In the past couple of weeks I’ve noticed a flurry of visualizations of global sea ice extent on social media. If you’re like me, and curious to see what the data look like yourself, here’s a bit of R code to fetch and visualize the most recent ... [Read more...]

Gaussian process (GP) models are computationally demanding for large datasets. Much work has been done to avoid expensive matrix operations that arise in parameter estimation with larger datasets via sparse and/or reduced rank covariance matrices (Datta et al. 2016 provide a nice review). What follows is an implementation of a ... [Read more...]

Design matrices unite seemingly disparate statistical methods, including linear regression, ANOVA, multiple regression, ANCOVA, and generalized linear modeling. As part of a hierarchical Bayesian modeling course that we offered this semester, we wanted our students to learn about design matrices to facilitate model specification and parameter interpretation. Naively, I thought ... [Read more...]

The Maungawhau volcano dataset is an R classic, often used to illustrate 3d plotting. Being on a Gaussian process kick lately, it seemed fun to try to interpolate the volcano elevation data using a subset of the full dataset as training data. Even with... [Read more...]

I had to read a lot of books in graduate school. Some were life-changing, and others were forgettable. If I could bring a reading list back in time for my ‘first year’ graduate self, it would include the following: Bayesian Data Analysis Third Edition, by Andrew Gelman, John B. Carlin, ... [Read more...]

I’ve uploaded 20+ R tutorials to YouTube for a new undergraduate course in Ecology and Evolutionary Biology at CU developed by Andrew Martin and Brett Melbourne, which in jocular anticipation was named IQUIT: an introduction to quantitative inference and thinking. We made the videos to address the most common R ... [Read more...]

The R package spdep has great utilities to define spatial neighbors (e.g. dnearneigh, knearneigh, with a nice vignette to boot), but the plotting functionality is aimed at base graphics. If you’re hoping to plot spatial neighborhoods as line segments in ggplot2, or ggmap, you’ll need the neighborhood ... [Read more...]

Thanks to a nice post by Meghan Duffy on the Dynamic Ecology blog (How do you make figures?), we have some empirical evidence that many figures made in R by ecologists are secondarily edited in other programs including MS Powerpoint, Adobe Illustrator, Inkscape, and Photoshop. This may not be advisable* ... [Read more...]

Inspired by this post about visualizing shrinkage on Coppelia, and this thread about visualizing mixed models on Stack Exchange, I started thinking about how to visualize shrinkage in more than one dimension. One might find themselves in this situation with a varying slope, varying intercept hierarichical (mixed effects) model, a ... [Read more...]

Ecologists increasingly use mixed effects models, where some intercepts or slopes are fixed, and others are random (or varying). Often, confusion exists around whether and when to use fixed vs. random intercepts/slopes, which is understandable given their multiple definitions. In an attempt to help clarify the utility of varying ... [Read more...]

Occupancy modeling is possible in Stan as shown here, despite the lack of support for integer parameters. In many Bayesian applications of occupancy modeling, the true occupancy states (0 or 1) are directly modeled, but this can be avoided by marginalizing out the true occupancy state. The Stan manual (pg. 96) gives an ... [Read more...]

Quantifying spatial data (e.g. land cover) around points can be done in a variety of ways, some of which require considerable amounts of patience, clicking around, and/or cash for a license. Here’s a bit of code that I cobbled together to quickly extract land cover data from ... [Read more...]

This is a guest post generously provided by Joe Mihaljevic. A common goal of community ecology is to understand how and why species composition shifts across space. Common techniques to determine which environmental covariates might lead to such shifts typically rely on ordination of community data to reduce the amount ... [Read more...]

In multiple regression, strong correlation among covariates increases the uncertainty or variance in estimated regression coefficients. Variance inflation factors (VIFs) are one tool that has been used as an indicator of problematic covariate collinearity. In teaching students about VIFs, it may be useful to have some interactive supplementary material so ... [Read more...]

Stochastic search variable selection (SSVS) identifies promising subsets of multiple regression covariates via Gibbs sampling (George and McCulloch 1993). Here’s a short SSVS demo with JAGS and R. Assume we have a multiple regression problem: We suspect only a subset of the elements of $\boldsymbol{\beta}$ are non-zero, i.e. ... [Read more...]

Dealing with proportion data on the interval $[0, 1]$ is tricky. I realized this while trying to explain variation in vegetation cover. Unfortunately this is a true proportion, and can’t be made into a binary response. Further, true 0’s and 1’s rule out beta regression. You could arcsine square root transform ... [Read more...]

In a previous post, I gave a cursory overview of how prior information about covariate measurement error can reduce bias in linear regression. In the comments, Rasmus Bååth asked about estimation in the absence of strong priors. Here, I’ll describe a Bayesian approach for estimation and correction for ... [Read more...]

Being in grad school, I do a lot of scholarly writing that requires associated or embedded R analyses, figures, and tables, plus bibliographies. Microsoft Word makes this unnecessarily difficult. Many tools are now available to break free from the tyranny of Word. The ones I like involve writing an article ... [Read more...]

Among-species comparisons can include phylogenetic information to account for non-independence arising from shared evolutionary history. Often, phylogenetic topologies and branch lengths are not known exactly, but are estimated with uncertainty. This uncertainty can be accounted for using methods recently described in a neat paper called Bayesian models for comparative analysis ... [Read more...]

The Metropolis algorithm, and its generalization (Metropolis-Hastings algorithm) provide elegant methods for obtaining sequences of random samples from complex probability distributions. When I first read about modern MCMC methods, I had trouble visualizing the convergence of Markov chains in higher dimensional cases. So, I thought I might put together a ... [Read more...]