Issues in structural equation modeling

1. Issues in structural equation modeling Hans Baumgartner Penn State University

2. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

3. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

4. Misinterpretation of overall model fit • Baumgartner and Homburg (1996) showed: • the median number of degrees of freedom in type III models was 49 (28, 124); • The median percentage contribution of the measurement model to the total number of degrees of freedom was 93 (81, 97); • the percentage of type III models for which R2 for structural equations was reported was 45;

5. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

6. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

7. Discriminant validity .80 1 1 1 .71 .74 .64 .75 .75 .78 .70 .76 2 AVE ( 1 ) = .51 AVE ( 2 ) = .56

8. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

9. Measurement model: 2(38)=45.16 RMSEA=.026 SRMR=.016 CFI=1.00 TLI=1.00 Latent variable model: 2(49)=151.55 RMSEA=.088 SRMR=.09 CFI=.96 TLI=.95

10. Measurement model: 2(38)=45.16 RMSEA=.026 SRMR=.016 CFI=1.00 TLI=1.00 Latent variable model: 2(49)=151.55 RMSEA=.088 SRMR=.09 CFI=.96 TLI=.95

11. Common problems • Incomplete information • 2 statistic and degrees of freedom • Misinterpretation of overall model fit • Covariance fit vs. variance fit • Reflective vs. formative indicators • Discriminant validity • Measurement model vs. latent variable model • Questionable model modification • Size of MI vs. conceptual meaningfulness • Correlated errors in equations vs. directed paths

13. Common problems (cont’d) Baron & Kenny and SEM Pooling data from multiple samples Assessment of measurement invariance

14. Mediation 1 1 3 2

15. Common problems (cont’d) • Baron & Kenny and SEM • Pooling data from multiple samples • Assessment of measurement invariance

16. Common problems (cont’d) • Baron & Kenny and SEM • Pooling data from multiple samples • Assessment of measurement invariance