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Hello, I am testing convergent & discriminant validity of higherorder CFA. My model is reflective first order and formative second order. Please refer to the command below. ANALYSIS: TYPE = general; ESTIMATOR = mlr; ITERATIONS 1000; CONVERGENCE = 0.00005; MODEL: per BY Q28@1 Q39; re BY Q6@1 Q16 Q50 Q24; pro BY Q37@1 Q61 Q58 Q30; account BY; account@0; account on re@1 pro; per ON account*; I tested convergent & discriminant validity by calculating average variation explained (AVE), referring to Fornell and Larcker (1981). My questions are following: 1) In higher order CFA with formative second order, do I still need to test convergent and discriminant validity? Are there distinguished ways to test the both validity depending on whether a model is reflective or formative? 2) Could you let me know other ways to test the both validity using Mplus? Or could you direct me to helpful sources? Thank you for reading my post! 


Given that this is a general modeling question and not specifically related to Mplus, you should post it on a general discussion forum like SEMNET. 

Tim Powers posted on Wednesday, November 04, 2015  10:07 pm



Hello Dr Muthen, I am trying to conduct a test of discriminant validity between 2 factors using MLR as my estimator, following the SatorraBentler chisquare test My question is: If I run, Model 1 = 2 factors (3 items each) Model 2 = 1 factor (all 6 items) (a) Is Model 2 considered a nested model which overcomes the issue of testing parameters on the border of admissible parameter space? (e.g., where the 2 factors have a correlation of 1) (b) If I get a negative SB scaled chisquare difference (I do), what would be the modified parameter constraint added to Model 1 to obtain the ‘c10’ scaling correction factor (i.e., following ‘Mplus Webnotes Number 12, Asparouhov & Muthen, 2013)? 


(a) Strictly speaking there is a bit of a problem in using LRT for this purpose (overfactoring) see http://www.statmodel.com/download/Schmitt%202011Jour%20of%20Psychoed%20Assmt%20%20EFA%20and%20CFA.pdf and http://www.tandfonline.com/doi/abs/10.1080/10705510701301891 You might want to consider using BIC or just Ttest for the correlation between the two factors being different from 1. (b) M10 would be easiest to do if the factor variance in M0 is fixed to 1, then all you need to do in M10 is f1@1; f2@1; f1 with f2*1; 

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