and general education samples. Roeper Review, 25, 61–65.
McCutcheon, A. L. (1987). Latent class analysis. Newbury Park, CA: Sage.
McKenna, P. (2007). The rise of cyberbullying. New Scientist, 195(2613), 60.
Muthén, B., & Muthén, L. K. (2000). Integrating person-centered and variable-centered analyses: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24(6), 882–891.
Muthen, L. K., & Muthen, B. O. (2010). MPLUS user’s guide (6th ed.). Los Angeles, CA: Muthen & Muthen.
Muthén, B. O., & Muthén, L. K. (2000). The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample. Journal of Studies on Alcohol, 61, 290–300.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill.
Nylund, K. L., Asparouhov, T., & Muthen, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 535–569.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danmarks Paedogogiske Institute.
Rasch, G. (1966). An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 19, 49–57.
Rensvold, R. B., & Cheung, G. W. (2001). Testing for metric invariance using structural equation models: Solving the standardization problem. In C. A. Schriesheim & L. L. Neider (Eds.), Research in management: Equivalence in measurement (pp. 25–50). Greenwich, CT: Information Age Publishing.
Sass, D. A. (2011). Testing measurement invariance and comparing latent factor means within a confirmatory factor analysis framework. Journal of Psychoeducational Assessment, 29(4), 347–363.
Schwartz, S. A. (1978). A comprehensive system for item analysis in psychological scale construction. Journal of Educational Measurement, 15, 117–123.
Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis [Special section]. Psychometrika, 52(3), 333–343.
Tormakangas, K. (2011). Advantages of the Rasch measurement model in analyzing educational tests: An applicator’s reflection. Educational Research and Evaluation: An International Journal on Theory and Practice, 17(5), 307–320.
Tovar, E., & Simon, M. A. (2010). Factorial structure and invariance analysis in sense of belonging scales. Measurement and Evaluation in Counseling and Development, 43(3), 199–217.
Vermunt, J. K., & Magidson, J. (2002). Latent class cluster analysis. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 89–106). Cambridge: Cambridge University Press.
Vermunt, J. K., & Magidson, J. (2004). Latent class analysis. In M. S. Lewis-Beck, A. Bryman, & T. F. Liao (Eds.), The sage encyclopedia of social sciences research methods (pp. 549–553). Thousand Oakes, CA: Sage Publications.
Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57(2), 307–333.
Weiss, D. J., & Yoes, M. E. (1991). Item response theory. In R. Hambleton & J. Zaal (Eds.), Advances in educational and psychological testing: Theory and applications (pp. 69–95). New York, NY: Kluwer Academic/Plenum Publishers.
Wilson, M. (2005). Constructing measures: An item response modeling approach. New York, NY: Taylor & Francis.
Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12(1), 58–79.
Wright, B. D., & Linacre, M. (1998). Winsteps. Chicago, IL: Mesa Press.
Wright, B. D., & Masters, G. N. (1982). Rating scale analysis. Chicago, IL: Mesa Press.
Wright, B. D., & Stone, M. H. (1979). Best test design. Chicago, IL: Mesa Press.
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McCoach, D.B., Gable, R.K., Madura, J.P. (2013). Additional Evidence Based on the Internal Structure of the Instrument. In: Instrument Development in the Affective Domain. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7135-6_5
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