Factor Indeterminacy in Simulation and Structural Equation Models

Due to the indeterminacy problem in factor analysis, factors are not uniquely determined by observed data.We investigate the consequences of this problem for the interpretation of simulation studies and for linear structural equation models.For simulation procedures, factor indeterminacy implies that as long as the simulated data have the correct covariance matrix, there exists a possibly large space of factors and error terms that can generate the simulated data via the model equations.For linear structural equation models, the linearity of the structural part of the model is only partly testable by the distribution of the data.Practical recommendations for conducting simulation studies are provided.We give numerical illustrations, including a case where the observed data are normal and fit a linear structural equation model perfectly, yet are generated by a highly non-linear structural equation model.