Reliability and factor metric in Mont... PreviousNext
Mplus Discussion > Structural Equation Modeling >
Message/Author
 Marcus Butts posted on Wednesday, May 31, 2006 - 8:13 am
Hello,
Iím varying levels of reliability I want to incorporate into a factor and test in my model statement. However, I'm unsure if I need to incorporate "setting the metric of the factors" into the population model or just the sample model. Using the reliability formula: (((sum lambda)sq)(var factor))/((((sum lambda)sq)(var factor))+ (sum item res var)) for a reliability .70 I would set my (unstandardized) loadings and residuals as follows in the population and model:

MODEL POPULATION:
X1-X4@.631;
LV BY X1-X4@.607;
LV1@1.0;

MODEL:
X1-X4*.631;
LV1 BY X1-X4*.607;
LV1@1.0;

However, parameterization of the model variance as 1.0 is not as "popular" as setting one loading to 1.0. Therefore, keeping my reliability at .70, alternatively would my MODEL POPULATION stay the same and my MODEL statement be as follows?

MODEL:
X2-X4*.631;
LV1 BY X1@1.0 X2-X4*.607;
LV1*1;

Thus, my fundamental question is how do we incorporate reliability while setting the metric of the factor? Is the only way to do this thru the factor variance or can it also be accomplished using factor loadings set to 1? Thank you for your time.
 Linda K. Muthen posted on Thursday, June 01, 2006 - 6:42 am
I think your calculations would change if the factor variance is not one. You would need to give the population value for the factor variance and use it in your equation.
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