  A problem that tends to be ignored in the statistical analysis of
experimental data in the language sciences is that responses often constitute
time series, which raises the problem of autocorrelated errors. If the errors
indeed show autocorrelational structure, evaluation of the significance of
predictors in the model becomes problematic due to potential anti-conservatism
of p-values. This paper illustrates two tools offered by Generalized Additive
Mixed Models (GAMMs) (Lin and Zhang, 1999; Wood, 2006, 2011, 2013) for dealing
with autocorrelated errors, as implemented in the current version of the fourth
author's mgcv package (1.8.9): the possibility to specify an ar(1) error model
for Gaussian models, and the possibility of using factor smooths for
random-effect factors such as subject and item. These factor smooths are set up
to have the same smoothing parameters, and are penalized to yield the
non-linear equivalent of random intercepts and random slopes in the classical
linear framework. Three case studies illustrate these issues.
