Indicators on different scales PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Rich Mohn posted on Friday, March 26, 2010 - 6:48 am
I have a latent variable with indicators on different scales, which I've not worked with before. I thought I could just change them to z-scores (the variables are normally distributed) and go from there, but I got an error message that there were serious convergence problems. I read about making it a formative construct, but wondered if anyone had any advice or could point me to a reference. Thanks.
 Rich Mohn posted on Friday, March 26, 2010 - 6:54 am
Just to clarify, there is not a compelling case at all to make it formative.
 Linda K. Muthen posted on Friday, March 26, 2010 - 9:22 am
I would not standardize the variables. If the variances are large, I would rescale them by dividing them by a constant of such size that their variances fall between one and ten after rescaling. I would run the model with all factor loadings free and the factor variances fixed to one to see if perhaps the problem is caused by the first factor indicator having a negative or small factor loading such that fixing it to one causes problem. If none of this helps, please send the full output and your license number to
 Rich Mohn posted on Friday, March 26, 2010 - 10:38 am
That got it to run. The latent variable that has the different scales, though, is endogenous . . . so should I still fix the disterbance term to 1? I do get different p-values for the unstandardized structural coefficients depending on which indicator path is fixed to 1.
 Linda K. Muthen posted on Friday, March 26, 2010 - 11:27 am
You should get the same fit whether you fix a factor variance to one or a factor loading to one. The choice of the factor indicator to fix at one sets the metric of the factor. You can do either parameterization. I would fix a factor loading to one that is estimated close to positive one.
 Rich Mohn posted on Friday, March 26, 2010 - 12:21 pm
Thanks, I just got concerned as I had p-values for unstandardized structural paths change from .01 ot .07 depending on which indicator was fixed to 1 (and the indicators did have disparate loadings, .8 versus .4). The standardized solution certainly does stay the same.
 Asti  posted on Thursday, August 04, 2011 - 2:00 am
"I would fix a factor loading to one that is estimated close to positive one".

Does the indicator chosen for the latent's metric have to have positive loading? I have a latent with 6 indicators. Fixing factor variance at one, i get 3 indicators with positive loadings and 3 with negative. The (unstandardized) loading closest to positive one is very low (<0.1), but I have one indicator with -1.05 loading. Can I fix factor loading to one for the indicator with -1.05 loading? This is a measurement model testing for one-, two-, or three-factors.

On a separate issue, I divided my observed variables (ranging from unit counts to thousands of milliseconds) by constants to restrict their means to 1-10 range. Though scaling doesn't affect standardized parameter estimates, I found scaling to greatly affect the loglikelihood (and derivative fit indices such as the AIC). I was under the impression that this is via the effect of measurement scaling on the covariance matrix which is considered in the estimation, but was told scaling shouldn't affect model fit. Is that right? What is the impact and importance of scaling the data? What is the place of the covariance matrix in the calculation of the loglikelihood--I can't seem to find it in the guide or tech appendices.
 Linda K. Muthen posted on Thursday, August 04, 2011 - 5:21 pm
I think it is most straightforward if you choose a positive loading to fix at one. If you choose a negative loading, it should be fixed to minus one.

The loglikelihood and AIC will be affected. They are not model fit statistics.

Rescaling by dividing by a constant to keep variances between one and ten helps model convergence.

See formula 111 in Technical Appendix 5 for one loglikelihood formula.
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