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Applied Structural Equation Modeling for Dummies, by Dummies February 22, 2013 Indiana University, Bloomington

Applied Structural Equation Modeling for Dummies, by Dummies February 22, 2013 Indiana University, Bloomington. Joseph J. Sudano, Jr., PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System Adam T. Perzynski , PhD

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Applied Structural Equation Modeling for Dummies, by Dummies February 22, 2013 Indiana University, Bloomington

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  1. Applied Structural Equation Modeling for Dummies, by DummiesFebruary 22, 2013Indiana University, Bloomington Joseph J. Sudano, Jr., PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System Adam T. Perzynski, PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System

  2. Acknowledgements • Thanks Joe. • Thanks to Bill Pridemore and all of you here at IU. • Thanks to Doug Gunzler. • Thanks to Kyle Kercher.

  3. Rejected Titles for this TalkFebruary 22, 2013Indiana University, Bloomington Joseph J. Sudano, Jr., PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System Adam T. Perzynski, PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System

  4. Structural Equation Modeling for Fashion Week

  5. We have lots of Models!

  6. Structural Equation Modelin’ fer Pirates

  7. Structural Equation Modelin’ fer Pirates SEM be a statistical technique for testin' and estimatin' causal relations usin' a combination o' statistical data and qualitative causal assumptions *From Wikipedia

  8. Assumptions • I do not actually assume you are dummies • Feel free to assume what you want about me • I do not assume you will be experts in SEM after this presentation • I assume you know something about means and regression (hopefully)

  9. Outline • Important SEM Resources • Measurement (and measurement error) • Examples • Measurement Invariance • Latent Class Analysis • Latent Growth Mixture Modeling • Model Specification

  10. Outline • Important SEM Resources • Measurement (and measurement error) • Examples • Measurement Invariance • Latent Class Analysis • Latent Growth Mixture Modeling • Model Specification

  11. SEM Resources

  12. SEM Resources

  13. SEM Resources

  14. SEM Resources: Statmodel.com

  15. SEM Resources

  16. SEM Resources

  17. SEM Resources

  18. SEM Resources

  19. SEM Resources

  20. SEM Resources

  21. SEM Resources

  22. Outline • Important SEM Resources • Measurement (and measurement error) • Examples • Measurement Invariance • Latent Class Analysis • Latent Growth Mixture Modeling • Model Specification

  23. Measurement Models • A special type of causal models • Survey items are assumed to have measurement error • Each question has its own amount of error • Your answer to a survey question is causally related to a latent, unobserved variable.

  24. health Self-rated health Perfect Measurement 1.0?

  25. Causality and the Latent Concept of Health • In general, how would you describe your health? • We assume that every individual varies along an infinite continuum from best possible health to worst possible health. • When any given individual answers this question, they are approximating their position on this latent continuum.

  26. health Self-rated health e4 Imperfect Measurement 1.0 Variance > 0 < 1.0

  27. Measurement Models using Multiple Indicators • Single items are unreliable • Single cases prevent generalizability • Use multiple indicators and large samples to estimate the values of the latent, unobservered variables or factors • The SF36 uses multiple indicators describing multiple factors in order to measure health more reliably.

  28. Outline • Important SEM Resources • Measurement (and measurement error) • Examples • Measurement Invariance • Latent Class Analysis • Latent Growth Mixture Modeling • Model Specification

  29. Acknowledgement: This study was funded by Grant number R01-AG022459 from the NIH National Institute on Aging. Measuring Disparities: Bias in Self-reported Health Among Spanish-speaking PatientsJ.J. Sudano1,2, A.T. Perzynski1,2, T.E. Love2, S.A. Lewis1,B. Ruo3, D.W. Baker31 The MetroHealth System, Cleveland, OH; 2 Case Western Reserve University School of Medicine, Cleveland, OH; 3 Northwestern University Feinberg School of Medicine

  30. Measurement Model of the SF36

  31. Objective & Significance • Do observed differences in SRH reflect true differences in health? • Cultural and language differences may create measurement bias • If outcomes aren’t measuring the same thing in different groups, we have a problem

  32. Measurement Equivalence &Factorial Invariance • It is only possible to properly interpret group differences after measurement equivalence has been established (Horn & McArdle, 1992; Steenkamp & Baumgartner, 1998). • “It may be the case that the groups differ … but it also may be the case that extraneous influences are giving rise to the observed difference.” Meredith & Teresi (2006 p. S69) • The external validity of any conclusion regarding group differences rests securely on whether the measurement equivalence of the scale has been established (Borsboom, 2006).

  33. Cross-sectional Study • N= 1281 • Medical patients categorized into four groups:White, Black, English-speaking Hispanic and Spanish-speaking Hispanic. • Multigroup Confirmatory Factor Analysis (MGCFA)

  34. Two Types of Invariance • Metric (Weak) Invariance • Are the item factor loadings equivalent across groups? • Is a one unit change in the item equal to a one unit change in the factor score for all groups? • Scalar (Strong) Invariance • Are the item intercepts equivalent across groups? • Unequal intercepts results in unequal scaling of factor scores

  35. health Self-rated health e4 Weak invariance What happens to the model fit when we constrain all of these paths (loadings) to be equal across groups?

  36. The Unconstrained Model Fits the Data Well

  37. The Unconstrained Model fits the data well The model with factor loadings constrained still fits the data well.

  38. Metric (Weak) Invariance was Confirmed

  39. I forget what an intercept is • Scalar (Strong) Invariance • Are the item intercepts equivalent across groups? • Intercept: the intercept in a multiple regression model is the mean for the response when all of the explanatory variables take on the value 0. • Could be called the “starting point”

  40. The Unconstrained Model fits the data well The model with factor loadings constrained still fits the data well. Constraining the intercepts results in a worsening of model fit

  41. The model with factor loadings constrained still fits the data well. Constraining the intercepts results in a worsening of model fit The fit is still poor if you allow intercepts for English-speaking Hispanics to vary

  42. The model with factor loadings constrained still fits the data well. The fit is acceptable if you allow intercepts for Spanish speaking Hispanics to vary

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