

Secondorder factor analysis 

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Anonymous posted on Tuesday, April 24, 2001  7:30 pm



I have a CFA model including 22 indicators and 6 factors. The types of these observed variables are ordinal one with 3 categories. I use MPLUS 2.01 to estimate the model, and it fits good. However, when I wanna set up a secondorder factor, it can't work well. Part of original programs are presented as follows: TITLE: problem behavior DATA: FILE IS e:\probeha.dat; VARIABLE: NAMES ARE y1y22 grade; USEV = y1y22; CATEGORICAL = y1y22; ANALYSIS: TYPE = MEANSTRUCTURE; ESTIMATOR = WLSMV; MODEL: abs BY y1* y2 y9; bul BY y6* y14 y17; lie BY y7* y8 y10 y11 y15 y16; des BY y12* y13; ego BY y18* y19y22; dru by y3* y4 y5; problem by abs@bul@lie@des@ego@dru@1; OUTPUT: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 73. Because it is my first time to use Mplus, I can't find what is wrong in my inp file. Would you please help me to modify it? thanks a lot! 


One problem that I see is that your firstorder factors are not identified because you have freed the first factor loading of each one but have not set the metric of the factor by then fixing the factor variances to one. Either one loading needs to be set to one for each factor or the factor variance needs to be set to one. Another problem is the BY statement for the secondorder factor. It looks like you are fixing all of the factor loadings which I don't understand. See Example 17.2 in the Mplus User's Guide to see how a secondorder factor model is set up. 


Hello Dr. Muthen, I learned in SEM class that a sufficiently high loading of a measured variable onto a latent factor is .3 or higher (though researchers should also consider sample size when using this rule of thumbso other rules of thumb such as .4, or the requirement that the loading be statistically significant, can also be used). Is it generally thought that loadings of firstorder factors onto a higherorder factor also be .3, in order to justify a higherorder model as opposed to using a group of intercorrelated firstorder factors in your structural model? If one firstorder factor only loads at .1 or .2, while others load a .3 or higher, would you have to remove the lowloading firstorder factors, since your data do not justify your hypothesized model? Or can a higherorder model be justified by theory alone (whether literature states that the trait being measured should have this higherorder structure)? Or can a higherorder model be justified with statistics other than the loadings of firstorder factors, such as good fit of the higherorder model as a whole, based on indices such as the RMSEA, CFI, and TLI? Thank you for your time, Lisa Yarnell 


I am not a proponent of rules of thumb. I would instead be guided by theory, model fit, and significance of factor loadings. You may find the following paper interesting: Cudeck, R., & O’Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations. Psychological Bulletin, 115, 475–487. 


Thanks, Dr. Muthen. 

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