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If it does make sense to do a sensitivity analysis how should one determine which priors to use? If flat "non-informative" priors are chosen to begin with because of a lack of information then it seems quite hypothetical choosing different informed priors to sensitivity check?

qgj92
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    Yes, because flat priors can lead to posterior impropriety which may be revealed by switching them out for something more informative. – John Madden Jul 28 '22 at 14:29
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    Flat priors are not "non-informative" and their choice carries consequences, hence must be assessed by a sensitivity check. – Xi'an Jul 28 '22 at 19:02
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    As @Xi'an wrote, flat priors are not non-informative. They are the formal equivalent of saying "every parameter value from $-\infty$ to $+\infty$ is equally unsurprising to me," which, if you think about it, is a meaningful statement. – Durden Mar 08 '24 at 18:37

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A couple of things. First, as @Xi'an points out, flat priors are not non-informative, as all priors contain some specification analogous to some type of information (see @Xi'an's previous answer here for more information). Second (and in light of the first point), I cannot think of a good reason why doing a sensitivity analysis is not a good idea. Sure, as $n \rightarrow \infty$, the impact of the prior on the likelihood diminishes. However, even with an absurdly large sample, I would still conduct a sensitivity analysis and place it in an Appendix. Finally, for more information on the use of priors in mplus, I recommend MacCallum, Edwards, & Cai (2012) and Smid & Winter (2020).

References

MacCallum, R. C., Edwards, M. C., & Cai, L. (2012). Hopes and cautions in implementing Bayesian structural equation modeling.

Smid, S. C., & Winter, S. D. (2020). Dangers of the defaults: A tutorial on the impact of default priors when using Bayesian SEM with small samples. Frontiers in Psychology, 11, 611963.

Preston Botter
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