Measurement invariance PreviousNext
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 Estee posted on Thursday, September 12, 2013 - 7:47 pm
I need to test measurement invariance at configural, metric and scalar level, which all the observations are continuous data. No covariate.

As the measurement invariance is to be tested between paternal and maternal parenting, each respondents have scores on both paternal and maternal parenting. It is somehow different from if the group is gender as each respondent is either male or female.

Is there any reference for the input file for this situation? Please kindly provide some suggestions/ advice.
 Bengt O. Muthen posted on Friday, September 13, 2013 - 5:24 pm
You can view this in line with testing longitudinal factor analysis invariance, where you also have correlated measures for subjects. So your paternal and maternal measures are arranged as different columns in the data, using a wide data approach. In other words, you are doing a single-group, wide-data analysis.

The invariance testing then proceeds just as if the two types of measures were for different groups. Mplus does not, however, have automatic metric/scalar model setups for this case.
 Ebrahim Hamedi posted on Tuesday, November 05, 2013 - 6:32 pm
On page 433 of the manual, you mention that for establishing scalar invariance, the means should be freely estimated in all but one group:

"3. Intercepts and factors loadings constrained to be equal across
groups; residual variances free; factor means zero in one group and
free in the others (the Mplus default)"

However, Barbara M. Byrne suggests in her books that when testing scalar invariance, we should fix factor means at zero in all groups, which is at variance with your recommendation. I personally agree with your recommendation, as it results in less estimation issues. However, I would like to know more about why you do not recommend fixing factor means at zero in all groups. Any clarification would be greatly appreciated.

many thanks in advance,
 Bengt O. Muthen posted on Wednesday, November 06, 2013 - 8:34 am
Scalar invariance is defined as your quote shows. This can be found in books such as Millsap (2011). When you hold the measurement intercepts and loadings invariant across groups, fixing factor means to zero in all groups implies that you have the means of each observed variable equal across all groups and this is typically not the case.
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