What kind of indices does PLS Graph generate to tell you about the quality of the model's fit. I realize that the indices used in EQS and LISREL (e.g., CFI, NNFI) will not be given, but Falk & Miller (1992) talk about the RMS COV (E, U) (i.e., root mean square of the covariance between the manifest variable residuals and the latent variable residuals). I'm unable to find this in any of the outputs.

There are at least two difficulties/issues that come to mind when  considering model fit in PLS analyses.  The first is whether all your constructs are modeled as reflective.  If not, fit indices dealing with explaining covariation among your measures cannot be used. The other issue deals with whether your emphasis is primarily focused on minimizing residual error and maximizing explained covariation among all measures - or in maximizing variance explained for certain constructs or measures.

If either of the two issues are being consider,  the RMS index you mentioned becomes problematic. So these and other such indices are currently not included to avoid confusion. Someday we may add it contingent on the exact model being examined.

Thus - I'd argue that the key approach is to demonstrate strong loadings, significant weights, high R-squares and substantial/significant structural paths.

Let me provide a brief quote from the following piece I wrote to further clarify the issue:

Chin, W. W.  (1998). Issues and Opinion on Structural Equation Modeling. MIS Quarterly, 22(1), pp. vii – xvi. Online: http://www.misq.org/archivist/vol/no22/issue1/vol22n1comntry.html

"A final issue is the over-reliance towards overall model fit (or goodness of fit) indices. "Where is the goodness of fit measures?" has become the 90s mantra for any SEM based study.  Yet, it should be clear that the existing goodness of fit measures are related to the ability of the model to account for the sample covariances and therefore assume that all measures are reflective.  SEM procedures that have different objective functions and/or allow for formative measures (e.g., PLS) would, by definition, not be able to provide such fit measures.  In turn, reviewers and researchers often reject articles using such alternate procedures due to the simple fact that these model fit indices are not available.

In actuality, models with good fit indices may still be considered poor based on other measures such as the R-square and factor loadings.  The fit measures only relate to how well the parameter estimates are able to match the sample covariances.  They do not relate to how well the latent variables or item measures are predicted. The SEM algorithm takes the specified model as true and attempts to find the best fitting parameter estimates.  If, for example, error terms for measures need to be increased in order to match the data variances and covariances, this will occur. Thus, models with low R-square and/or low factor loadings can still yield excellent goodness of fit.

Therefore, pure reliance of model fit follows a Fisherian scheme similar to ANOVA which has been criticized as ignoring effect sizes (e.g., Cohen, 1990, p. 1309).  Instead, closer attention should be paid to the predictiveness of the model.  Are the structural paths and loadings of substantial strength as opposed to just statistically significant?  Standardized paths should be around 0.20 and ideally above 0.30 in order to be considered meaningful.  Meehl (1990) has argued that anything lower may be due to what he has termed the crud factor where “everything correlate to some extent with everything else” (p. 204) due to “some complex unknown network of genetic and environmental factors” (p. 209).  Furthermore, paths of .10, for example, represents at best a 1 percent explanation of variance.  Thus, even if they are “real”, are constructs with such paths theoretically interesting?