Little is known about the behavior of LISREL estimates when distributions are contaminated by outlying observations. Monte Carlo approaches have typically been used to investigate the robustness of maximum likelihood techniques in factor analysis models (Fuller & Hemmerle 1966; Olsson 1979; Gallini & Mandeville 1984; Boomsma, Chapter 9 in this volume) or to examine departures from normality (Andrews, Gnanadesikan, & Warner 1973; Gnanadesikan 1977). Such studies have yielded important results concerning the robustness of maximum likelihood estimates under various conditions. However, the Monte Carlo approach is atypical of the situation faced by the practicing researcher dealing with a data set in which the “true” structure in the population is unknown.

In this chapter the influence of outliers on parameter estimates is addressed in a real data set. The LISREL model is examined using real data in which the relationships may be atypical owing to the influence of outliers. A robust estimation technique (Tukey 1960) is employed to identify outlying observations. The consequences for model fit in samples of variable sizes are examined when these outliers are removed from the sample. The major aim of the chapter is to provide the researcher with a practical strategy for the detection of outliers in the context of structural modeling and an indication of their effects on parameter estimates.

The model

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