1. v.2 N.K. Bowen, 2014

2. GROUP 1 CONFIGURAL INVARIANCE AS TESTED WITH MPLUS INVARIANCE SHORTCUT (WLSMV) Loadings (except first) and thresholds free  = factor loading;  threshold; Black lines indicate FIXED paths and variances Blue lines indicated paths and variances CONSTRAINED to be equal across groups Red lines indicated FREELY estimated paths or variances. Variance s of x and y variables are not estimated. Scale factors (if Delta) or Residual variances (if Theta) Scale factors (if Delta) or Residual variances (if Theta) 1 1 1 factor mean=0 1 GROUP 2 (and subsequent groups) factor mean=0 1 1 1 1 N.K.Bowen, 2014

3. GROUP 1 1 1 1 1 GROUP 2 (and subsequent groups) METRIC INVARIANCE AS TESTED WITH MPLUS INVARIANCE SHORTCUT (WLSMV) Loadings (except first) constrained; thresholds free except those constrained for identification  = factor loading;  threshold; Black lines indicate FIXED paths and variances Blue lines indicated paths and variances CONSTRAINED to be equal across groups Red lines indicated FREELY estimated paths or variances. Variance s of x and y variables are not estimated. Scale factors (if Delta) or Residual variances (if Theta) Scale factors (if Delta) or Residual variances (if Theta) factor mean=0 factor mean free N.K.Bowen, 2014

4. GROUP 1 Scale factors (if Delta) or Residual variances (if Theta) Scale factors (if Delta) or Residual variances (if Theta) 1 1 1 factor mean=0 1 GROUP 2 (and subsequent groups) factor mean free SCALAR INVARIANCE AS TESTED WITH MPLUS INVARIANCE SHORTCUT (WLSMV) Loadings (except first) and thresholds constrained across groups  = factor loading;  threshold; Black lines indicate FIXED paths and variances Blue lines indicated paths and variances CONSTRAINED to be equal across groups Red lines indicated FREELY estimated paths or variances. Variance s of x and y variables are not estimated. N.K.Bowen, 2014