Forecast with lme4 at new levels

Question

I am trying to fit a mixed effects model, and then use this model to generate estimates of a new dataset, which can have different levels. I expected that the estimates of the new dataset will use the average value of the estimated parameters, but this does not seem to be the case. Here's a minimal working example:

library(lme4) d = data.frame(x = rep(1:10, times = 3), y = NA, grp = rep(1:3, each = 10)) d$y[d$grp == 1] = 1:10 + rnorm(10) d$y[d$grp == 2] = 1:10 * 1.5 + rnorm(10) d$y[d$grp == 3] = 1:10 * 0.5 + rnorm(10) fit = lmer(y ~ (1+x)|grp, data = d) newdata = data.frame(x = 1:10, grp = 4) predict(fit, newdata = newdata, allow.new.levels = TRUE) 

In this example, I essentially define three groups with different regression equations (slopes 1, 1.5, and 0.5). However, when I try to predict a new dataset with an invisible level, I get a constant estimate. I expected the expected slope and intercept value to be used to generate forecasts for this new data. I expect something wrong? Or what am I doing wrong with my code?

Answer 1

I would usually not turn on a random tilt without turning on a fixed tilt. It seems that predict.merMod agrees with me because it just uses only fixed effects to predict for new levels. The documentation says that “prediction will use unconditional (demographic) values ​​for data with previously unobservable levels,” but these values ​​do not seem to be evaluated using the specification of your model.

So I propose this model:

 fit = lmer(y ~ x + (x|grp), data = d) newdata = data.frame(x = 1:10, grp = 4) predict(fit, newdata = newdata, allow.new.levels = TRUE) # 1 2 3 4 5 6 7 8 9 10 #1.210219 2.200685 3.191150 4.181616 5.172082 6.162547 7.153013 8.143479 9.133945 10.124410 

This is the same as using only part of the fixed effects of the model:

 t(cbind(1, newdata$x) %*% fixef(fit)) # [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] #[1,] 1.210219 2.200685 3.19115 4.181616 5.172082 6.162547 7.153013 8.143479 9.133945 10.12441 

Answer 2

This may not be clear enough, but I think the documentation for ?predict.merMod (reasonably) states what happens when allow.new.levels=TRUE . I think ambiguity may be what "Unconditional (demographic) meanings" mean ...

allow.new.levels : boolean if new levels (or NA values) in 'newdata are allowed. If FALSE (default), such new values ​​in 'newdata will cause an error; if TRUE, then forecasting will use unconditional (demographic) values ​​for data with previously unobserved levels (or NA).