# amos: zero chi-quare and zero df confusion

I have five concepts in a theoretical model (animosity, ethnocentrism, religiosity, patriotism, satisfaction). The EFA result shows that there is only one actor for each construct:

• f1 (animosity) with 3 indicators.
• f2 (ethnocentrism) with 9 indicators.
• f3 (religiosity) with 3 indicators.
• f4 (patriotism) with 5 indicators.
• f5 (satisfaction) with 8 indicators.

according to SPSS results: the relations between each two factors are linear, with normal distribution. the test of multivariate normality by AMOS gives a Mardia of 2.654. Sample size = 650.

But: when i try to conduct a CFA in AMOS for each factor separately AMOS shows great results for f2,f4 & f5. With F1 there is no df also no chi-square. The same thing with F3.

I searched the internet for an explanation & I found that this means the measurement model with no df & no chi-square is saturated & nothing can be reported. And here there is who would say that this model has a well fit while others may say that this is not the case. So, what i really need to know is:

1. how to treat such case (df=0 & chi2=0) in my thesis?
2. can I include such factors with such case in the overall measurement model & the path model to test hypothesis?
3. Which better: to have a CFA for each concept separately or to do it for an overall model?

1. A CFA with three indicator variables and one latent variable is saturated (it's also called just-identified). It has zero degrees of freedom, and it cannot have a chi-square. It is impossible for the model to be wrong, and the fit is meaningless. It doesn't matter what your data look like, the model will fit perfectly.
2. Yes, they are identified when you have additional factors. A factor analysis with two factors with three items each is identified.
3. Overall.
• @JeremyMiles is it possible to add references?
– Iman
Sep 28, 2018 at 17:18
• Any intro SEM/CFA book will cover model identification. A search gave me: davidakenny.net/cm/identify_formal.htm Sep 28, 2018 at 17:46