What graphical techniques are used in Structural Equation Modeling? I'm curious if there are graphical techniques particular, or more applicable, to structural equation modeling.  I guess this could fall into categories for exploratory tools for covariance analysis or graphical diagnostics for SEM model evaluation.  (I'm not really thinking of path/graph diagrams here.) 
 A: This is a very interesting question. Suppose that we have a 2 dimensional covariance matrix (very unrealistic example for SEM but please bear with me). Then you can plot the iso-contours for the observed covariance matrix vis-a-vis the estimated covariance matrix to get a sense of model fit.
However, in reality you will a high-dimensional covariance matrix. In such a situation, you could probably do several 2 dimensional plots taking 2 variables at a time. Not the ideal solution but perhaps may help to some extent.  
Edit
A slightly better method is to perform Principal Component Analysis (PCA) on the observed covariance matrix. Save the projection matrix from the PCA analysis on the observed covariance matrix. Use this projection matrix to transform the estimated covariance matrix. 
We then plot iso-contours for the two highest variances of the rotated observed covariance matrix vis-a-vis the estimated covariance matrix. Depending on how many plots we want to do we can take the second and the third highest variances etc. We start from the highest variances as we want to explain as much variation in our data as possible. 
A: I suppose you could do a multidimensional scaling of the correlation or covariance matrix. It's not exactly structural equation modelling, but it might highlight patterns and structure in the correlation or covariance matrix. This could then be formalised with an appropriate model.
A: I met Laura Trinchera who contributed a nice R package for PLS-path modeling, plspm. It includes several graphical output for various kind of 2- and k-block data structures.
I just discovered the plotSEMM R package. It's more related to your second point, though, and is restricted to graphing bivariate relationships. 
As for recent references on diagnostic plot for SEMs, here are two papers that may be interesting (for the second one, I just browsed the abstract recently but cannot find an ungated version):


*

*Sanchez BN, Houseman EA, and Ryan LM. Residual-Based Diagnostics for Structural Equation Models. Biometrics (2009) 65, 104–115

*Yuan KH and Hayashi K. Fitting data to model: Structural equation modeling diagnosis using two scatter plots, Psychological Methods (2010)

*Porzio GC and Vitale MP. Discovering interaction in Structural Equation Models through a diagnostic plot. ISI 58th World Congress (2011).

A: If there is an interaction effect(or even otherwise) you could use the sofware ITALASSI v1.2 (free software) to get 2D and 3D views
