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The implications of ignoring correlated error on parameter estimates in some simple structural equation models are examined. Ignoring correlated measurement error not only affected the acceptability of a model based on goodness-of-fit measures, but also affected the parameter estimation. Ignoring within-construct correlated error does not affect the estimates of the structural parameter but overestimates the associated measurement parameters. It is shown analytically and empirically that ignoring positive between-construct correlated error overestimates the structural parameter linking the two constructs. The effects become more pronounced with decreasing reliability in measurement.
Srinivas K. Reddy (Tue,) studied this question.