

Alignment Method Question 

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We collected mental health data on 4 continents and want to examine the invariance of 5 separate measures with a sample size of 1000. One obstacle that I've run into is that running the analysis with all 5 measures at once leads to more parameters than people, and I get a warning that the model is not positive definite. I've tried running it with fixed and it did not resolve the problem. Would it make sense to run separate alignment analyses for each of the 5 measures? When I try this, the problem seems to be resolved. Also, is there a method to use the values from alignment analysis for future analyses? We want to see how each measure below (P, D, R, S, and A) relates to a few other outcome variables. Below is the syntax: data: file = CFA.dat; variable: names are cont P1P8 D1D24 R1R5 S1S4 A1A30; usevar = P1P8 D1D24 R1R5 S1S4 A1A30; MISSING ARE ALL (999); classes = c(4); knownclass = c(cont = 1 2 3 4); ANALYSIS: type = mixture; estimator = ml; alignment = free; model: %overall% P by P1P8; D by D1D24; R by R1R5; S by S1S4; A by A1A30; output: tech1 tech8 align SVALUES; plot: type = plot2; 


Yes, run it separately for each of the 5 factors. Regarding relating the factors to other variables, see the extended alignment method described in http://psycnet.apa.org/record/201701642001 


Dear professors, Hello! I ran a real data with alignment and the output indicates that all the loadings and intercepts for all the 4 groups are approximately invariant. But the R square statistic for some intercepts are zero, which indicates the noninvariance. How do we explain this result? Thank you! 


It is true that R2 can be close to zero even for invariant items even though that is somewhat unusual. The best way to understand this is to compute the R2 by hand, see formula (13) and (14) https://www.statmodel.com/download/webnotes/webnote18.pdf This can happen for example if the power was not sufficient to establish the noninvariance (such as small sample size or many missing values for that item or unusually large SE due to empty cells in bivariate tables). Or it can happened if the average aligned loading is close to 0. 


Thanks for your quick and detailed answer! 

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