Structural Equation Modelling....The simplest explanation you can give....

Ever since last year that i started my research SEM has proved to be a daunting task. Reading a lot of books and articles....I still have some simple questions that I like answers for....Being familiar with other regression analyses, SEM has tested my limits to stats and I am finally here to ask some important questions....

Please Help ME!

- What are Fit indices? are they similar to R squared in regression? For example chi square and RMSEA are the 2 most are these calculated and what do they represent?

- If a model with 5 variables is created on AMOS... what do these fit indices mean? a book says software compares observed covariances with predicted covariances...What does this in simple terms mean?

Best Regards,


Phineas Packard
Question 1:
SEM takes a model that you specify and uses it to create an expected covariance matrix. This expected covariance matrix is then compared to a coviarance matrix that is derieved from the data that you collect. The two are then compared and that is where you get fit from. There are two types. Absolute (e.g. RMSEA) will give a value of 0 if the observed and expected covariance matrix match up exactly. Incremental fit indexes compare your model against a null model (a model in which all variables have a variance but have a zero relationship with each other). Here is a good link or look at the slides of a recent talk I gave (this will show you exactly how an observed and expected/predicted covariance matrix is developed).

2. Traditionally a models fit would be tested statistically using a chi-square test. If this test was NOT significant then you can say that the model you developed leads to an expected covariance matrix that is not that much different from the one you observed using your data. However, the problem with this is that chi-square values get larger with larger sample sizes and that is why we have fit indices which are not as heavily influenced by sample sizes. There is no agreed upon p<.05 type thing for these indices but values for the RMSEA of <.08 and values of the CFI and TLI above .90 are generally considered acceptable.
Thanks everyone...So how would the software create expected co variance matrix...suppose I am studying that negative thinking mediates the impact of being picky on depression...

Being picky---> negative thinking---> Depression

So if I have collected a data set with these variables in the model....the software compares the co variance matrix created using these data points with what expected.....what does expected mean in this context....

Thanks everyone for your great answers
I have a question involving the interpretation of a correlation matrix associated with a SEM in an article I am reviewing:

The correlation matrix (see p. 503) shows significant relationships between "9. Exhaustion" and "10. Cynicism" (both central issues of my work) and several of the "Job Demands and Resources" variables (items 1-5). A colleague says that these correlations, even though shown here to be stat sig, are in fact not meaningful extracted from the SEM as a whole. In short, I am trying cite this study as part of a larger review of evidence linking Exhaustion and Cynicism to various predictors/antecedents. Is my colleague correct that these correlations are not meaningful (in general) apart from this specific SEM? I am usually a qualitative researcher so please keep that in mind when providing any response! Many thanks in advance.