Supplemental Material for Parameter Uncertainty in Structural Equation Models: Confidence Sets and Fungible Estimates

Abstract

have been fully presented in the paper. We only report parameter estimates in this document. The last example by Schmitt, Branscombe, Kobrynowicz, and Owen (2002) is presented in detail for two reasons: (a) to serve as an additional empirical example illustrating the computation and interpretation of confidence sets (CSs) and fungible parameter estimate (FPE) contours, and (b) the targeted illustration made use of this example to determine population generating models.In all four examples, the covariance structure can be expressed aswhere Λ is the matrix of standardized factor loadings, D is a diagonal matrix of manifest variable standard deviations, and Φ is the correlation matrix of the latent variables implied by the standard path coefficients among them. The diagonal matrix Ψ of the standardized unique variances are functions of the other parameters rather than independent parameters. Example 1: Conversation with a StrangerThis example from Bagozzi and Warshaw (1988) as reported in Bagozzi and Yi (1988) investigates what motivates people to talk to an attractive stranger.