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A conceptual distinction is drawn between indicators, which serve to define latent variables, and outcomes, which do not. However, commonly used frequentist and Bayesian estimation procedures do not honor this distinction. They allow the outcomes to influence the latent variables and the measurement model parameters for the indicators, rendering the latent variables subject to interpretational confounding. Modified Bayesian procedures that preclude this are advanced, along with procedures for conducting diagnostic model-data fit analyses. These are studied in a simulation, where they outperform existing strategies, and illustrated with an example.