  Statistical inference for high dimensional parameters (HDPs) can be based on
their intrinsic correlation; that is, parameters that are close spatially or
temporally tend to have more similar values. This is why nonlinear
mixed-effects models (NMMs) are commonly (and appropriately) used for models
with HDPs. Conversely, in many practical applications of NMM, the random
effects (REs) are actually correlated HDPs that should remain constant during
repeated sampling for frequentist inference. In both scenarios, the inference
should be conditional on REs, instead of marginal inference by integrating out
REs. In this paper, we first summarize recent theory of conditional inference
for NMM, and then propose a bias-corrected RE predictor and confidence interval
(CI). We also extend this methodology to accommodate the case where some REs
are not associated with data. Simulation studies indicate that this new
approach leads to substantial improvement in the conditional coverage rate of
RE CIs, including CIs for smooth functions in generalized additive models, as
compared to the existing method based on marginal inference.
