A quantile count model of water depth constraints on Cape Sable seaside sparrows

Abstract

Summary 1.A quantile regression model for counts of breeding Cape Sable seaside sparrows Ammodramus maritimus mirabilis (L.) as a function of water depth and previous year abundance was developed based on extensive surveys, 1992-2005, in the Florida Everglades. The quantile count model extends linear quantile regression methods to discrete response variables, providing a flexible alternative to discrete parametric distributional models, e.g. Poisson, negative binomial and their zero-inflated counterparts. 2.Estimates from our multiplicative model demonstrated that negative effects of increasing water depth in breeding habitat on sparrow numbers were dependent on recent occupation history. Upper 10th percentiles of counts (one to three sparrows) decreased with increasing water depth from 0 to 30 cm when sites were not occupied in previous years. However, upper 40th percentiles of counts (one to six sparrows) decreased with increasing water depth for sites occupied in previous years. 3. Greatest decreases (-50% to -83%) in upper quantiles of sparrow counts occurred as water depths increased from 0 to 15 cm when previous year counts were ≥ 1, but a small proportion of sites (5-10%) held at least one sparrow even as water depths increased to 20 or 30 cm. 4. A zero-inflated Poisson regression model provided estimates of conditional means that also decreased with increasing water depth but rates of change were lower and decreased with increasing previous year counts compared to the quantile count model. Quantiles computed for the zeroinflated Poisson model enhanced interpretation of this model but had greater lack-of-fit for water depths > 0 cm and previous year counts ≥ 1, conditions where the negative effect of water depths were readily apparent and fitted better with the quantile count model.

Effects of environmental variables on invasive amphibian activity: using model selection on quantiles for counts

“…Estimates in the artificial continuous scale are then back‐transformed with a ceiling function, Q y (τ| X ) = , to recover the quantile estimates in the discrete random variable scale (counts y ). Our quantile count model had the typical multiplicative exponential form used with other parametric count models (Cade and Dong ) that ensures that all estimates are greater than or equal to zero. For each season, we estimated five candidate quantile count models with environmental predictors (humidity, minimum temperature, rainfall, wind speed, and moon luminosity) and one null quantile count model with just an intercept.…”

“…Models were estimated for τ ∈ {0.05, 0.10, 0.15, …, 0.95}. To integrate out the artificial noise introduced by jittering toad counts to a continuous variable ( z = y + U [0, 1)), we estimated each model m = 500 times, using m random samples between 0 and 1 ( U [0, 1)) and averaged the estimates (Machado and Santos Silva , Cade and Dong ).…”

“…The confidence intervals for parameter estimates and AIC model selection statistics were all obtained in the continuous log scale, but interpretation of the model estimates was made in the discrete count scale. We back‐transformed quantile estimates of the strongest model from the continuous log scale to the discrete count scale using the ceiling function (Machado and Santos Silva , Cade and Dong ). In cases where the strongest model included more than one predictor variable, we calculated quantile estimates for each variable while holding all other variables included in the model at their median values.…”

Influences of size and sex on invasive species aggression and native species vulnerability: a case for modern regression techniques

“…Higher levels in the response variable, aggression, which are associated with the upper quantiles or percentiles used in these analyses (Cade and Noon 2003;Chamaillé-Jammes and Blumstein 2012;Schmidt et al 2012), are more important in this case as lower or zero aggression rates will be ineffective. Although conventional quantile regression (Cade and Noon 2003;Koenker 2011) is robust to outliers and does not assume a normal error distribution so that a higher frequency of zeros can be tolerated (Scharf et al 1998; Chamaillé-Jammes and Blumstein 2012), it is sensitive to highly discrete response variables, so that special methods need to be used (Cade and Dong 2008). Our results suggest that aggression is often performed by a few individuals, thus increasing heteroscedasticity in the relationships and making it difficult to find significance in central tendencies.…”

“…Scharf et al 1998;Dunham et al 2002;Johnson and VanDerWal 2009;Menge et al 2011;Schmidt et al 2012), it has only recently been applied to behavioural studies (Chamaillé-Jammes and Blumstein 2012; Beauchamp 2013). However, although quantile regression does not assume normality, it is not well suited to highly discrete data that require a specific alternative (Cade and Dong 2008). A technique similar to quantile regression but that to our knowledge has not been applied to behavioural data is expectile regression, which can be used under both Poisson and binomial error distributions (Yee 2008(Yee , 2014.…”