Scale or metric scale
Message/Author
 MBH posted on Saturday, May 17, 2014 - 2:51 pm
Dear Dr. Muthen,

There is something I'm not finding the answer to anywhere.

For CFA, when a factor is fixed @1, its usually to define a metric or a scale for the CFA to be identified. I do not have a statistical background but am wondering what the latent scale represents or what it means?

For example with continuous variables if one variable is fixed @1, how would the latent variable scale be interpreted and do they have a range?

And when a categorical variable with 3 categories is fixed @1, how would the latent variable scale be interpreted? then?

I'm very confused as to what the metric or scale really mean.

Thank you
 Linda K. Muthen posted on Saturday, May 17, 2014 - 3:47 pm
A factor indicator with loading fixed at 1 means that as the factor changes one unit the indicator changes one unit.

With categorical indicators you don't have an easy interpretation.
 MBH posted on Thursday, May 29, 2014 - 2:55 am
Thanks Linda,

Just a couple of questions more.

1) Variables that are specified as either CATEGORICAL or NOMINAL, in Mplus will the response option of these variables with the lowest level becomes 0, with other options assigned higher values in increment of 1?

2) When a factor loading is constrained to 1, does this specification assign to a factor a scale related to that of explained variance of the reference variable?

Thanks
 Linda K. Muthen posted on Thursday, May 29, 2014 - 11:52 am
1. Yes. See the CATEGORICAL option for further details.

2. The factor is in the metric of the indicator variable. A one unit change in the factor is equal to a one unit change in the indicator.
 MBH posted on Friday, May 30, 2014 - 2:33 am
Thanks Linda,

I have tried to measure metric or statistics of a measurement model but my syntax is wrong I think. This is what I'm doing:

model:

y1 by x1 x2 x3;
metric scalar;

Is that correct?
 Linda K. Muthen posted on Friday, May 30, 2014 - 11:28 am
I'm not sure why you have

metric scalar;

in the MODEL command. If you want to test measurement invariance using these options, you would specify

MODEL = METRIC SCALAR;

in the ANALYSIS command. This is discussed in the Version 7.1 Mplus Language Addendum on the website with the user's guide.
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