Using and calculating Factor scores
Message/Author
 sarah vidal posted on Sunday, January 26, 2014 - 12:42 pm
I conducted CFA on 2 constructs-- construct 1 has 3 latent factors and construct 2 has 4. I wanted to use these factors for follow-up analyses; more specifically, path analysis. I'm not sure about the best way to use the factor scores in path analysis. I know there are pros and cons about different methods and the following methods have been suggested to me:

-average the indicator scores by factors
-weighted sum scores
-factor scores via CFA

Does using any of these methods significantly affect the results of path analysis? Can I use latent variables in path analysis?

I plan to include other variables in my model-- and these are all observed variables.

I'd greatly appreciate any input. Thanks!
 Bengt O. Muthen posted on Sunday, January 26, 2014 - 12:59 pm
I would recommend using neither of your 3 approaches but instead use the latent variables in your path analysis. They can be used together with your other observed variables.
 s2014 posted on Sunday, January 26, 2014 - 1:39 pm
Thanks for your quick response. I tried to use the latent variables in my path analysis; however, I got the following message:

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE
DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A
LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.
CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y8DSDELI.

I'm new to MPlus so I'm not sure if it's my model specification or if it's how I coded the outcome variable Y8DSDELI.
 Linda K. Muthen posted on Sunday, January 26, 2014 - 3:15 pm
Please send the output and your license number to support@statmodel.com.
 s2014 posted on Friday, February 07, 2014 - 7:29 pm
Hi Drs. Muthen and Muthen,

I have a question about specifying a correlation in a model:

outcome on latent1 latent2 latent3;

1. Does MPlus automatically assume that latent1 latent2 latent3 are correlated with one another? And the same goes for all independent variables in a regression model?

2. If I want to specifically specify that latent1 and latent2 are positively correlated and neither is correlated with latent 3, is the following syntax correct:

outcome on latent1 latent2 latent3;
latent1 with latent3;
latent3 with latent1@0 latent2@0;

3. If #1 is correct and I would not like for variables to correlate, do I always specify this in my model by using a command such latent3 with latent1@0?

4. Do the following commands differ from one another mathematically (i.e., how MPlus would fit my model)?

command 1:
latent1 latent2 on x1 x2 x3 ;
[does this mean that latent1 is correlated with latent2? and if not, do I specify it in my model as latent1 with latent2?]

command 2:
latent1 on x1 x2 x3;
latent2 on x1 x2 x3;

Thank you!
 Linda K. Muthen posted on Sunday, February 09, 2014 - 9:19 am
The best way to see what is correlated by default is to run the analysis and look at the results.

You fix a factor correlation/covariance to zero by f1 WITH f2@0.

latent1 latent2 on x1 x2 x3 ;

is the same as

latent1 on x1 x2 x3;
latent2 on x1 x2 x3;
 Tan Bee Li posted on Saturday, July 02, 2016 - 2:41 am
I examined the factor structure of items from a questionnaire. The two models examined were:
Model 1: A correlated five-factor model
Model 2: A higher-order five factor model whereby a higher-order factor explains the variances of the five first-order factors.

Will the factor scores generated for the five factors be the same for both models? Or will additional variances be extracted from the five factors in model 2?

Is there a reference I can refer to for the formulas?

Thanks.
 Bengt O. Muthen posted on Saturday, July 02, 2016 - 6:10 pm
Model 2 has a different fit than Model 1 - it constrains the factor covariance matrix for Model 1. So given that they are different models your factor scores will be different.

I don't know about a reference.
 Tan Bee Li posted on Sunday, July 03, 2016 - 6:18 am
Dear Dr. Muthen,

Thanks for the prompt response.