Skyler Hawk posted on Thursday, October 09, 2014 - 8:46 pm
I conducted a 3-factor CFA on a single-group sample, and then compared the observed means of each factor in an RM-ANOVA. My reviewer has asked that I instead report and compare the latent factor means (so that the comparisons are free of measurement error). I am familiar with how to obtain and compare latent means in a multi-group analysis but the [Var] (m1) syntax doesn't seem to work in a single group model. The same reviewer has already asked that I add gender as a control variable after I had established measurement invariance so grouping the results by gender isn't feasible.
Is it even possible to do this in a single-group model? My understanding was that a latent factor mean in a cross-sectional study is basically meaningless and there is no basis for comparing them unless it is across time or across groups. Thanks very much for your advice.
Skyler Hawk posted on Thursday, October 09, 2014 - 9:08 pm
Maybe I can clarify slightly further. The reviewer in this case has suggested that:
The authors compare the three mean frequency scores using ANOVA. Given that the authors already have computed latent factors for each dimension, I would encourage comparing the factor scores from Mplus (savedata: fscores) rather than the observed means. By staying within the SEM framework to answer these questions, the authors would eliminate measurement error from the monitoring variables and be able to estimate missing data more efficiently.
My understanding of factor scores is that they are the factor loadings, and not the latent means of the constructs that would be more free of measurement error than the observed means. Thus, it doesn't seem like this reviewer's suggestion is really addressing the same issue that we set out to examine. It is also not clear to me how I would go about comparing the factor scores of each dimension simply by saving them to the .dat file. Can they then be compared via a Wald test?
In a single-group analysis, factor scores are fixed at zero for purposes of model identification. Factor means can be identified only in multiple group analysis and multiple time point analysis where they must be fixed at zero in one group/time point and can be free in the other groups/time points.
Skyler Hawk posted on Sunday, October 12, 2014 - 11:06 pm
Thanks for your help. I managed to obtain and save factor scores into my SPSS file and then examined the means in a RM-ANOVA. However, the mean score for one of my dimensions is negative, which shouldn't be possible. I've carefully reviewed the scores for all of the indicators in the dataset but there are no anomalies. What could produce this result? Perhaps I'm not clear as to what exactly is being saved to the SPSS file with the SAVE = FSCORES command. I appreciate your advice.
Factors have means of zero. Factor scores do not. A slightly negative value can occur.
Paula Vagos posted on Thursday, January 14, 2016 - 3:40 am
Dear Doctors Muthen, good evening. I have conducted a measurement invariance analysis with three groups, and then proceeded with latent mean comparisons among those groups. To do so, I alternatively fixed the mean of each measure/ factor to 0, so that I got the results when group 1 = 0 Vs group 2 and 3, group 2= 0 Vs group 1 and 3, and group 3 = 0 Vs group 1 and 2. The thing is the results I got when group 2 = 0 Vs group 3 were different than when group 3 = 0 Vs group 2. They were similar in the direction (i.e., the mean of group 3 was always inferior) but in the first case the difference was not significant and the in the second it was.
Is this a possible result or am I doing something wrong? And if this is a possible result, could you please explain why? Which result would you recommend I present, for example, when trying to publish?