Lecture Outline:

An example from Bentler

Basic measurement model with fixed equality constraints and over-time errors

insert sem1.If we convert this to a causal model with:
stability of the original dependent construct, rather than causation, and
an additional cause at time 1 with contemporaneous and lagged effects

This can also be represented as linear equations:

V1 = 1F1 + E1
V2= .833F1 + E2
V3 = 1F2 + E3
V4 = .833F2 + E4
V5 = 1F3 + E5
V6= .5* F3 + E6
F1 = -.5*F3 + D1
F2 = .5*F1 -.5*F3 + D2

How to examine direct and indirect effects, decompose correlations.

Practical Issues from Hatcher, Chapter 6

Why use MLE and latent variables?  MLE is now a standard estimation approach.  path models in manifest variables can be modeled this way by assuming that the loading of one indicator on it's factor is 1.00.  But, if reliability information is available, we can correct for attenuation

Develop the structural model and measurement models separately.  Evaluate identification of each can usually be done separately.

Analysis:
1.  did it run OK?  do you and it agree about the model?
2.  evaluate global fit:  x2 as twice df; Comparative fit index, NNFI greater than .9; residual outliers and normality?
3.  evaluate local fit:  are loadings significant?  are paths significant? Are R2 of latent endogenous vars big and significant?
4.  does the full model fit better than one where the substantive effects are assumed to be zero?
5.  consider modifications:  Wald tests -- can any effects be fixed to zero without significantly worsening chi square (also, relative to actual residual chi square size).   LaGrange Mulitplier tests -- are there any interpretable effects that, if added, make a significant and substantively important difference in chisquare?
6.  report standardized effects in a diagram, calculate direct, indirect, total effects.

Proving Identification of SEMs

see web reading