Just a quick question. I have used maximum likelihood estimation to find the best-fit parameters of a model. In doing so I get a log likelihood value, which obviously is the highest log likelihood value of all parameter sets. However, when reporting these parameters in a paper, should the log likelihood value of that set be reported as well, or does that not have any significant value on its own?

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    $\begingroup$ If you do report it, it's essential you provide a formula, because many algorithms and software packages do not actually compute the log likelihood: they compute a value that will differ from the true log likelihood by some (uncomputed) constant. $\endgroup$
    – whuber
    Aug 16 '19 at 11:17

Many papers report the output chart of the optimization, especially those using Matlab or other softwares that have a standard output table when the optimization is completed.. So if you have time you could replicate one of those with all the info reported. However, the value of the loglik does not say much if taken alone in the context of a MLE: it becomes relevant instead when you want to compare multiple models. So it depends on what your final purpose is: if you just wish to draw a MLE estimate, then the value of the function at the optimum does not say much and, for brevity, you can skip it with no theoretical damage to the paper. On the contrary, if you have a model comparison of any kind (AIC, BIC, LR tests,...), it is recommendable to report it because it will be used within the comparison for the calculation of the above mentioned statistics (AIC, BIC,...). Also in that case however you can just report the different AICs/BICs derivated from the loglik

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    $\begingroup$ It is also adequate to report a pseudo $R^2$ that is derived simply from the model likelihood ratio $\chi^2$ statistic (and for some indexes the maximum attainable log likelihood). $\endgroup$ Aug 16 '19 at 11:34
  • $\begingroup$ Thanks for the answer, this is not a model comparison, but parameter estimations of different models, so I don't think the AIC/BIC is necessary. @FrankHarrell would that count as the goodness of fit for this model, or am I missing something? $\endgroup$ Aug 16 '19 at 11:47
  • $\begingroup$ @DenverDang ok in that case $\endgroup$
    – Fr1
    Aug 16 '19 at 11:49
  • $\begingroup$ None of this has directly to do with goodness of fit. For that I'd do directed assessments, e.g., related to linearity and additivity. $\endgroup$ Aug 16 '19 at 15:17

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