Hi Bengt and Linda, I am runing a second-order CFA. The goodness-fit indices shows that the model fits data well, but the loading coeffecients of some first order factors on a second order factor are 999.00. The following is the syntax and the problematic part of output: data: file is a:\cfa4.dat;
variable: names are y1-y35;
model: intra by y1-y5; famil by y6-y10; forbe by y11-y15; respe by y16-y20; relun by y21-y25; fatal by y26-y30; socia by y31-y35;
coll by intra famil respe relun socia; order by forbe fatal;
The 999 values for the standardized coefficients are the result of the negative variance of order. You will need to change your model.
Sally Czaja posted on Monday, December 18, 2006 - 1:32 pm
I am not sure that I am correctly interpreting the factor loading coefficients for CFA with continuous and dichotomous factor indicators. My understanding is that estimates for dichotomous factor indicators are probit coefficients, and estimates for continuous indicators are linear regression coefficients. Assuming this is correct, my questions are:
1. Does this mean that the standardized estimate (std) is, in the case of continuous indicators, equivalent to beta in linear regression? If so, what does it mean that several of the std estimates for continuous indicators are above 1?
2. Similarly, several of the unstandardized estimates for dichotomous factor indicators are well above 1, above 3 even, which seems extremely high for a probit regression coefficient.
I am conducting the CFA to evaluate my measurement model before proceding with SEM and want to be able to interpret the factor loadings. The associate z-scores all indicate statistical significance, but I want to be able to report and comment upon the strength of the factor loadings themselves.
1. StdYX would be what you refer to as beta I believe if by beta you mean the regular standardized coeffieint. See Karl's Corner on the Lisrel website for a discussion of standardized coefficients greater than one.
2. The could happen depending on the variances of the factors.
Eulalia Puig posted on Wednesday, November 28, 2007 - 5:47 pm
Hi, Should we be wary of CFA with loadings more than 1? Is this different than LISREL? Thanks
Factor loadings can be greater than one. Karl Joreskog has a discussion of this on the Lisrel website.
ehsan malek posted on Saturday, April 19, 2008 - 12:30 pm
Using SEM, when I use correlation matrix (which I think Mplus use it as default and I don't know how to change it?) some of factor loads in measurement model are greater than 1.0, which is not ok as HAIR 1995 states in his book.how can I solve it? How can I fix the residual variance of an indicator in Mplus?
SEM uses a covariance matrix. Factor loadings can be greater than one. There is a discussion of this on the Lisrel website by Karl Joreskog. You fix a residual variance of variable y by saying y@1; if you want to fix it at one.
Which reference(s) (articles and/or books) would you recommend for interpreting CFA factor loadings as regression coefficients? I've looked for "Karl's Corner" at the LISREL site as you suggest in several postings, and it doesn't seem to be there anymore. Nor was I able to find any discussion there about interpreting loadings with a quick (10min) search. I've run a 2-group CFA with some correlated errors and need references to help interpret the differences between the two results in the output (factor loadings the same, but SDYX different, for example). Thanks! Bruce
Thank you very much for the recommendation and the quick reply, Linda - I've ordered the book and should have it Monday! Meanwhile, reading Long's old Sage QASS Paper #33 & some chapters from Thompson's APA book. Best, Bruce
We have run a CFA with binary indicators, and it is our understanding that the STDXY factor loadings are coefficients in a probit regression. How can we evaluate the factor loadings -- is there some rule-of-thumb about probit coefficients?
I know of no rule of thumb. I would look at significance.
Brewery Lin posted on Sunday, October 02, 2011 - 11:07 pm
When we conduct CFA by Mplus, the default is to fix the first indicator's loading to 1 for scaling. That's why the unstandardized solution wouldn't show the significance of that indicator. However, when we look at the standardized solution, the indicator DOES has a significance test. Is it estimated under the standardized solution? How does this happen? I might have some misunderstanding. Please give me some advice.
I am wondering if you know some references about the validity of small factor loadings in CFA. I have a latent variable with 3 indicators, one of which has a standardized loading of .17. Do you think this is problematic?
Yes, that does sound problematic. If you look at the factor determinacy - which is a measure of the precision with which the factor is measured - you will probably see a value far below the max of 1. See also
2) That's a large topic discussed in IRT books. I assume you consider a growth model, although you don't say that specifically, in which case you should look at the literature for binary growth models.
my model is a cross sectional model. If i ve got a latent variable with two binary indicators for which one binary indicator loading is not significant in the unstandardized solution although significant in the standardized solution you would suggest that this is not a good indicator? EFA with geomin suggests this indicator.
It may be that the indicator is not good for the factor, but it may also be that how you use the indicator in the two-part model is different from the EFA model where you saw the significant loading - the two-part model may have other variables in it that make the model mis-specified wrt this item.
When means, variances, and covariances are not sufficient statistics for model estimation chi-square and related fit statistics are not available. In such cases nested model can be tested using -2 times the difference in the loglikelihoods which is distributed as chi-square.
Mher B. posted on Thursday, November 28, 2013 - 2:57 am
Hello dear professors, Regarding WLSMV based CFA, Brown (in CFA for Applied Research, 2006) says "Squaring the completely standardized factor loadings [which are probit coefficients] yields the proportion of variance in y* [latent continuous response variable] that is explained by the latent factor, not the proportion of variance explained in the observed measure (e.g., Y1), as in the interpretation of CFA with continuous indicators". If this is correct, can we apply conventional cutoffs for small and large loadings (e.g. 0.5) as they are also reflecting amount of explained variance? If not, than we can think the statement in the book is not correct, right?
The book is correct and the size of loadings on a standardized metric for y* can be understood as with continuous indicators. But (a) this does not inform fully about how y relates to the factor and (b) I would not slavishly go with specific cutoffs for what is a small loading in either the continuous or categorical case. It depends on the standard error of the loading and therefore the significance of it. For more related to this, look for the Mplus ESEM and BSEM papers.
Mher B. posted on Thursday, November 28, 2013 - 12:43 pm
Thanks a lot for your reflections and suggested papers! I'll look there for more detailed treatment of the issue.