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

Applied Structural Equation Modeling for Dummies, by Dummies

February 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

Acknowledgements

Thanks Joe.

Thanks to Bill Pridemore and all of you here at IU.

Thanks to Doug Gunzler.

Thanks to Kyle Kercher.

Rejected Titles for this Talk

February 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

Structural Equation Modeling for Fashion Week

We have lots of Models!

Structural Equation Modelin fer Pirates

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

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)

Outline

Important SEM Resources

Measurement (and measurement error)

Examples

Measurement Invariance

Latent Class Analysis

Latent Growth Mixture Modeling

Model Specification

Outline

Important SEM Resources

Measurement (and measurement error)

Examples

Measurement Invariance

Latent Class Analysis

Latent Growth Mixture Modeling

Model Specification

SEM Resources

SEM Resources

SEM Resources

SEM Resources: Statmodel.com

SEM Resources

SEM Resources

SEM Resources

SEM Resources

SEM Resources

SEM Resources

SEM Resources

Outline

Important SEM Resources

Measurement (and measurement error)

Examples

Measurement Invariance

Latent Class Analysis

Latent Growth Mixture Modeling

Model Specification

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.

Perfect Measurement

Self-rated health

health

1.0?

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.

Imperfect Measurement

Self-rated health

health

e4

< 1.0

1.0

Variance > 0

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.

Outline

Important SEM Resources

Measurement (and measurement error)

Examples

Measurement Invariance

Latent Class Analysis

Latent Growth Mixture Modeling

Model Specification

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

Measurement Model of the SF36

Objective & Significance

Do observed differences in SRH reflect true differences in health?

Cultural and language differences may create measurement bias

If outcomes arent measuring the same thing in different groups, we have a problem

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).

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)

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

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Self-rated health

health

e4

What happens to the model fit when we constrain all of these paths (loadings) to be equal across groups?

Weak invariance

In evaluating overall model fit, we use standards described by Hu and Bentler (1999) and summarized by Brown (2006): models with RMSEA values .05 and CFI values .90 are considered acceptable fit. In comparing the iterative testing of models, we use cutoff points for two fit measures, the Root Mean Square Error of Approximation (RMSEA) and the Comparative Fit Index (CFI), as recommended by simulation studies of model fit comparisons (Chen, 2007; Cheung & Rensvold, 2002). For all tests a decrease in CFI of -.010 and an increase in RMSEA of .010 suggest non-invariance and the rejection of the model. When the CFI and RMSEA results are mixed, the CFI results will be used because RMSEA results have been demonstrated to be less stable across changes in sample size and model complexity (Chen 2007).

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Table 1: Goodness of Fit for SF36 Multigroup Factorial Invariance Testing (N = 1281)ModelDescriptionRMSEA (95% CI)CFIB-S 2*dfRefRMSEACFIB-S 2df1Unconstrained Model0.028(.017 - .030)0.936300121722Metric Invariance (Factor Weights)0.029(.028 - .030)0.9313110225310.001-0.005109813Scalar Invariance (Intercepts)0.033(.032 - .034)0.9073215235820.004-0.0241051054Partial Scalar Invariance (B=W=HS not HE)0.033(.032 - .034)0.9093179232320.004-0.02269705Partial Scalar Invariance (B=W=HE not HS)0.030(.029 - .032)0.9213180232320.001-0.010707062nd Order Structural Invariance**0.030(.029 - .032)0.9213187233320.001-0.010778072nd & 3rd Order Structural Invariance**0.030(.029 - .032)0.9213196233920.001-0.0108686* The bootstrapped Bollen - Stine 2 value is reported because of significant (p