Correlation matrix of lataent variables
Message/Author
 Richard Wonner posted on Tuesday, July 09, 2013 - 12:37 pm
Hello all,

I am doing a SEM with a dataset. I was asked to provide a correlation matrix for the latent variables and was provided with the following sample:

****************Sample start*************
Variables_______1_______2_______3_____4

1. LatentVarA 1.00
2. LatentVarB 0,768** 1.00
3. LatentVarC 0,561** 0,677** 1.00
4. LatentVarD 0,060__ 0,000__ 0,05__1.00

Notes: * Correlation is significant at the 0.01 level (2-tailed), ** = Correlation is significant at the 0.05 level (2-tailed), *** = Construct measured through single indicator
****************Sample end*************

I learned that I would have to use TECH4 to get the correlation matrix. My question would be - how do I get the significance levels?
I would be interested:
1) In the command I have to use.
2) How to interprete the output of that command.
 Linda K. Muthen posted on Tuesday, July 09, 2013 - 2:57 pm
If they are available, you will get them automatically. They came out in Version 7.1.
 Richard Wonner posted on Tuesday, July 09, 2013 - 10:04 pm

Would the significance levels be available in the table as askerisk or do I have to interprete a certain parameter - which one?

If they would be not available, what would be the cause?
 Linda K. Muthen posted on Wednesday, July 10, 2013 - 12:24 pm
We give the estimates and standard errors. You would have to determine the significance yourself by looking at the ratio of the estimate to its standard error which is a z-score in large samples.

If they are not available, they have not yet been developed.
 Richard Wonner posted on Wednesday, July 10, 2013 - 2:36 pm
So to see if my two constructs RM and WOM have a significant correlation I got the following output:

Correlations
________RM_______RM_SE____WOM____WOM_SE
RM______1.000
RM_SE___0.013____1.000
WOM_____0.495___-0.029____1.000
WOM_SE_-0.011____0.988___-0.035__1.000

Now I would devide
(a) |0.495/-0.029|
(b) |0.495/-0.011|

(if >2.58 => 0.495**)

I can't decide if (a) or (b) would be right or if I got you wrong.
 Linda K. Muthen posted on Wednesday, July 10, 2013 - 2:40 pm
You divide the correlation by its standard error. I can't follow what you are showing. If the ratio is greater than 1.96, it is significant. If this does not answer your question, send the output and your license number to support@statmodel.com.
 Richard Wonner posted on Wednesday, July 10, 2013 - 10:09 pm
Maybe it is a problem with my English. I understand ratio as

something / something else

and I understood you the way that

something = estimate (of the correlations?)
something else = standard error.

Sorry for me asking such basic questions but I could not find a description of "How to do a correlation matrix of latent variables" anywhere.
 Linda K. Muthen posted on Thursday, July 11, 2013 - 7:01 am
The ratio is

correlation/standard error of correlation
 Richard Wonner posted on Thursday, July 11, 2013 - 11:56 am
Now I got it - thanks for you patience.
 Angelique van Rensburg posted on Monday, January 06, 2014 - 3:18 am
Dr's Muthen,

I am really new to Mplus - I am trying to calculate the significance of the correlations between various latent variables - I get a correlation matrix (TECH4) but not matrix for standard errors - how will I be able to do this?
 Angelique van Rensburg posted on Monday, January 06, 2014 - 3:54 am
Or wont you be able to calculate them because latent variables don't have means?
 Angelique van Rensburg posted on Monday, January 06, 2014 - 4:07 am
Or wont you be able to calculate them because latent variables don't have means?
 Linda K. Muthen posted on Monday, January 06, 2014 - 7:02 am
The current version of Mplus gives standard errors for TECH4 in most cases. If you don't have this, you will need to define the correlations in MODEL CONSTRAINT.
 Angelique van Rensburg posted on Monday, January 06, 2014 - 7:14 am
Dr Muthen,

Thank you for your response - I have tried using WITH statements, but I get errors. Does this possibly mean my model is incorrectly specified?
 Bengt O. Muthen posted on Monday, January 06, 2014 - 8:19 am
Not enough information to go on. If TECH4 doesn't give you what you want, send your output to Support.
 Sindra Sharma-Khushal posted on Monday, October 06, 2014 - 5:16 am
Hi there, I was hoping to include a correlation matrix with latent and endogenous variables for my paper. My question is with v6 of MPlus how can I go about creating this matrix. I have the correlations from Tech4 but how do I get the standard errors so that I can calculate the p values?

Do we use the correlations and p values offered by 'with' statements?
 Bengt O. Muthen posted on Monday, October 06, 2014 - 7:53 am
You would use Model Constraint to express the correlations in terms of the labels of model parameters. This gives you the SEs.
 Sindra Sharma-Khushal posted on Monday, October 06, 2014 - 9:12 am
Thank you for your reply. I don't quite understand - would I specify model constraints as for example:
family with x1 (a1)
x2 (a2)
x3 (a3) etc;
 Bengt O. Muthen posted on Monday, October 06, 2014 - 10:49 am
No. Look at the UG ex 5.20 to give you and idea of the general approach.