I have a CFA with latent factors (each measured with multiple Likert-scale [-3;3] indicators). For the descriptive statistics, I would like to list mean and std. deviation for each latent factor. The TECH 4 output gives me 0 as mean for every factor. What should I do to get the "real" means and the standard deviations? Does the fact that I get 0 as mean for each factor mean that something with my model is wrong?
In cross-sectional studies, the means of latent variables are zero. In multiple group analysis or with repeated measures, the means of latent variables are zero in one group or at one time point and are estimated in the other groups or time points.
thank you very much for your reply. As far as I understand, you wrote how Mplus handles factors in cross-sectional studies.
However, in many publications, I find means and std. dev.s of latent factors in the descriptive statistics part.
When indicators are e.g. all skewed to the right (avg>0), then the mean of the latent variable should (e.g. in my example with Likert scales from -3 to 3) not be zero. Is there a way with Mplus to get this mean? Should I use an average of the indicators of each factor weighted by the indicators' yx-standardized factor loading and then calculate the mean and the std. dev. for each factor?
This is not how Mplus handles factors in cross-sectional studies, it is the conventional way to do this. A factor mean in a cross-sectional study has no meaning. You can't compare it to other factor means because there is no basis for comparison. It makes sense to compare factor means only across groups or across time after measurement invariance has been established.
I would imagine in the studies you mention, factor score means are being reported. Factor scores are generally not good approximations of true factor values.
The mean of a factor indicator is equal to the intercept of the factor indicator plus the factor loading times the mean of the factor. When the factor mean is zero, the mean of the factor indicator is equal to its intercept. This is why the factor mean can be zero even when the observed variable indicator mean is not zero.
Brewery Lin posted on Friday, April 06, 2012 - 12:12 am
In Byrne's book (2012), p.211 Appearing below these specifications, however, you will see the following: [Fl@OF2@0F3@0]......in structuring the input file for a configural model, it is necessary to void this default by fixing all factor means to zero.
Is it more appropriate to do that constriain? Thank you.
The configural model is factor means free across groups, intercepts free across groups, and factor means zero in all groups. You may find the multiple group section of the Topic 1 course handout on the website useful. It shows all of the inputs needed to test for measurement invariance.
I am unsure whether this is true in my case where I am interested in comparing means of 2 latent variables. One assessed at time 0 (and set equal to 0) and the other assessed at time 1 (which is estimated). Does dividing the z-test value corresponding to the mean at time 1 by the variable's SD correspond to a cohen's d?
I am unsure as we are forcing the first mean to be 0...
This is a mean difference even if one mean is zero. The difference in means is the mean parameter that is not zero. You divide this value by the standard deviation of that latent variable which you can find in the results or TECH4.
I have been looking at this a bit more and was discussing it with someone at work.
This conversation has brought to my attention the fact that I am not sure how MPLUS constructs the factors and how the free mean at time 2 is calculated, especially since the latent factor consists of questionnaires with different scales.
Grateful for your response and please feel free to point me to any relevant reference.
To compare means, you should keep the loadings and thresholds constrained to be equal across time. The two models to use for testing mean differences across time are the model with means zero at both time points versus the model with the mean fixed at zero at one time point and free at the other.
With constrained loadings and thresholds, the difference in probabilities of the items at the two time points is expressed by the free factor mean.
Francesca posted on Thursday, August 14, 2014 - 2:20 am
So to double check, with fixed loadings and thresholds:
1. do I need to assess the difftest for the model with both means set to 0 and the one with one mean at zero and the other free? is this what tells me if the means are different?
2. I am not 100% sure I understand what the free factor mean tells me - I thought this tested if the free mean is significantly different from 0 and therefore if data differ at followup (vs. baseline)