Covariance between items loading onto a latent variable

[Anna Warren]

Hello,

I am using SEM to perform factor analysis. I have 16 items from a questionnaire which are not from a validated measure. I am therefore using factor analysis to load these items onto a latent variable. I am aware that you can add covariances between the errors of variables. I have added in covariances between the errors of any items which correlate with each other by r = .5 or more (based on Cohen's benchmarks that effect sizes above .5 are considered to be large).

I just wondered firstly whether it makes sense to add covariances between the errors when the correlations I am basing these on are of the effects rather than of their errors. Is there a way to create a correlation matrix of just the errors if not?

Secondly I wondered whether it is theoretically sound to add the covariances as described.

I have included my code below:

sem (ypb8002 ypb8003 ypb8006 ypb8007 ypb8000 ypb8001 ypb8004 ypb8005 ypb8052 ypb8053 ypb8056 ypb8057 ypb8050 ypb8051 ypb8054 ypb8055<-Self),
latent(Self) method(mlmv)
cov(e.ypb8000*e.ypb8001 e.ypb8050*e.ypb8000 e.ypb8001*e.ypb8002 e.ypb8004*e.ypb8001 e.ypb8001*e.ypb8051 e.ypb8002*e.ypb8004 e.ypb8002*e.ypb8052 e.ypb8004*e.ypb8005 e.ypb8004*e.ypb8006 e.ypb8004*e.ypb8007 e.ypb8004*e.ypb8054 e.ypb8005*e.ypb8006 e.ypb8005*e.ypb8007 e.ypb8005*e.ypb8055 e.ypb8005*e.ypb8056 e.ypb8006*e.ypb8007 e.ypb8006*e.ypb8055 e.ypb8006*e.ypb8056 e.ypb8006*e.ypb8057 e.ypb8007*e.ypb8056 e.ypb8007*e.ypb8057 e.ypb8050*e.ypb8051 e.ypb8051*e.ypb8052 e.ypb8052*e.ypb8053 e.ypb8052*e.ypb8054 e.ypb8052*e.ypb8055 e.ypb8052*e.ypb8056 e.ypb8052*e.ypb8057 e.ypb8053*e.ypb8055 e.ypb8053*e.ypb8056 e.ypb8053*e.ypb8057 e.ypb8054*e.ypb8055 e.ypb8054*e.ypb8056 e.ypb8054*e.ypb8057 e.ypb8055*e.ypb8056 e.ypb8055*e.ypb8057 e.ypb8056*e.ypb8057 e.ypb8000*e.ypb8003 e.ypb8000*e.ypb8051 e.ypb8001*e.ypb8052 e.ypb8002*e.ypb8003 e.ypb8002*e.ypb8051 e.ypb8002*e.ypb8054 e.ypb8002*e.ypb8055 e.ypb8002*e.ypb8056 e.ypb8003*e.ypb8053 e.ypb8004*e.ypb8052 e.ypb8004*e.ypb8055 e.ypb8004*e.ypb8056 e.ypb8005*e.ypb8052 e.ypb8007*e.ypb8055 e.ypb8051*e.ypb8054 e.ypb8053*e.ypb8054 e.ypb8000*e.ypb8002 e.ypb8001*e.ypb8005 e.ypb8001*e.ypb8006 e.ypb8001*e.ypb8054 e.ypb8001*e.ypb8055 e.ypb8002*e.ypb8053 e.ypb8002*e.ypb8057 e.ypb8003*e.ypb8004 e.ypb8004*e.ypb8051 e.ypb8004*e.ypb8053 e.ypb8004*e.ypb8057 e.ypb8005*e.ypb8054 e.ypb8005*e.ypb8057 e.ypb8006*e.ypb8052 e.ypb8006*e.ypb8053 e.ypb8006*e.ypb8054 e.ypb8007*e.ypb8052 e.ypb8007*e.ypb8053 e.ypb8007*e.ypb8054 e.ypb8050*e.ypb8052 e.ypb8051*e.ypb8055)
estat gof, stats(all)

Thanks for your help,
Anna