Solved – “The model is probably unidentified” AMOS

amosconfirmatory-factorstructural-equation-modeling

I am doing a CFA in AMOS and I keep getting the error message: "The model is probably unidentified. In order to achieve identifiability, it will probably be necessary to impose 1 additional constraint."

I have attached the model that I am trying to run. So I have 6 factors with 3 – 6 items in each factor. I have a sample of 350.

Is there anything wrong that I am doing with my analysis? Thanks!

Best Answer

It looks to me like you don't have one of the loadings from the first latent constrained to 1, but you do on the others. Make sure each of the latent variable have at least a path to the observed variables fixed to 1. This is required for identifiability of the model.

Main Point

With only two observed variables per factor, the latent variable can not generally be estimated. Having correlations between factors presumably adds enough constraints to the model to allow estimation of the latent factors, but without those correlations, the latent factors are not estimatable.

What should you do?

Add more observed variables per factor. If you have three or more observed variables, your latent factors will generally be estimatable.
Constrain factor loadings to be equal. As a secondary option, you could constrain you factor loadings for the two items to be equal. Make sure they are on the same scale so that this makes sense.

I think the option of having at least three observed variables per factor is preferable.

Note also that setting the covariance between each factor to 1 will not create uncorrelated factors. If the factors have unit variance (i.e., like z-scores), then your factors will perfectly correlated (r=1). Thus, it would be equivalent to having a single factor. If the factors do not have unit variance, then it be constraining some other specific correlation structure that is related to the variance of each of the factors.

Comments below relate to the original post prior to the update.

Degrees of freedom

If you constrain a parameter to be a constant, then you should get an additional degree of freedom in an SEM. Thus, when you specify $k$ latent factors to be uncorrelated, then that implies you are specifying $k(k-1)/2$ potential parameters to be zero and you should have that many additional degrees of freedom.
If you are constraining $k$ latent factors to have a common covariance, then you should get $k(k-1)/2 - 1$ additional degrees of freedom, because you are still estimating one parameter.

So why might your degrees of freedom not be changing? Here are a few thoughts:

Have you included the second order factor in your model testing the first-order model? If you have, remove the second-order factor.
Have you specified constraints correctly in Amos?

Constraining factor correlations to be equal

Note that in social sciences, it is often the correlation between factors that is conceptualised to be approximately the same from a theoretical perspective. Thus, you may want to ensure that your factors are all on the same scale before constraining covariances. For example, you could constrain the covariance of the factors to be one, rather than constraining one of the loadings, as is the default in Amos. By placing the factors on the same scale, constraining covariances to be equal is the same as constraining correlations to be equal.

Negative variances

In terms of errors, it may be that the factors are so highly correlated that forcing the factors to be uncorrelated is causing estimation problems.
You may want to just try removing the double headed arrows in Amos rather than specifying constraints to see whether that makes a difference to see whether that makes a difference
You may have issues with number of items per factor.

There's also some discussion here

Solved – Issues with SEM and CFA in AMOS

The last question can be peeled off. If I have understood you correctly, you have just cloned the data to get a big enough sample size. That makes no sense at all. Even if you can fool the software, it is still statistical nonsense. Think of it this way: if it is valid, why isn't it prominent in every statistical text as a simple to understand, low technology way of fixing many data problems, such as large standard errors or disappointing P-values?

The earlier questions are outside my area of expertise. Unfortunately, much of your post boils down to your thinking that you asked something valid, but the software doesn't agree, so why is that? Saying that you watched a video and did something similar is not informative. People using the same software will almost certainly want to know exactly what instructions you gave the software.

Best Answer

Related Solutions

Solved – causing degrees of freedom and negative variance issues when estimating CFA with uncorrelated factors

Main Point

Degrees of freedom

Constraining factor correlations to be equal

Negative variances

Solved – Issues with SEM and CFA in AMOS

Related Question