An R package to interpret a Tweedie generalized linear model (GLM) or generalized additive model (GAM) involving multiple classes as an estimate of proportions for each class, implicitly involving a multivariate-logit transformation for parameters and predictions. This approach generalizes the Poisson-to-multinomial transformation to allow for non-integer responses, and can analyze either pre-processed (transformed to proportions) or raw (zero-inflated positive real values) data.
This approach is helpful, e.g., when analyzing diet samples that are heavily zero inflated without pre-processing the samples prior to analysis. In these cases, the Tweedie distribution can be interpreted mechanistically as a thinned and double-marked Poisson point process representing foraging processes.
library( ggplot2 )
library( mgcv )
library( mvtweedie )
# Load data
data( "Middleton_Island_TUPU", package="mvtweedie" )
Middleton_Island_TUPU$Year = as.numeric(as.character( Middleton_Island_TUPU$Year_factor ))
# Fit GAM
fit = mgcv::gam( Response ~ group + s(Year, by=group), data=Middleton_Island_TUPU, family="tw" )
class(fit) = c( "mvtweedie", class(fit) )
# Predict values
newdata = expand.grid("group"=levels(Middleton_Island_TUPU$group),
"Year"=min(Middleton_Island_TUPU$Year):max(Middleton_Island_TUPU$Year))
pred = predict( fit,
se.fit=TRUE,
origdata = Middleton_Island_TUPU,
newdata = newdata )
newdata = cbind( newdata, fit=pred$fit, se.fit=pred$se.fit )
newdata$lower = newdata$fit - newdata$se.fit
newdata$upper = newdata$fit + newdata$se.fit
# Plot
theme_set(theme_bw())
ggplot(newdata, aes(Year, fit)) +
geom_pointrange(aes(ymin = lower, ymax = upper)) +
facet_wrap(vars(group)) +
scale_color_viridis_c(name = "SST") +
ylim(0,1) +
labs(y="Predicted proportion")Thorson, J. T., Arimitsu, M. L., Levi, T., & Roffler, G. (2022). Diet analysis using generalized linear models derived from foraging processes using R package mvtweedie. Ecology. 103(5): e3637.