Farimah,

I'm going to offer some different answers.

1.

Using scale scores as observed variables in SEM (technically, then, path analysis) is a reasonable way to deal with such a large number of variables. However, you should keep in mind that it assumes a measurement model: specifically, one with equal loadings and residual variances for all items in each scale, and no cross-loadings between scales. This is also the model assumed, but not tested, when you use coefficient alpha. I suggest you at least do basic measurement modeling (confirmatory factor analysis, not exploratory) within each scale, even if you can't model all the scales at once. This will highlight any major problems with the individual scales so that you can have more justification for moving forward.

Omitting items with low loadings has its own drawbacks in terms of being post-hoc model modification, and is not necessary with a full measurement model. In a path model, though, it's not as straightforward a tradeoff.

2.

I usually allow disturbance/residual covariances among mediators. Most SEM programs by default allow covariances among the exogenous variables and among disturbances of the "endpoint" variables -- those with no outgoing paths. The reason to allow them among the endpoint variables is that omitting those covariances is to assume that the observed correlation between two endpoint variables is entirely due to the common causes that you've modeled. This is, in my fields, usually not a reasonable assumption.

The same logic applies to the mediators. Leaving out those covariances indicates you believe your two (or more) mediators covary only because of the common causation from your exogenous variables--again, usually not plausible.

3.

For the last question, that largely depends on the norms in your field and your sample size. If your sample does not contain enough information to estimate a single larger model, you'll need  to break it up. Otherwise, I'd ask your advisor.

Hope that helps,

Pat

I would say yes. The actual variability of the items do not need to be explicit in the model. These items are parts of a scale, i.e. they are a supposed to share a large proportion of variance in common (look for a high Cronbach alpha) and load highly to a single factor. Once you have established these criteria, the sum or average of the items is an equal interval measurement in its own sake, and can enter the model as an observed  variable.

Dear Mr. Giallousis

Thank you for your reply. I rewrite this question in 3 sections. It is greatly appreciated if you have a look to the other parts. 

Best regards,

Dear Farimah,

1. Yes, you can apply the total score and you can name the variable as composite score.But, i prefer you to apply EFA first in order to eliminate any item that below 0.60. in this stage, you manage to reduce the item that can be used to model the construct.

2. Plus, your measurement model looks problem since the factor loading is below 0.60 and thus impair your reliability and validity as exhibited in your figure.

3. About the covariance drawing is only acceptable for exogenous construct. Because when you click on the standardised estimate to obtain the correlation estimate. The correlation is present for the correlation between independent construct.

4. Yes, you can draw different model based on your hypothesis but should have a logic of why you apply dfferent model

Best regards

Farimah,

I'm going to offer some different answers.

1.

Using scale scores as observed variables in SEM (technically, then, path analysis) is a reasonable way to deal with such a large number of variables. However, you should keep in mind that it assumes a measurement model: specifically, one with equal loadings and residual variances for all items in each scale, and no cross-loadings between scales. This is also the model assumed, but not tested, when you use coefficient alpha. I suggest you at least do basic measurement modeling (confirmatory factor analysis, not exploratory) within each scale, even if you can't model all the scales at once. This will highlight any major problems with the individual scales so that you can have more justification for moving forward.

Omitting items with low loadings has its own drawbacks in terms of being post-hoc model modification, and is not necessary with a full measurement model. In a path model, though, it's not as straightforward a tradeoff.

2.

I usually allow disturbance/residual covariances among mediators. Most SEM programs by default allow covariances among the exogenous variables and among disturbances of the "endpoint" variables -- those with no outgoing paths. The reason to allow them among the endpoint variables is that omitting those covariances is to assume that the observed correlation between two endpoint variables is entirely due to the common causes that you've modeled. This is, in my fields, usually not a reasonable assumption.

The same logic applies to the mediators. Leaving out those covariances indicates you believe your two (or more) mediators covary only because of the common causation from your exogenous variables--again, usually not plausible.

3.

For the last question, that largely depends on the norms in your field and your sample size. If your sample does not contain enough information to estimate a single larger model, you'll need  to break it up. Otherwise, I'd ask your advisor.

Hope that helps,

Pat

Dear Mr. Wan Mohamad

Thank you very much for your reply.

But EFA should be done on a different sample. However, I have only one sample and it is not possible for me to divide them by two. Also, EFA is run in the cases that the scales are self-developed. Please let me know if I am wrong.

Regards,

Dear Dr. Malone

Thank you very much for your complete answer. Yes! it helps me a lot. 

Would you please introduce a reference to be cited in my thesis regarding the covariance drawn between two mediators?

Regards,

Farimah,

I can't help you with a reference offhand -- my argument is from logic of path analysis. But David MacKinnon's 2008 book on mediation might be of help.

Pat

Once again, thank you very much dear Dr. Malone.

Regards,

2. You can first try checking for discriminant and convergent validity Fornell and Larcker (1981). The very little I know, drawing a covariance between the mediators as shown in your model will raise questions, unless you can support with credible references.

Also see attached.

Dear Dr. Moslehpour

Thank you very much or your reply and the attached file.

Best,