Hello,

I would like to specify a structural model in LISREL with 7 latent variables.

Consistent with other studies in my field, I want to parcel the indicators of the multi-item latent variables into a single composite (i.e. using the average of all 3 indicators as a single predictor of the latent variable) and account for error variance by setting each composite's error variance to (1-α)*σ2, where α is the construct reliability and σ is the variance of the composite taken from the variance-covariance matrix of composites.

This model gets reasonable model fit indices and no warning messages, except for the THETA-DELTA matrix not being positive definite, which I think is normal because I set the error variances of 3 single-indicator variables variables to 0 (the other 4 are the multi-item variables).

So I looked at the completely standardized solution (indicator loadings and their error variances) to calculate the composite reliability of each multi-item construct.

In a next step, I imported a variance-covariance matrix of the composites (i.e. I averaged the means of the multiple indicators of a construct into a single variable, for those that have multiple indicators) and specified them as observed variables. I set their loadings to 1. I set the error variances of all indicators to (1-α)*σ2. For the 3 single indicators, I assumed a construct reliability of 0.8 and also fixed their error variance according to the formula. However, now I end up with the following warnings:

W_A_R_N_I_N_G: PSI is not positive definite

W_A_R_N_I_N_G: Error variance is negative

I just cannot seem to figure out why these warnings occur. My specified model is supported by previous theory and the method of setting error variance to (1-α)*σ2 has also been used before in other studies in which multiple indicators of a single latent variable were parcelled (i.e. averaged). All construct reliabilities are greater than 0.7, by the way.

Does anybody know what might be the source of the error?

Any help or hint is greatly appreciated.

Thank you very much in advance!