Dear Stephanie (and others),

as stated, single-indicator models do not allow to freely estimate the error variance, as the model contains just one empirical entity (the variance of the indicator) and you want to estimate two entities (the error variance and the latent variance). I doubt, thus, that you were able to do this ;)

Fixing the error variance to zero, as you said by yourself, implies perfect measurement and makes the indicator *identical* to the latent. Obviously, that is a very unreasonable assumption.

Hence, better choose a nonzero-value that reflects a plausible value. Critics will now jump in with a "you never know" - but consider: Zero is nonsense with almost 100% probabilty, hence every value that is a bit farer away from zero is better.

Using reliability information may be a choice, but consider that measurement error in a latent variable model is not only random measurement error but includes all random and nonrandom omitted causes of the indicator (like the error term of any other dependent variable).

In addition, reliability information almost always relies on Cronbach's alpha, which assumptions (causal unidimensionality and equal loadings) are almost never fullfilled. Consequently, alpha is much lower than the true reliability. Using alpha then to fix the error variance leads to an overcorrection.

In this regard, authors like Leslie Hayduk view the fixing procedure as a means to specifiy the intented meaning of the respective latent: The smaller the amount of error you assign to an indicator, the closer the conceptual gap between the indicator and the latent. If you move higher, the gap becomes larger. See:

http://www.biomedcentral.com/content/pdf/1471-2288-12-159.pdf

(The link is temporarilly down but should provide the paper soon again)

Best, 

Holger

I have also had this problem using AMOS.  Unfortunately, the way I was able to get my models to run was to have the single indicator variables was to have them on their own and not load onto a latent variable.  The website below was what helped me when I was trying to understand why AMOS wouldn't allow me to use a single indicator latent variable. 

http://www-01.ibm.com/support/docview.wss?uid=swg21478291

Hopefully this gives you a little more insight.  Overall, I think this is just a limitation of AMOS but I may be wrong.

Reason for not using single indicator latent variable is correctly stated.

One way to circumvent such a problem is to drop the latent variables and make the two observable variables as manifest variables.

I have used this approach. It works. Refer in Case Centre: BUILDING COMPETITIVE ADVANTAGE IN AFTER SALES SERVICE MARKET: A CASE OF PASSENGER CARS IN INDIA Reference no. 514-033-1

Thank you very much for your helpful comments and info!

I have decided to fix my error variance to 0 for all three variables. as theoretically it has the same implications than just using the observed variable (I assume perfect measurement). There are just two things I really would like to understand better and I would appreciate if you could explain:

a) My model fit is better when I use latent varibales with fixed error variables than just the observed variables. How come? By fixing the variance the number of parameters to be estimated does not really change....

b) As I understand no error variance can be calculated for a single indicator because there are no other 'reference' indicators. For one of my three single-indicator latents the model ran without fixing the error variance- what is the magic there?

Thanks a lot!

Having df > 0 does not guarantee that your model will be identified. It just means that mathematically it cannot be solved.

Unidentified models may caused by a number of factors. The easiest issue that some people may overlook is that they forget to fix the factor loading of a single indicator to 1.

If you are not a fan of fixing the loading to 1, you may use Munck (1979)'s formula to calculate a factor loading and error variance directly based on a reliability index in somebody else's publication.

Dear Stephanie (and others),

as stated, single-indicator models do not allow to freely estimate the error variance, as the model contains just one empirical entity (the variance of the indicator) and you want to estimate two entities (the error variance and the latent variance). I doubt, thus, that you were able to do this ;)

Fixing the error variance to zero, as you said by yourself, implies perfect measurement and makes the indicator *identical* to the latent. Obviously, that is a very unreasonable assumption.

Hence, better choose a nonzero-value that reflects a plausible value. Critics will now jump in with a "you never know" - but consider: Zero is nonsense with almost 100% probabilty, hence every value that is a bit farer away from zero is better.

Using reliability information may be a choice, but consider that measurement error in a latent variable model is not only random measurement error but includes all random and nonrandom omitted causes of the indicator (like the error term of any other dependent variable).

In addition, reliability information almost always relies on Cronbach's alpha, which assumptions (causal unidimensionality and equal loadings) are almost never fullfilled. Consequently, alpha is much lower than the true reliability. Using alpha then to fix the error variance leads to an overcorrection.

In this regard, authors like Leslie Hayduk view the fixing procedure as a means to specifiy the intented meaning of the respective latent: The smaller the amount of error you assign to an indicator, the closer the conceptual gap between the indicator and the latent. If you move higher, the gap becomes larger. See:

http://www.biomedcentral.com/content/pdf/1471-2288-12-159.pdf

(The link is temporarilly down but should provide the paper soon again)

Best, 

Holger

Hi Stephanie!

I encountered a similar problem as you did. And instead of fixing error variances to zero (which is simply not justifiable, just like Holger already mentioned), I was looking for another solution where I don't have to manipulate any constraints by hand. I ended up using another SEM-Software: Smart PLS. Compared to AMOS, it uses partial least squares for estimating the parameters, whereas Amos uses covariances. However, the results are fairly the same (but please don't cite me :) ). And one major advantage of Smart PLS is, that you don't have to put as many constraints on your model. 

The software is 100% free for use. You can download it here: http://www.smartpls.de/forum/ 

You will have to register to get your free license key.

Good luck with your research!

I guess the benefit of PLS is that it always returns you an answer - but that doesn't make it valid.

McIntosh, Edwards and Antonakis (2014) (Reflections on Partial Least Squares Path Modeling - Organizational Research Methods

) demonstrate that PLS should never be used if a model contains common factors - not for measuring them or testing models that contain them. McIntosh, Edwards and Antonakis have no commercial interest in PLS either, and so are providing an unbiased assessment of it.

see http://m.orm.sagepub.com/content/early/2014/04/09/1094428114529165

Unless I mistake, the major difference between PLS and Lisrel (or similar covariance-based) structural equation modelling is the measurement system.

I mean, latent variables with PLS use formative approach and indicators. On the other hand, Lisrel and other covariance-based measurement systems use a reflective indicator set.

I would suggest considering this decisive trait before considering PLS.

Hope this helps and good luck!