Sensitivity Analysis in Structural Equation Models: Cases and Their Influence

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability ( Holzinger & Swineford, 1939 ) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data ( Bollen, 1989 ; Bollen & Arminger, 1991 ). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced-these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.