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 Tao posted on Friday, April 25, 2003 - 9:06 am
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;

output: standardized;

FORBE 1.000 0.000 0.000 999.000 999.000
FATAL 0.989 0.453 2.184 999.000 999.000

COLL 0.835 0.164 5.094 1.000 1.000
ORDER -0.407 0.183 -2.219 999.000 999.000

Could you please tell me what is the possible problem in the output, and how should I solve it?
Thank you very much.

 Linda K. Muthen posted on Friday, April 25, 2003 - 9:13 am
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.

Thank you!
 Linda K. Muthen posted on Monday, December 18, 2006 - 5:19 pm
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?
 Linda K. Muthen posted on Thursday, November 29, 2007 - 6:31 am
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?
 Linda K. Muthen posted on Saturday, April 19, 2008 - 2:01 pm
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.
 Bruce A. Cooper posted on Friday, May 16, 2008 - 11:45 am
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).
 Linda K. Muthen posted on Friday, May 16, 2008 - 5:04 pm
You should find this in factor analysis texts like:

Brown, T.A. 2006). Confirmatory Factor Analysis For Applied Research. New York: The Guilford Press.

I was not able to find Karl's Corner either.
 Bruce A. Cooper posted on Saturday, May 17, 2008 - 10:56 am
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.
 John Stewart posted on Tuesday, October 19, 2010 - 9:19 am
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?
 Linda K. Muthen posted on Tuesday, October 19, 2010 - 3:41 pm
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.
 Linda K. Muthen posted on Monday, October 03, 2011 - 11:31 am
In standardizing, the factor variance is fixed at one so the metric is set in this way. The factor loading is a free parameter.
 Laura Valadez posted on Tuesday, November 22, 2011 - 9:15 am
Dear Profs. Muthén and Muthén,

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?

Thank you vey much for your time,

Laura Valadez
 Bengt O. Muthen posted on Tuesday, November 22, 2011 - 5:46 pm
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

Cudeck & O'Dell (1994) in Psych Bull
 Laura Valadez posted on Wednesday, November 23, 2011 - 1:13 am
Dear Bengt,

Thank you very much for your response. Just to confirm, is Cudeck and O´Dell´s paper applicable to both EFA and CFA ?

Thanks again,

 Linda K. Muthen posted on Wednesday, November 23, 2011 - 10:22 am
 Alexander Kapeller posted on Wednesday, February 08, 2012 - 3:44 pm

i am running a two part modell. i have several latent variables each composed by two of the binary variables.

1) in the mplus output the unstandardized p value for the factor loadings differ from the standardized solution. which is relevant for me.

2) how to interpret the value of the latent variable of the binary indicators.

 Bengt O. Muthen posted on Wednesday, February 08, 2012 - 10:19 pm
1) The unstandardized is often the better choice.

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.
 Alexander Kapeller posted on Thursday, February 09, 2012 - 9:04 am
HI Bengt,

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.

what else can i check.

thanks in advance
 Bengt O. Muthen posted on Thursday, February 09, 2012 - 1:54 pm
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.
 Alexander Kapeller posted on Friday, February 10, 2012 - 1:32 pm
Thanks Bengt,

I will have a look at several solutions. What fit indicator can i use to decide which model fits best as with two part there are no fit measures.
 Linda K. Muthen posted on Friday, February 10, 2012 - 2:51 pm
You can use BIC to compare non-nested models and loglikilihood difference testing of nested models.
 Alexander Kapeller posted on Saturday, February 25, 2012 - 12:23 am
Thanks Linda,

I've done this so far. Is there a measure like the chi-square ratio or rmsea available for two part models to say something about the overall modell alone and not in relation to other models.

 Linda K. Muthen posted on Saturday, February 25, 2012 - 7:48 am
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?
 Bengt O. Muthen posted on Thursday, November 28, 2013 - 8:03 am
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.
 Steven John posted on Thursday, December 15, 2016 - 8:15 am
Dear Muthéns,

I run a measurement model with four dichotomous indicators. The standardized factor loadings are fairly high and even, all significant. However, the unstandardized are not significant. What does this indicate? and is this a problem?

 Linda K. Muthen posted on Thursday, December 15, 2016 - 8:16 am
The sampling distributions of the two coefficients are not the same so significance is not necessarily the same. One may be non-normal.
 M posted on Monday, April 23, 2018 - 5:12 am
I have not been able to find a clarifying discussion on how to interpret a standardized loading above 1.0. I know that factor loadings can be greater than one since Karl Joreskog discuss this on the Lisrel website. But the answer is not straightforward.

Is it that this specific indicator is closely related to the factor predicting it?
Or is it a problem with the model?

Thanks in advance!
 Bengt O. Muthen posted on Monday, April 23, 2018 - 4:43 pm
First, be sure you are looking at the STDY section.

With several factors this can happen due to very high factor correlations. Also look for negative residual variances.
 M posted on Tuesday, April 24, 2018 - 6:40 am
Ok, thank you for the suggestions.
 Rocio Martinez posted on Monday, July 09, 2018 - 12:52 pm
Dear Profs. Muthén and Muthén,

I am too wondering if you know some references about the validity of small factor loadings in CFA. I could not find the Cudeck & O'Dell (1994) in Psych Bull reference.
I have a latent variable with 6 indicators, which range on STDYX estimate from of .425 to .706. I read that this loadings should be around .70. What does this mean and is it problematic?

Thank you vey much for your generous knowledge,

Rocío Martínez
 Bengt O. Muthen posted on Monday, July 09, 2018 - 6:00 pm
These are good questions for SEMNET.
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