## Controls on subannual variation in pCO2 in productive hardwater lakes

#### 15 October 2018 /posted in: Science

This year is looking like a bumper year for papers from the lab and collaborations, past and ongoing. Over the summer hiatus three papers came out online in their version-of-record form. The first of these was a paper on work that Emma Wiik, a former postdoc in my lab and Peter Leavitt’s lab, conducted to further our research on the controls on CO2 exchange between lakes and the atmosphere.

## Summer hiatus

#### 15 October 2018 /posted in: Science

It’s been quite some time since I last posted anything here. Mostly this was due to a very busy schedule since May that included teaching an online stats course, attending & presenting at three conferences, giving workshops at two of those conferences, and taking some well-earned vacation in Europe. Summer was also a busy time for manuscripts moving through the pipeline to being accepted and published. One thing I had hoped to do with the blog this year was publicize some of the work I do a little more. So, as normal service resumes here I hope to post some short pieces highlighting new papers that came out over the summer, and a few of these will be coming out over the next week or two.

One of the reasons for having this blog in the first place was to get me back into “writing mode”; I find it difficult at times, especially when the to-do list is long, to force myself to carve out time to both think and write. And as I get more and more out of practice writing, it takes more and more time to start or pick up work on manuscripts describing new results, and the words don’t flow easily at all. I find it much easier to write when I am towards the end of a writing period because I’ve literally forced myself to write. And, whilst blog posts aren’t the same kind of writing as for manuscripts, I hope that by just doing a little writing each week, it’ll be that bit easier to pick up work on a languishing manuscript or start something new.

Let’s see how I get on…

## Fitting GAMs with brms: part 1 a simple GAM

#### 21 April 2018 /posted in: R

Regular readers will know that I have a somewhat unhealthy relationship with GAMs and the mgcv package. I use these models all the time in my research but recently we’ve been hitting the limits of the range of models that mgcv can fit. So I’ve been looking into alternative ways to fit the GAMs I want to fit but which can handle the kinds of data or distributions that have been cropping up in our work. The brms package (Bürkner, 2017) is an excellent resource for modellers, providing a high-level R front end to a vast array of model types, all fitted using Stan. brms is the perfect package to go beyond the limits of mgcv because brms even uses the smooth functions provided by mgcv, making the transition easier. In this post I take a look at how to fit a simple GAM in brms and compare it with the same model fitted using mgcv.

Bürkner, P.-C. (2017). brms: An R package for bayesian multilevel models using Stan. Journal of Statistical Software 80, 1–28. doi:10.18637/jss.v080.i01.

## Comparing smooths in factor-smooth interactions II ordered factors

#### 14 December 2017 /posted in: R

In a previous post I looked at an approach for computing the differences between smooths estimated as part of a factor-smooth interaction using s()’s by argument. When a common-or-garden factor variable is passed to by, gam() estimates a separate smooth for each level of the by factor. Using the (Xp) matrix approach, we previously saw that we can post-process the model to generate estimates for pairwise differences of smooths. However, the by variable approach of estimating a separate smooth for each level of the factor my be quite inefficient in terms of degrees of freedom used by the model. This is especially so in situations where the estimated curves are quite similar but wiggly; why estimate many separate wiggly smooths when one, plus some simple difference smooths, will do the job just as well? In this post I look at an alternative to estimating separate smooths using an ordered factor for the by variable.

## First steps with MRF smooths

#### 19 October 2017 /posted in: R

One of the specialist smoother types in the mgcv package is the Markov Random Field (MRF) smooth. This smoother essentially allows you to model spatial data with an intrinsic Gaussian Markov random field (GMRF). GRMFs are often used for spatial data measured over discrete spatial regions. MRFs are quite flexible as you can think about them as representing an undirected graph whose nodes are your samples and the connections between the nodes are specified via a neighbourhood structure. I’ve become interested in using these MRF smooths to include information about relationships between species. However, these smooths are not widely documented in the smoothing literature so working out how best to use them to do what we want has been a little tricky once you move beyond the typical spatial examples. As a result I’ve been fiddling with these smooths, fitting them to some spatial data I came across in a tutorial Regional Smoothing in R from The Pudding. In this post I take a quick look at how to use the MRF smooth in mgcv to model a discrete spatial data set from the US Census Bureau.

## Comparing smooths in factor-smooth interactions I by-variable smooths

#### 10 October 2017 /posted in: R

One of the really appealing features of the mgcv package for fitting GAMs is the functionality it exposes for fitting quite complex models, models that lie well beyond what many of us may have learned about what GAMs can do. One of those features that I use a lot is the ability to model the smooth effects of some covariate (x) in the different levels of a factor. Having estimated a separate smoother for each level of the factor, the obvious question is, which smooths are different? In this post I’ll take a look at one way to do this using by-variable smooths.

## Fitting count and zero-inflated count GLMMs with mgcv

#### 04 May 2017 /posted in: R

A couple of days ago, Mollie Brooks and coauthors posted a preprint on BioRχiv illustrating the use of the glmmTMB R package for fitting zero-inflated GLMMs (Brooks et al., 2017). In the paper, glmmTMB is compared with several other GLMM-fitting packages. mgcv has recently gained the ability to fit a wider range of families beyond the exponential family of distributions, including zero-inflated Poisson models. mgcv can also fit simple GLMMs through a spline equivalent of a Gaussian random effect. So, whilst I was waiting on some Bayesian GAMs to finish sampling, I decided to see how mgcv compared against glmmTMB on the two examples used in the paper.

Brooks, M. E., Kristensen, K., Benthem, K. J. van, Magnusson, A., Berg, C. W., Nielsen, A., et al. (2017). Modeling Zero-Inflated count data with glmmTMB. bioRxiv, 132753. doi:10.1101/132753.

## Prediction intervals for GLMs part II Poisson GLMs

#### 01 May 2017 /posted in: R

One of my more popular answers on StackOverflow concerns the issue of prediction intervals for a generalized linear model (GLM). Comments, even on StackOverflow, aren’t a good place for a discussion so I thought I’d post something hereon my blog that went into a bit more detail as to why, for some common types of GLMs, prediction intervals aren’t that useful and require a lot more thinking about what they mean and how they should be calculated. I’ve broken it into two and in this, the second part, I look at Possion models.

## Prediction intervals for GLMs part I Binomial GLMs

#### 01 May 2017 /posted in: R

One of my more popular answers on StackOverflow concerns the issue of prediction intervals for a generalized linear model (GLM). My answer really only addresses how to compute confidence intervals for parameters but in the comments I discuss the more substantive points raised by the OP in their question. Lately there’s been a bit of back and forth between Jarrett Byrnes and myself about what a prediction “interval” for a GLM might mean. Comments, even on StackOverflow, aren’t a good place for a discussion so I thought I’d post something here that went into a bit more detail as to why, for some common types of GLMs, prediction intervals aren’t that useful and require a lot more thinking about what they mean and how they should be calculated. For illustration, I thought I’d use some small teaching example data sets, but whilst writing the post it started to get a little on the long side. So, I’ve broken it into two and in this part I look at logistic regression.

## Simultaneous intervals for derivatives of smooths revisited

#### 21 March 2017 /posted in: R

Eighteen months ago I screwed up! I’d written a post in which I described the use of simulation from the posterior distribution of a fitted GAM to derive simultaneous confidence intervals for the derivatives of a penalized spline. It was a nice post that attracted some interest. It was also wrong. In December I corrected the first part of that mistake by illustrating one approach to compute an actual simultaneous interval, but only for the fitted smoother. At the time I thought that the approach I outlined would translate to the derivatives but I was being lazy then Christmas came and went and I was back to teaching — you know how it goes. Anyway, in this post I hope to finally rectify my past stupidity and show how the approach used to generate simultaneous intervals from the December 2016 post can be applied to the derivatives of a spline.