Target rotation
Message/Author
 Sung Kim posted on Friday, September 14, 2012 - 5:23 pm
In the Mplus Users Guide (p. 540), "a minimum number of target values must be
given for purposes of model identification." For example, "For the orthogonal TARGET rotation, the minimum is m(m-1)/2."

I am a little confused. Is it "the minimum or less" or "the minumum or more"? For example, I have 6 orthogonal factors and the minimum is 15. Can I specify more than 15 target values? I guess it is 15 or less. Is that correct?
 Linda K. Muthen posted on Friday, September 14, 2012 - 6:12 pm
You can specify more than the minimum but not less. So 15 or more.
 david  posted on Thursday, February 14, 2013 - 6:36 am
Hello Dr's

I am running an EFA over bootstrap samples. For each output loadings matrix i would like to be able to keep the same factors with each group of similarly loading variables i.e. to stop the factor / factor names 'jumping about'.

Within R i do this by rotating to the original data loading matrix. I have tried this in mplus using the target rotation option but i dont think this is what its for - a model is not identified if i supply a target loading for each variable for each factor - or if it is possible whether i am doing it corretly.

a bit of my (nonsense) code

ANALYSIS: TYPE = general;
ROTATION = target(orthogonal);

MODEL:
f1 BY var1 var2 var3 var4....
var1~0.857
var2~-0.099
var3~0.615
...
(*1);

f2 BY var1 var2 var3 var4...
var1~0.062
var2~0.204
var3~0.211
...
(*2);

f3 by var1 var2 var3 var4...
var1~0.125
var2~-0.068
var3~0
...
(*3);

Am i pursuing a wrong path here?

thnaks, david
 Tihomir Asparouhov posted on Thursday, February 14, 2013 - 9:03 am
Mplus doesn't currently implement the bootstrap for EFA. If you have generated however your bootstrap samples you can get the bootstrap standard errors by analyzing them with external montecarlo using an ESEM model. You don't need to worry about factor names jumping around because that is taken care of within the program. For that take a look at Appendix D in
 david  posted on Friday, February 15, 2013 - 3:18 am
Thank you Tihomir.

This is what i am looking for. Unfortunately i am having problems in getting the montecarlo method to run.

The DOS screen indicates that the first sample is geting analysed but i then receive a warning 'The input setup produced syntax warnings/errors causing Mplus to abort.'

I get the limited output when i run the commands below.

Errors for replication with data file c:\myaddress

*** FATAL ERROR
FACTOR LOADING STARTING VALUES OF A FACTOR ARE ALL ZERO. LEASTSQUARES ALIGNMENT METHOD REQUIRES AT LEAST ONE NON-ZERO STARTING VALUE.'

The model produces results if i run the commands (with montecarlo excluded) on the individual datasets.

I have set up a directory with all bootstrap samples and a .dat file with a list of the bootstrap sample names - as is shown in ex12.6, part 2.

Do the warnings over zero cells prohibit using montecarlo or do you notice an omission in my syntax?

Sorry to bother you again and thanks for any help.

bw, david

Syntax:
TYPE = MONTECARLO;

VARIABLE: NAMES = var1 var2 ....... var40;

CATEGORICAL = var1 - var40;

MISSING = .;

MODEL: f1-f4 BY var1 - var40 (*1);

ANALYSIS: ROTATION = oblimin;
 Linda K. Muthen posted on Friday, February 15, 2013 - 10:40 am
 C. Lechner posted on Tuesday, June 07, 2016 - 2:30 am
I applied an ESEM with oblique target rotation and an ESEM model with geomin rotation to the same set of variables.
I specified target loadings of 1, -1, or 0 for each variable and factor.

In comparing the models, I noticed that the factor correlations between the EFA factors were very different. Despite strikingly similar patterns of primary and secondary loadings, correlations were roughly twice as high in the target rotated ESEM compared to the geomin rotated ESEM. Even in a CFA applied to the same set of variables, factor correlations were much lower than in the target-rotated EFA.

Note that...
a) my EFA model consists of a brief instrument measuring 5 factors by only 11 items (4 factors by 2 items, 1 factor by three items)
b) the output gave no error message in any of the models, and model fit was good
c) Increasing rstarts, riterations and iterations does not remedy this finding.

Do you have any idea what the reason for this marked difference in factor intercorrelations is? Could it point to problems in identifying the optimal rotation?

Thank you!
 Tihomir Asparouhov posted on Tuesday, June 07, 2016 - 3:23 pm
Using -1 and 1 as targets is fairly unusual and you might be forcing in a strange rotation. Pick a minimum of 4 zero targets for each of the 5 factors and estimate teh target rotation again. I would guess that geomin is better as it picks more clear and independent dimensions.

Note that fit is identical. If the loadings are the same the factor correlations will be the same.
 Juan Ramón posted on Monday, July 31, 2017 - 7:15 am
When I run this:
MODEL: F1 BY i1 i5 i13 i16 i20 i23 i25
i30 i32 i3 i8 i10 i28
i4~0 i7~0 i11~0 i14~0 i17~0 i19~0 i22~0
i26~0 i29~0 i31~0
i2~0 i6~0 i9~0 i12~0 i15~0 i18~0 i21~0
i24~0 i27~0 i33~0 (*1);
F2 BY i4 i7 i11 i14 i17 i19 i22
i26 i29 i31
i1~0 i5~0 i13~0 i16~0 i20~0 i23~0 i25~0
i30~0 i32~0 i3~0 i8~0 i10~0 i28~0
i2~0 i6~0 i9~0 i12~0 i15~0 i18~0 i21~0
i24~0 i27~0 i33~0 (*1);
F3 BY i2 i6 i9 i12 i15 i18 i21
i24 i27 i33
i1~0 i5~0 i13~0 i16~0 i20~0 i23~0 i25~0
i30~0 i32~0 i3~0 i8~0 i10~0 i28~0
i4~0 i7~0 i11~0 i14~0 i17~0 i19~0 i22~0
i26~0 i29~0 i31~0 (*1);
i3 WITH i8 i10 i28;
i8 WITH i10 i28;
i10 WITH i28;
i2 WITH i6;
i4 WITH i19;
i26 WITH i29;

I get this warning message:
*** WARNING in MODEL command
Fewer than 6 loadings have been given target values in EFA set *1.
The model may not be identified.

After that, I get all the results without problems.

I don't understand why it says that "fewer than 6 loadings have been given target values". As I understand the code, much more than six have received 0 values (~0).

Thank you very much.
 Linda K. Muthen posted on Monday, July 31, 2017 - 9:00 am