Hello,

In the first step of a study I am currently working on, I want to see whether I can replicate the results of a study published in a renowned journal by using the same procedure and specifying the same structural model in LISREL as the original authors, but using my own newly collected sample (N=162).

There are 7 latent variables:

PBG, PBL, BATT, and PINT each have 3 indicators (=observed variables)

COMP, WARM, and BFAM only have a single indicator

Consistent with other studies in my field as well as the original study, 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.

So, in a first step (in order to get the numbers needed to calculate the construct reliability), I specified the full model including all observed variables, based on a variance-covariance matrix I created with SPSS.

My relationships are as follows:

PBG1 = 1*PBG

PBG2 PBG3 = PBG

PBL1 = 1*PBL

PBL2 PBL3 = PBL

COMP1 = 1*COMP (COMP only has 1 indicator as mentioned above)

WARM1 = 1*WARM (WARM only has 1 indicator as mentioned above)

BATT1 = 1*BATT

BATT2 BATT3 = BATT

PINT1 = 1*PINT

PINT2 PINT3 = PINT

BFAM1 = 1*BFAM (BFAM only has 1 indicator as mentioned above)

BATT = PBG PBL COMP WARM BFAM

PINT = BATT BFAM

I set the error variances of the 3 single indicators (BFAM1, COMP1, WARM1) to 0.000.

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 observed variables to 0.

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, so I end up with the following relationships:

PBG_AVG = 1*PBG

PBL_AVG = 1*PBL

COMP_AVG = 1*COMP

BATT_AVG = 1*BATT

PINT_AVG = 1*PINT

BFAM_AVG = 1*BFAM

BATT = PBG PBL COMP

PINT = BATT

I set the error variances of all indicators to (1-α)*σ2. For the 3 single indicators (BFAM, COMP, WARM), 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 (for BATT as well as PINT in the structural equations part of the ouput)

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 Cronbach Alpha and construct reliability values 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!