Message/Author 

Anonymous posted on Friday, October 29, 1999  11:43 am



What kind of rotations does Mplus use? 


Mplus uses the varimax for orthogonal rotations and promax for oblique rotations. 

Anonymous posted on Wednesday, July 04, 2001  12:33 am



I am sorry but I am experiencing some difficulties having Mplus read my summary data set (corr matrix) for a EFA. I am receing this error message: (Err#: 29) Error opening file: EIHMa.dat Here is my syntax: DATA: FILE IS EIHMa.dat; NOBSERVATIONS = 650; TYPE=CORRELATION; VARIABLE: NAMES ARE v1v10; ANALYSIS: TYPE = EFA 1 2; ESTIMATOR=ML; Here is my data file: 1.000 0.610 1.000 0.361 0.292 1.000 0.679 0.664 0.358 1.000 0.602 0.501 0.397 0.560 1.000 0.800 0.663 0.374 0.710 0.601 1.000 0.478 0.493 0.218 0.447 0.439 0.491 1.000 0.421 0.359 0.322 0.419 0.377 0.441 0.241 1.000 0.280 0.291 0.142 0.288 0.319 0.339 0.404 0.328 1.000 0.315 0.293 0.162 0.330 0.278 0.318 0.320 0.230 0.241 1.000 0.466 0.439 0.306 0.481 0.505 0.487 0.537 0.432 0.542 0.369 1.000 


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 MPlus 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 LawleyMaxwell's factor analysis book, page 77, the exponent is stated as "m1", 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 crossproduct 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 ? 


No, it is not complicated. I will add it to our long list of future development ideas. 

Hervé CACI posted on Wednesday, September 11, 2002  7:12 am



Just a reference I picked up recently: Tataryn DJ, Wood JM and Gorsuch RL (1999) "Setting the value of k in PROMAX: a MonteCarlo study", Educational & Psychological Measurement, 59(3), pp.384391. 

bmuthen posted on Saturday, September 14, 2002  8:17 am



The note below by Joreskog gives a good account of why standardized values greater than one are acceptable: http://www.ssicentral.com/lisrel/column2.htm 

Anonymous posted on Tuesday, November 16, 2004  10:09 am



Does MPLUS EFA with dichotomous variables have a method for partialing out the variance contributed to a factor structure by a covariate? or is this something that can only be done through CFA? 


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 OneFactor 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 1factor 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 Thanks 


No. This cannot be done. 

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 multigroup CFA in LISREL for continuous data? Thanks! 


The models tested are not the same but the chisquare 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. 

gerry leyna posted on Sunday, February 05, 2006  5:17 am



Hi what is the commonly used default (delta)in CFA when attempting an oblique rotation? G Leyna 


We use m=4. See page 77 of Factor Analysis as a Statistical Method by Lawley and Maxwell. 

Bani posted on Wednesday, February 08, 2006  10:39 am



Please assist! How do I specify oblique rotation in EFA. Thanks so much. 


You don't need to specify it. Both oblique and orthogonal are given as the default. 

Nitikul C posted on Thursday, October 05, 2006  12:04 am



I don't know what MPlus is, but I'm only interested in SPSS. In SPSS, how do I use varimax rotation? And what results do we actually look for in this? Any websites? Also, factor analysis, regression and correlation do not compute the categorical variables such as male=1, female=2, or Secondary grade 1,2,3,4,5,6. How do I recode this? I have checked dummy coding, I couldn't understand when one variable has more than 3 values (or up to 6). Any other ways to input categorical into factor analysis, regression (stepwise), and correlation (spearman)? Please please help. 

Nitikul C posted on Thursday, October 05, 2006  12:09 am



Oh are you only discussing MPlus? Anyone who could help me with SPSS please....... 


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+? Thank you so much. 


There is no option to do this in Mplus currently. 

Maggie Chun posted on Tuesday, January 29, 2008  8:16 am



Dear Dr. Muthen, How was your trip? I met a basic problem: a scale with severe right skewed data. I tried to dichotomize all items, but EFA could not continue because of lossing too much information. Could I just delete all cases with zero sum score of the scale but keeping it as a ordinal scale? Is this method acceptable? Thank you very much for your time! Maggie 


I'm not sure I totally understand your problem. If your original variables were ordinal with a floor or ceiling effect, I would use WLSMV on the original variables. 


Why does Mplus output no CFI/TLI with promax rotation? 


We did not implement these fit statistics for the old rotations. I suggest using the better performing rotations of Geomin or Quartimin. 


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, CFVARIMAX, CFEQUAMAX, CFPARSIMAX, CFFACPARSIM. 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 57 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 CudeckO'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 CFVarimax (Orthogonal) which is the new Mplus version of Varimax. I would not say that the Varimax method (cfvarimax 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. 


Hello Linda and Bengt. I'm running some EFAs and would like to have two different rotations for the same solution in the same output, is there a command, or some trick? I tried "ROTATION = GEOMIN CFVarimax (Orthogonal)" but it's not working, only the geomin was computed. 


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! 


You are reading the output correctly. 


Hello Linda and Bengt: 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! Tom 


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. 


Hello Linda and Bengt: 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, Tom 


(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 pvalue. If so, the same procedure applies to the Mplus standard errors. 


Thank you Tihomir! 

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



Dr. Muthen, When you recommended "CFVarimax (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! 


Yes, Mplus has added quite a lot to its EFA capabilities, also including EFASEM (see ESEM paper on our web site under SEM). CFVarimax(Orthgonal) is the same as the old Varimax, except that the old Varimax automatically includes row standardization (which you can request in the new rotation). 

Qi posted on Monday, December 08, 2008  8:37 am



Thanks, Dr. Muthen! So CFVarimax is better than the old Varimax? Why? Thanks again. 


They are the same if you use row standardization in CFVarimax. CFVarimax is our newer track for doing Varimax and can also be used in exploratory SEM, so I would recommend it on those grounds. 


Hello, Concerning example 11.5, could you tell me how the residual values of .51 and .36 where calculated. Thank you! Tom 


Just to clarify this question a little further. I understand that you took 1.49^2=.51, but don't you have to take into account the correlation between factors when calculating the residual? 


Correction: 1.7^2=.51 


The covariance between the factors is not involved when the factors have different factor indicators as in Example 11.5. 


Hello Linda, We used Mplus for an EFA simulation and it seems that we should take the crossloadings 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, crossloadings, and interfactor correlations, which in turn affects the size of the residuals. We used the equation: residual=1lamda1^2+lambda2^2, with lambda1=loading on factor1 and lambda2=crossloading 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 1lambda^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? Tom 


When an item loads on 2 correlated factors with unit variances and loadings lambda1 and lambda2, the variance of the item is V(y)= lambda1^2 + lambda2^2 + 2*lambda1*lambda2*psi21 + V(e), where psi21 is the factor covariance (correlation) and V(e) is the residual variance. So the factor correlation certainly needs to be taken into account. I don't think the AM ESEM paper claims a total V(y)=1, so maybe that's where the confusion arises. 


If I understand you correctly, it sounds like it is a standardization issue. If V(y) is not set equal to 1, then the value of the residual is arbitrary? 


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. 


TYPE=COMPLEX with ESTIMATOR=ML gives maximum likelihood. TYPE=COMPLEX with ESTIMATOR=MLR gives pseudo maximum likelihood. When Chisquare is available CFI is automatically given. I don't know what you mean by PLL. 


Thank you Bengt and Linda! 

Lise Jones posted on Tuesday, October 13, 2009  12:05 pm



Hello, 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.. 


Typically, the loadings ("factor pattern") are of primary interest. Negative loadings can be interpretable. 


Hi! I may miss something very elementary, but using syntax in 5.21: VARIABLE: NAMES ARE r g c e1e40 a1a18 ; USEVARIABLES ARE e1e40 ; USEOBS IS c eq 2 ; ANALYSIS: TYPE = EFA 6 6 ; ROTATION = GEO ; ESTIMATOR = ML ; the run fails. If I remove (or exclamete) the ROTATION line it gives VARIMAX and PROMAX rotations. Using it like above I get the following error: *** ERROR in Analysis command Unknown option: ROTATION How should ROTATION be defined? 


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 support@statmodel.com. 


This was printed in the outfile: Mplus VERSION 4.1 MUTHEN & MUTHEN 11/10/2009 4:12 PM Really!!! Mplus 5.21 syntax run activates Mplus 4.1 which executes the commands! How is this possible? Should the earlier version be unistalled? These program versions are installed (of course) in different subfolders in Program files directory. The new 5.12 just (two weeks ago) came from Statmodel and I did the installation today. 


You should uninstall Version 4 before you install Version 5.21. Mplus uses the first Mplus.exe file it finds and it sounds like that is Version 4.1. 


I renamed the old version exefiles with extension .old (e.g. mplus.exe.old). It solved the problem. Thanks! 

luke fryer posted on Tuesday, September 07, 2010  11:41 pm



Dr. Muthen 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? luke 


See the following two papers on the website: Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397438. Sass, D.A. & Schmitt, T.A. (2010). A comparative investigation of rotation criteria within exploratory factor analysis. Multivariate Behavioral Research, 45, 73103. and the Browne (2001) reference from the user's guide. PROMAX and VARIMAX have a limited set of fit statistics. The newer rotations have a larger set of fit statistics. 

Bo Fu posted on Thursday, October 21, 2010  11:25 pm



May I ask whether ROTATION is available in version 4.21? I don't see any example using ROTATION in the three examples provided (4.1,4.2,4.3) 


The ROTATION option was added in Version 5. 

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 y1y12; MODEL: f1f4 BY y1y12 (*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? 


It sounds like you are using an older version of the program where ESEM is not available. If not, please send your output and license number to support@statmodel.com 


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? Thank you! 


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 AsparouhovMuthen (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



This is very very helpful! Thank you! 

Back to top 