Threshold models improve estimates of molt parameters in datasets with small sample sizes

The timing of events in birds’ annual cycles is important to understanding
life history evolution and response to global climate change. Molt timing
is often measured as an index of the sum of grown feather proportion or
mass within the primary flight feathers.  The distribution of
these molt data over time has proven difficult to model with standard
linear models. The parameters of interest are at change points in model
fit over time, and so least squares regression models that assume molt is
linear violate the assumption of even variance.  This has led to
the introduction of other nonparametric models to estimate molt
parameters. Hinge models directly estimate changes in model fit, and have
been used in many systems to find change points in data distributions.
Here, we apply a hinge model to molt timing, through the introduction of a
double-hinge threshold model. We then examine its performance in
comparison to current models using simulated and empirical data. We find
that the Underhill-Zuchinni (UZ) and Pimm models perform well under many
circumstances, and appears to outperform the threshold model in datasets
with very high variance. The double-hinge threshold model outperforms the
UZ model at low sample sizes of birds in active molt, and shorter molt
durations, and provides more realistic confidence intervals at small
sample sizes.