

Factors in exploratory bifactor anal... 

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Xu, Man posted on Wednesday, March 06, 2013  2:50 am



I am trying to interpret the factors in bifactor rotated solutions. Say I get a 4 factor soluation in EFA (f1, f2, f3, f4). Then in an equaivalent bifactor version of the EFA I still have 4 factors (bf1, bf2, bf3, bf4), but the first factor has become the general factor(bf1), with 3 others (bf2, bf3, bf4), as the "group/specific" factor. I was wondering if it makes sense at all to try to match the factors from the EFA to the "group/specific" factors from the bifactor EFA? For example, would bf2 correspond to f2 and bf3 correspond to f3? Or has the substantive meaning of factors structures and their loadings all changed completely due to rotation methods? Thanks a lot! Kate 


The substantive meaning of the factors has changed with the two rotation methods. 

Xu, Man posted on Wednesday, March 06, 2013  4:05 pm



Thank you. If the a priori is to have n factors in data, and EFA indeed indicated a nfactor structure, does this mean that under bifactor rotation, instead of the n factor, it is the n+1 factor solution that will be most likely to reveal a structure with 1 general factor and n group factors, correspondng to the a priori? 


A model with n factors corresponds to a model with 1 general and n1 specific factors. With EFA these 2 models will have the same fit. 

Xu, Man posted on Thursday, March 07, 2013  10:06 am



Thank you. So, if ndimension data can be adequately explained under n EFA factors, then under bifactor rotation, only n1 groups of items will be able to show up as group factors. I guess I was a bit confused because I tried to look at the fifactor EFA structure in the same route as the typical EFA to CFA type of model development. e.g., if I see n factors in EFA, then I will go on to specify a CFA with n factors. If I see n1 group factors under bifactor EFA, would I only specify n1 group factors, or would I specify n group factors as in typical CFA bifactor analysis? 


One observation is that in some data it may be easier to find an interpretable loading pattern when using a general factor. For instance, EFA with regular rotation may suggest 4 factors while a 5factor solution has problems. EFA with bifactor rotation, however, may find that 4 specific factors come out interpretable together with a general factor. This despite fit being the same for regular EFA with 4 factors and bifactor EFA with only 3 specific and 1 general factor. I have seen this in the classic HolzingerSwineford data. If bifactor EFA points to n1 specific factors, bifactor CFA would also specify n1 specific factors. 

Xu, Man posted on Thursday, March 14, 2013  7:15 am



Thank you  and yes  I read your recent teaching slides on bifactor and saw that 4 factors from regular EFA were sufficient to explain the 24variable HolzingerSwineford data. In the bifactor EFA, 5 factor (instead of 4) were requested as a priori (if I understood correctly), and each of the 5 factors do correspond to the hypothesis  a general factor, and 4 specific factors. So maybe, if one knows the expected number of dimensions, say n, perhaps one should look at the bifactor rotation EFA output both under n and n+1 factors? 


Yes. 

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