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The difference between the two approaches is actually a difference between an Empirical Bayes versus a fully Bayesian approach to estimate the same thing. If you fit the mixed model using maximum likelihood, then you typically follow the first option, whereas, under the fully Bayesian approach from which you take posterior samples also for $\theta$, you ...


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There are many predictive models for binary classification, but yes, logistic regression augmented with a decision rule is one way to go about it. But it seems you have some slight misunderstandings with respect to how to apply it. So, I can create a logistic model, and feed it records of doctors who have been observed to switch from Drug A to Drug B. ...


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You have reported that you have transaction data . Since you don't have observations every day, you will need to aggregate/bucket your data to a time series i.e. some level of accumulation ...where non-zero observations are present. An example might be weekly or monthly buckets or even quarterly buckets. Buying patterns are seldomly weekly-based with ...


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If you know that this next observation comes from a specific group $i$, then the best prediction would be $$\exp(\hat \beta_0 + \hat b_i).$$ However, if you do not know from which group it comes from, then it would make more sense to use as prediction the average over the groups, which in your specific random intercepts model would be $$\exp \Bigl ( \hat \...


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To address the "when is this appropriate" part of your question: If you fit a mixed model, it may still be appropriate to do inference for the grand mean, provided you interpret it correctly. Specifically, prediction intervals around the grand mean that include the relevant variance components are useful tools for inference. But, given that each observation ...


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Assessing the performance on all data conflates the out-of-sample performance estimate on the test set, with the in-sample performance on the train set. You shouldn't assess the performance of your model on all data, only on the test set. In addition, a different random split may give widely different results. You may therefore want to look into cross-...


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You need to include the new data points with NA values for the response variable, in your training set. The model will calculate posterior probability distribution for them using data augmentation. If you save your model in the object model, you can access those posterior distributions through model$samples$Y. Unfortunately, this is only possible with ST....


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As you have correctly noticed, the term 'independent' has completely different meanings depending on context. Statistical independence is what you are describing between the weather and your dinner. These two events are independent in the sense that the value of one does not affect the other. There are more formal mathematical definitions of this ...


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@NickCox gave an excellent answer. A couple additions: You ask But in statistics, can the independent variables be regarded as the "things we are using to make the prediction," while the dependent variable is the "thing being predicted?" To give an explicit answer: Yes, that is often how the terms are used. I use them that way, myself. Second, the ...


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The questions "What do you want to predict?" and "What is the outcome or result here?" often have the same answer, but not always. The terminology of independent variables is widely considered overloaded in statistical sciences. Numerous writers and researchers -- over at least the last several decades -- have suggested using other terms, although there is ...


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Comparing error to predicted value is frequently done: the result is a relative error. Whether relative or absolute error is more important depends on your data/application/the task at hand. However, relative errors are most useful if the denominator gives a good impression of what the encountered values are like. In some cases, the mean is suitable, ...


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It seems that you are relating the value of MAE to the value of mean of the time series? Thats not a good idea imho: if you shift the whole series by a constant, its mean would also shift by that constant, but the MEA / quality of your model should stay the same (if your model is e.g. some regression with intercept, the intercept would just shift by that ...


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Yes, and Yes. Note that you predict coefficients "only in-sample". To say something about statistical significance, you need a distribution for coefficients. But this is estimated using the in-sample only. You can make a OOS prediction, but technically speaking you cannot say anything about out-of-sample statistical significance. In your minor concern, I ...


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I believe your colleague made a mistake in claiming that the $R^2$ stays the same. This is because $R^2$ is defined as: $R^2 = 1- {(SS_{res})\over(SS_{tot})}$ The reason they have to be different is because both 1 and $SS_{tot}$ are fixed by the data set. The only thing that changes between the two models is $SS_{res}$. So this seems to suggest there ...


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