Searching for an authoritative answer about the implications of holding random effects to zero in predictions of mixed effects models

Question

Let's say a large population was sampled, and data to construct a model to predict Y were gathered at part of the sample units. To account for correlation among individuals from the same site, sampling unit was included as a random effect in a mixed effects model. There is interest to predict Y of every individual on all sampling units, thus part of them does not pertain to a level found in the model fitting dataset.

This issue was already discussed in some posts, but IMHO answers were somehow divergent. Some say one should not use a mixed model to predict for new data that do not pertain to a level found in the fitting dataset. Some say you can, by holding random effects to 0. Therefore, I am looking for a clear an "authoritative" solution for this issue.

I would also like to hear about the validity of following approaches:

1. Using random effects for predictions of individuals of known levels, and holding random effects to 0 for individuals of unknown levels;

2. Holding random effects to 0 for all predictions, including for those individuals of known levels.

These approaches would be used under the following situation: predictions for individuals on sampling units are aggregated to compute predictions of Y at the sampling unit level, and probability-based estimators (e.g., simple expansion estimators) are used to estimate the population mean and variance based on sampling unit-level predictions.

Probably, approach (2) would generate less sampling variability, and thus a narrower confidence interval for the estimated population mean. Here, I am not considering the effects of model prediction uncertainties on the population estimates.

Thank you very much!

Answer 1

I find it hard to think of scenarios, where predictions with random effects set to zero are of interest (there are of course inference situations for contrasts and comparisons where the random effects are irrelevant/cancel out). If there is variation and unexplained differences between random effects levels, why would we ignore that when making predictions? For unseen random effects levels, this implies assuming an added random effect that follows the overall random effects distribution.

There's some scenarios, where ignoring the random effects (seeing them to zero) is okay. But, if so, it's only okay, because it results in the same answer as having the random effect. One example would be if we want point predictions for new random effects levels from a linear (mixed effects) model with normally distributed random effects and are not interested in prediction intervals. However, for something like mixed effects logistic regression this is not the same thing.

Perhaps someone else can think of some scenarios where we'd want to set random effects to zero, but I can't (outside of hypothetical "if only we could eliminate this variability"-scenarios).