This message means that Mplus can't find the file that contains the data. So be sure that the data file exists under the name you have given it in the directory that you are running from or give the path as part of the file name. I also notice that you say you have 10 variables but your correlation matrix is for 11 variables. You also need to correct this.
Anonymous posted on Friday, December 14, 2001 - 11:08 am
When the Promax rotation is used, are the resulting factor "loadings" in the Mplus output factor pattern coefficients (i.e., regression weights) or factor structure coefficients (i.e., correlations)?
bmuthen posted on Friday, December 14, 2001 - 1:28 pm
They are the factor pattern coefficients.
Anonymous posted on Thursday, May 02, 2002 - 2:59 am
In an EFA with continuous indicators I tried to reproduce a factor loading table found in Mplus in SPSS using the same estimator (ULS) and rotation (Promax). One of the factors was dominated by high negative loadings in Mplus but high positive in SPSS while the loadings were numerically equal/similar. Is that because Mplus does NOT use Kaiser normalization as does SPSS? Does the same apply for categorical indicators?
I don't know if the difference has anything to do with the Kaiser normalization but in EFA the signs of the factor loadings is indeterminate, that is, you can change all of the signs in a column of the factor loading matrix and reproduce the same correlation matrix.
Anonymous posted on Thursday, July 25, 2002 - 6:32 am
A couple of quick questions: Is it possible to output the unrotated factor solution? What tuning constant does M-Plus use for promax rotation (eg SPSS uses a "kappa" default of 4)? And is it possible to alter this? (eg, so as to reduce promax loadings from being greater than 1 to be <1)?
bmuthen posted on Thursday, July 25, 2002 - 9:38 am
No, Mplus does not output the unrotated factor solution. But any rotation can be obtained from a solution such as the Varimax.
The Promax rotation uses the exponent value 3. In Lawley-Maxwell's factor analysis book, page 77, the exponent is stated as "m-1", which means that Mplus uses m=4.
Hervé CACI posted on Wednesday, September 04, 2002 - 1:41 am
In some of my EFAs (i.e. the same variables in independent groups) I get loadings greater than 1.00 after PROMAX rotation. In other statistical packages, I used to resolve the problem by reducing the exponent. Wouldn't it be nice to add this option to Mplus ?
bmuthen posted on Wednesday, September 04, 2002 - 3:46 pm
In this situation the residual variances are negative. The residual variances are not affected by the rotation. You probably want to avoid this by extracting fewer factors.
bmuthen posted on Wednesday, September 04, 2002 - 4:34 pm
Correction - I was thinking VARIMAX and you said PROMAX - yes, different PROMAX exponents might be of some use in some situations.
Anonymous posted on Wednesday, September 04, 2002 - 7:56 pm
On the same note as above, is there anything fundamentally wrong with a Promax loading being greater than 1.00 given that these loadings are regression coefficients between the latent variables and the latent (continuous) indicators, rather than correlation coefficients?
bmuthen posted on Thursday, September 05, 2002 - 5:52 am
I think you are right. With say 2 factors, the PROMAX factor correlation can be negative so that the variance in an item due to the factors can be less than one, and the residual variance therefore positive, even with a loading greater than one.
Anonymous posted on Thursday, September 05, 2002 - 10:29 pm
Just to add my $0.02 to the above, another valid situation with Promax loadings greater than one in the two factor case is when the Promax factor correlation is positive (eg 0.7), one loading is negative (eg -0.5) and the other > 1.00 (eg 1.1), in which case the the explained variance for that item is less than one (=69% for the above) due to the cross-product term in the expression for the explained variance in an item being less than zero.
bmuthen posted on Friday, September 06, 2002 - 6:22 am
Good; taken together, this establishes that PROMAX loadings greater than one can legitimatly occur quite often, which reduces the need for choosing other PROMAX rotation exponents. Some reviewers, however, may incorrectly get nervous about loadings greater than one, but...
Hervé CACI posted on Friday, September 06, 2002 - 7:20 am
OK. Anyway, wouldn't it be useful to check that the loading>1 remains after the exponent has been reduced ? Some reviewers may ask for that ? Is it complicate to implement the option in Mplus ?
Covariates cannot be included in an EFA. CFA or EFA in a CFA framework can include covariates.
Anonymous posted on Wednesday, February 23, 2005 - 9:43 pm
I am new to Mplus and am exploring the use of it for my analysis. Does Mplus v.3 have a limit on the number of dichotomous variables and number of cases for EFA?
bmuthen posted on Saturday, February 26, 2005 - 4:47 pm
Mplus currently has a limit of 500 variables; no limit on cases.
Anonymous posted on Tuesday, August 23, 2005 - 11:44 am
Is there a way for MPLUS to show rotated factor loadings for a One-Factor EFA? Why are these values not shown in the output?
bmuthen posted on Tuesday, August 23, 2005 - 12:11 pm
There is no rotation with 1 factor. With m**2 indeterminacies in EFA with m factors, a 1-factor model has only one indeterminacy and that is taken care of by fixing the factor variance to 1. Beyond that there is no rotation/indeterminacy (except for changing signs of all the loadings).
amerywu posted on Wednesday, February 01, 2006 - 10:07 am
I am working on a new technique for EFA which needs the structure matrix output.
Can Mplus produce structure coefficients(i.e., correlations)in the output when the Promax rotation is used? I
amerywu posted on Wednesday, February 01, 2006 - 7:59 pm
Thank you very much.
If you don’t mind, I have another question regarding CFA. Can one use Chi squared difference test to investigate factorial invariance (i.e., strong & full invariance) between two groups for categorical data in the same manner as the multi-group CFA in LISREL for continuous data?
The models tested are not the same but the chi-square difference test can be used.
Model A: A model in which factor loadings and thresholds are freely estimated across groups. Factor means are fixed at zero and scale factors are fixed at one in all groups. Model B: (A model in which factor loadings and thresholds are held equal in all groups. Factor means are fixed to zero in one group and free in the others and scale factors are fixed to one in one group and are freely estimated in the other groups.
Is it possible to change the kappa for an EFA with a promax rotation? I understand that the default in M+ (from previous posting) is 3. The default for SPSS is k=4 but this can be modified in SPSS. Can I do it in M+?
I recently upgraded to MPLUS version 5 and am trying to find the best rotation option for my analysis.
Prior to the upgrade, I was using VARIMAX rotation for an Exploratory Factor Analysis with uncorrelated factors. But after reading the other posts that discuss the new (and improved) default settings in version 5, I am concerned that VARIMAX might be outdated and that version 5 might now offer better options. I see that orthogonal rotations can also be specified using other criteria: CRAWFER, GEOMIN, OBLIMIN, CF-VARIMAX, CF-EQUAMAX, CF-PARSIMAX, CF-FACPARSIM. Can you clarify whether or not VARIMAX is the best option?
For my specific analysis, the dataset has 378 observations; 36 factor indicators (a mix of continuous, binary, and ordinal variables), and anticipate that approximately 5-7 factors will be extracted. I want to get uncorrelated factors with high loadings on more than one factor. I am using the WLSMV estimator.
Thank you in advance for any feedback you can provide.
To learn more about EFA rotations, you may want to read the Cudeck-O'Dell article that the Mplus UG refers to as well as the Fabrigar et al (1999) Psych Meth article. Both are very useful factor analysis overviews. Many argue that correlated factors better represent substantive phenomena and give a simple factor loading pattern. In such cases the Mplus quartimin (default in v5) or geomin (default in v5.1) are suitable. But if your substantive reasoning calls for uncorrelated factors, then use CF-Varimax (Orthogonal) which is the new Mplus version of Varimax. I would not say that the Varimax method (cf-varimax orthogonal) is outdated.
For more technical comparisons of the rotation methods, see the technical appendix Exploratory Structural Equation Modeling - a new version of this, version 2, is to be posted shortly.
Only one rotation type is allowed for an analysis.
Kihan Kim posted on Thursday, October 16, 2008 - 7:08 pm
Hi, I ran a EFA with GEOMIN ratation (Mplus 5.1 default). The output shows "Geomin Rotated Loadings," and "Factor Structure." I'm reading "Geomin Rotated Loadings" as the factor loadings, and the "Factor Structure" as the correlation between each item and factor. Just want to confirm whether I'm reading the output correctly. Many thanks!
I have a few questions related to interfactor correlations and the factor weights in the pattern matrix. I have read in Gorsuch (1983) that the quartimin criterion produces solutions where factors are very highly correlated. Is this the same rotation procedure applied within Mplus? Also within Mplus, what is estimated first, the interfactor correlations or the factor weights, or are both estimated simultaneously? Does this depend on the rotation selected and how do the weights and interfactor correlations affect one another in the different rotations? It is somewhat convoluted to me as to how interfactor correlations and weights affect one another across the rotation methods within Mplus. Thank you!
Gorsuch refers to the old Carroll approach to quartimin, not the Jennrich direct quartimin Mplus uses. For a good and modern overview of rotations, see the Browne (2001) overview in MBR that the Mplus UG refers to.
As does most factor analysis programs, Mplus first estimates the factor loadings of an orthogonal model and then rotates from there. In the rotation, the orthogonality may be kept or relaxed to give a simpler pattern. Again, Browne is good reading here.
I've read the Brown (2001) article carefully as you suggested and have some questions. (1) From the ESEM paper with Asparouhov should the Varimax criterion in Appendix A be 1/p as opposed to 1/m? (2) I know that choosing a rotation is difficult, and I’m really struggling with how to say this, but can we not state that certain rotation methods will more accurately represent complex data structures? What I guess I’m really struggling here with is what is “truth.” I do understand that there is no right or wrong rotation, but can’t we say that certain ones will reproduce the true complex loading patterns better than other rotation methods? For this I mean within a simulation study with simulated data matrices looking at bias. Because when I look at simulation results it seems some rotation criteria reproduce known data patterns “better” than others. I guess my question is can we look at rotation methods and think of them in the confines of a simulation and look at bias? (3) Lastly, is a question about the standard errors for individual loadings in EFA. Cudeck (1994) provide a method for getting the critical Z under oblique rotation that takes into account the number of items and number of factors. I’m wondering if this is necessary for the standard errors from Mplus? As always thank you for the wonderful insight provided on this board. Best,
(1) There are typos in Appendix A. The new corrected Vesrion 5 of the technical paper will be posted next week. Thank you for pointing this out.
(2) I see nothing wrong with looking at the bias for different rotation methods. The true simple loading structure is easy to define usually, especially in a simulation study. Different rotation methods do lead to different MSE and bias when the estimated loading structure is compared with the simple loading structure. Looking at Bias and MSE should lead to the best rotation method, i.e., the method that recovers best the simple structure.
(3) I think you are referring to Cudeck O'Dell (1994) considerations regarding multiple testing for significance of loading parameters, where they propose a Bonferroni type adjustment of the p-value. If so, the same procedure applies to the Mplus standard errors.
Qi posted on Thursday, December 04, 2008 - 1:06 pm
I didn't realize the big change Mplus did in EFA until I ran it. It seems that geomin and quartimin are the default rotation in Mplus now and recommended oblique rotation methods. But what would be the recommended rotation method for orthogonal rotation? Thanks a lot!
Qi posted on Thursday, December 04, 2008 - 1:10 pm
When you recommended "CF-Varimax (Orthogonal)" which is the new Mplus version of Varimax, is it the same as the option of "Varimax" that's also available in Mplus? Thanks!
We used Mplus for an EFA simulation and it seems that we should take the cross-loadings and possibly also the interfactor correlations into account when calculating the residuals. From what I can see is that the communality calculations for a variable from (e.g., Gorsuch 1983, p.30) are a function of the primary loading, cross-loadings, and interfactor correlations, which in turn affects the size of the residuals. We used the equation: residual=1-lamda1^2+lambda2^2, with lambda1=loading on factor1 and lambda2=cross-loading on factor2. Notice, we did not take the interfactor correlation into account. We noticed in the Asparouhov and Muthen ESEM manuscript that they calculate the residual as 1-lambda^2 (p.27) and did not take into account the cross loading or interfactor correlation. Is there a reference or rationale for doing it this way? Perhaps more importantly, what equation is used to calculate the residuals?
Yes. In general the residual variance is a free parameter, not restricted to making the y variance add up to 1. With categorical outcomes and in EFA it is common to consider unit y (or y*) variance, but this is not necessary.
Lise Jones posted on Tuesday, October 13, 2009 - 12:05 pm
I have resently started using Mplus as I have a scale (20 items and 577 cases) with dichotomous variables and wanted to perform a FA. I have run an EFA with promax rotation as the variables are correlated. When reporting my 2 factor solution, do I report the promax rotated loadings or the factor structure? In the promax rotated loading some of the loading are negative..
It sounds like you are not using a version of Mplus that has the ROTATION option. Look at the top of the output to see which version of Mplus you are running. If you can't figure this out, please send the full output and your license number to firstname.lastname@example.org.
I renamed the old version exe-files with extension .old (e.g. mplus.exe.old). It solved the problem. Thanks!
luke fryer posted on Tuesday, September 07, 2010 - 11:41 pm
I have carefully read your most recent manual. I would like to read more about the rotations employed by Mplus so I can make sound choices. Could you point me in the right direction? Also, some of the rotations provide fit statistics some do not or only provide a few (the older ones I think). Is there a list somewhere describing which have them and which don't and why?
Bo Fu posted on Friday, October 22, 2010 - 8:56 am
Could the R package of mPlus can run all functions in mPlus, such as EFA and CFA, with all options, such as rotation?
Because I only have a 4.21 mPlus, and would like to do rotation in EFA. And today find that the R package is available. And have no enough time to read the document well. Just wondering whether I could do EFA with rotation in this R package. Thank you so much for answering!
No, the R package will not extend the features of the version of Mplus you are using.
QianLi Xue posted on Thursday, November 11, 2010 - 9:50 am
Hi, The following is the example given in the user's guide on page 44:
TITLE: this is an example of an exploratory factor analysis with continuous factor indicators using exploratory structural equation modeling (ESEM) DATA: FILE IS ex4.1b.dat; VARIABLE: NAMES ARE y1-y12; MODEL: f1-f4 BY y1-y12 (*1); OUTPUT: MODINDICES;
In the text following this, it states "When no rotation is specified using the ROTATION option of the ANALYSIS command, the default oblique GEOMIN rotation is used." But when I added the ANALYSIS with rotation=PROMAX, it gave an error message saying rotation is only available for Type=EFA. Is there a different way to request other types of rotations in ESEM?
I understand that a good way to do an Exploratory Factor Analysis is to do an oblique rotation first and then an orthogonal rotation. Is there any way to do this in Mplus - I can't seem to figure out how to do this. Thank you
See the ROTATION option in the user's guide where several oblique and orthogonal rotation settings are available.
Elina Dale posted on Monday, October 28, 2013 - 10:51 pm
Dear Dr. Muthen,
I have read Sass & Schmitt article. Thank you for recommending it.
However, I'd greatly appreciate it if you could clarify the following 3 points: 1. Geomin a default oblique rotation in MPlus. Why? From Sass & Schmitt it didn't seem like it always outperformed other oblique rotation methods.
2. Promax seems to be used far more often than Geomin, but Sass & Schmitt don't discuss its (dis)advantages compare to Geomin. My prof thinks I should use Promax instead of Geomin. Could you please, clarify what are the main minuses of Promax, beside what you wrote earlier about limited fit stats?
3. They say that when using Geomin, a researcher should decide whether to modify ϵ parameter. What is the default value of this parameter in Mplus? How does one modify it?
I would try several different rotations to learn about your data. Note that all rotations fit the data the same.
1. The 2001 Browne article that we refer to in the UG gives good arguments for the value of Geomin. The simulations that Sass & Schmitt do are difficult to draw conclusions from as they point out on page 99 in the paragraph starting with "Despite..." - see also the Asparouhov-Muthen (2009) reference they refer to on that.
2. Promax is an older (superseeded?) rotation. Quartimin was developed to replace it and quartimin is outperformed by Geomin according to Browne (2001). One Promax drawback is that you have to choose the degree of correlatedness among the factors. Furthermore, Browne(2001) on page 117 says:
"Although a simple structure is known to exist, and can be recovered making use of prior knowledge, Thurstone’s box data pose problems to blind rotation procedures (Butler, 1964; Eber, 1966; Cureton & Mulaik, 1971). Well known methods, such as varimax and direct quartimin, that are available in statistical software packages, fail with these data. This is due to the complexity of the variables rather than to their nonlinearity. Other artificial data can be constructed to yield similar problems (e.g. Rozeboom, 1992) without any involvement of nonlinearity." - You may want to try Promax on the Box data.
3. No need to modify the Geomin settings in Mplus.
Elina Dale posted on Tuesday, October 29, 2013 - 6:34 pm
I have a set of 18 ordinal or likert type items for doing EFA..I have some specific queries: 1. Which rotation method is appropriate for ordinal data? can we use VARIMAX...or GEOMIN has to be used.
2. How do we fix the factor loading to a minimum value so that the values lower to that do not appear on the final rotatted matrix.
3. How to find % variance explained by each factor?
4. Based on 1-F, 2-F, 3-F,4-F models for my data two of them are having adequate GOF for being significant from CFI/TLI, RMSEA, Chi square for base/ SRMR....all means as per your technical appendices TLI>0.95, CFI>0.95, RMSEA<0.06 so how to choose over one model than another?
5. If there is any specific issue related to selection of Estimator for Ordinal data.
6. As I am a new user of MPlus please suggest me if there are some other guidelines for using Ordinal data for EFA..in MPLus
3. With orthogonal factors, sum the squared factor loadings and divide by the number of factor indicators.
4. Substantive theory and the dimensions for which the items were developed.
5. You can use weighted least squares or maximum likelihood. Maximum likelihood has better missing data handling. Maximum likelihood requires one dimension of integration per factor so can become computationally heavy. Weighted least squares has an advantage when there are many factors because it does not require numerical integration.
You should study the Topic 1 course video and handout on the website. It goes over EFA in detail. See also, the PARALLEL option in the user's guide.
Cheng posted on Sunday, December 27, 2015 - 9:07 pm
This is my first time to run EFA in Mplus. Just would like to confirm: 1.The factor loading (pattern structure) I suppose to read is "Geomin rotated loadings" right? 2. I have one item with negative loading >0.5. Can this be due to the item is reverse score? Or is there any other reason why it can be negative? 3. For model fitness, can we just rely on SRMR<0.05 (I followed your video on topic 1)? Or we need to make sure other fit indices (CFI/TLI, RMSEA) are fit like in CFA?
Juerg Schmid posted on Wednesday, August 24, 2016 - 10:39 am
Dear Linda In doing bifactor-ESEM using orthogonal target rotation (Mplus version 7.3), we ran into convergence problems (WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED VARIABLE, ...). We are pointed towards a particular observed variable which has a small negative residual variance. When we tried to restrict this residual variance to a value > 0 (using the MODEL CONSTRAINT OPTION in the MODEL block), we observed that this constraint is not taken into account and the problem persists. Moreover, no warning is issued that, for example, this option is not available. However, if we just apply another rotation technique, i.e., orthogonal BI-CF-QUARTIMAX and orthogonal BI-GEOMIN, the MODEL CONSTRAINT command works perfectly alright. May we kindly ask you for a pointer into the right direction?