Separate Models vs Combined Model: Why are they Different?

[E. Bernardo]

Dear ALL,

 

I have three constructs (X, Y and Z), each with three indicators ( 6-point likert scale response format). 

 

The model is simply: X causes Y and Z .  Symbolically,  X-->Y and X-->Z. Using n=500, the model has an ill fit (chisquare=915.112, df=25, p=.000).

 

However, when the model was separated, each model has an acceptable fit as follows:

 

Model 1: X causes Y: (chisquare=10.4, df=8, p=.24) 

 

Model 2: X causes Z (chisquare=11.6, df=8  p=.18)

 

Any comment why the results are different?

 

Thank you.

Eins

 

 

[Mike]

I admit to being somewhat confused by what you say below.  You say

you have a model but don't specify what analysis you're doing.  At first

glance, one might think that you are doing a multivariate regression of

Y and Z on X (for a Stats example of this, see:

http://www.ats.ucla.edu/stat/stata/dae/mvreg.htm )

But you say that X, Y, and Z each has three indicator variables which

(a) suggests that you have a measurement model of each construct and

(b) you are doing a structural equation (SEM) analysis for the latent variable

X, Y, and Z. 

 

If you are doing a SEM analysis, which software package are you using

and what type of analysis are you doing (e.g., Maximum likelihood, etc.)?

A simplistic answer to your question is that the errors of Y are correlated

with the errors of Z and this causes your model to fail under the assumption

of independent errors.  Obviously, when run as seperate models, the

correlated error are not apparent because there is no opportunity for

them to manifest themselves.  Allowing some of the errors to correlate

may give the more comprehensive model a better fit but  I note that this

is a simplistic explanation because there is so much more that needs to be

known about the data and your analysis before a more credible answer

can be given.

 

If this is a SEM question, you might want to try the asking the SEMNET

list as well.

 

-Mike Palij

New York University

[hidden email]

 

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Sunday, November 07, 2010 9:01 AM

Subject: Separate Models vs Combined Model: Why are they Different?

Dear ALL,

 

I have three constructs (X, Y and Z), each with three indicators ( 6-point likert scale response format). 

 

The model is simply: X causes Y and Z .  Symbolically,  X-->Y and X-->Z. Using n=500, the model has an ill fit (chisquare=915.112, df=25, p=.000).

 

However, when the model was separated, each model has an acceptable fit as follows:

 

Model 1: X causes Y: (chisquare=10.4, df=8, p=.24) 

 

Model 2: X causes Z (chisquare=11.6, df=8  p=.18)

 

Any comment why the results are different?

 

Thank you.

Eins

 

 

[David Marso]

As Mike stated.
  You are in no way accounting for any structural relations between Y and Z.
Probably need to review your SEM and other things.
David

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