Issues in structural equation modeling Hans Baumgartner Penn State University

Issues in structural equation modeling 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

Issues in structural equation modeling 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

Issues in structural equation modeling 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 R 2 for structural equations was reported was 45;

Issues in structural equation modeling 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

Issues in structural equation modeling 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

Issues in structural equation modeling 22 1 AVE (  1 ) =.51AVE (  2 ) =.56 Discriminant validity

Issues in structural equation modeling 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

Issues in structural equation modeling Measurement model:  2 (38)=45.16 RMSEA=.026 SRMR=.016 CFI=1.00 TLI=1.00 Latent variable model:  2 (49)= RMSEA=.088 SRMR=.09 CFI=.96 TLI=.95

Issues in structural equation modeling Measurement model:  2 (38)=45.16 RMSEA=.026 SRMR=.016 CFI=1.00 TLI=1.00 Latent variable model:  2 (49)= RMSEA=.088 SRMR=.09 CFI=.96 TLI=.95

Issues in structural equation modeling 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

Issues in structural equation modeling

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

Issues in structural equation modeling 11 22 11 33 Mediation

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

Issues in structural equation modeling Common problems (cont’d)  Baron & Kenny and SEM  Pooling data from multiple samples  Assessment of measurement invariance