Make Some Noise: Generating Data from Imperfect Factor Models

Researchers simulating covariance structure models sometimes add model error to their data to produce model misfit. Presently, the most popular methods for generating error-perturbed data are those by Tucker, Koopman, and Linn (TKL), Cudeck and Browne (CB), and Wu and Browne (WB). Although all of these methods include parameters that control the degree of model misfit, none can generate data that reproduce multiple fit indices. To address this issue, we describe a multiple-target TKL method that can generate error-perturbed data that will reproduce target RMSEA and CFI values either individually or together. To evaluate this method, we simulated error-perturbed correlation matrices for an array of factor analysis models using the multiple-target TKL method, the CB method, and the WB method. Our results indicated that the multiple-target TKL method produced solutions with RMSEA and CFI values that were closer to their target values than those of the alternative methods. Thus, the multiple-target TKL method should be a useful tool for researchers who wish to generate error-perturbed correlation matrices with a known degree of model error. All functions that are described in this work are available in the fungible <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math> library. Additional materials (e.g., <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math> code, supplemental results) are available at https://osf.io/vxr8d/.