# linear mixed models

### The ‘softer kind’ of tutorial on linear mixed effect regression

I recently was pointed to this nice and very accessible tutorial on linear mixed effects regression and how to run them in R by **Bodo Winter **(at UC Merced). If you don’t have much or any background in this type of model, I recommend you pair it with a good conceptual introduction to these models like Gelman and Hill 2007 and perhaps some slides from our LSA 2013 tutorial.

There are a few thing I’d like to add to Bodo’s suggestions regarding how to report your results:

- be clear how you coded the variables since this does change the interpretation of the coefficients (the betas that are often reported). E.g. say whether you sum- or treatment-coded your factors, whether you centered or standardized continuous predictors etc. As part of this, also be clear about the
*direction*of the coding. For example, state that you “sum-coded gender as female (1) vs. male (-1)”. Alternatively, report your results in a way that clearly states the directionality (e.g., “Gender=male, beta = XXX”). - please also report whether collinearity was an issue. E.g., report the highest fixed effect correlations.

Happy reading.

### The serial founder hypothesis and word order universals

Check out this article in ScienceNews summarizing commentaries on two recent language studies in Science (Atkinson, 2011: ) and Nature (Dunn et al., 2011). Each of the studies has received a lot of attention and they are the subject of two special issues in press for Linguistic Typology, to which HLP Lab contributed on three articles. I will add a link to the special issue(s) once it comes out. Read the rest of this entry »

### Two interesting papers on mixed models

While searching for something else, I just came across two papers that should be of interest to folks working with mixed models.

- Schielzeth, H. and Forstmeier, W. 2009.
**Conclusions beyond support: overconfident estimates in mixed models**. Behavioral Ecology Volume 20, Issue 2, 416-420. I have seen the same point being made in several papers under review and at a recent CUNY (e.g. Doug Roland’s 2009? CUNY poster). On the one hand, it should be absolutely clear that random intercepts alone are often insufficient to account for violations of independence (this is a point, I make every time I am teaching a tutorial). On the other hand, I have reviewed quite a number of papers, where this mistake was made. So, here you go. Black on white. The moral is (once again) that no statistical procedure does what you think it should do*if you don’t use it the way it was intended to*. - The second paper takes on a more advanced issue, but one that is becoming more and more relevant.
**How can we test whether a random effect is essentially non-necessary – i.e. that it has a variance of 0?**Currently, most people conduct model comparison (following Baayen, Davidson and Bates, 2008). But this approach is not recommended (and neither do Baayen et al recommend it) if we want to test whether*all*random effects can be completely removed from the model (cf. the very useful R FAQ list, which states “*do not*compare lmer models with the corresponding lm fits, or glmer/glm; the log-likelihoods […] include different additive terms”). This issue is taken on in Scheipl, F., Grevena, S. and Küchenhoff, H. 2008.**Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models.**Computational Statistics & Data Analysis.Volume 52, Issue 7, 3283-3299. They present power comparisons of various tests.

### Tutorial on Regression and Mixed Models at Penn State

Last week (02/3-5/10), I had the pleasure to give the inaugura*l CLS Graduate Student Young Scientist Colloquium* (“An information theoretic perspective on language production”) at the Center for Language Science at Penn State (State College).

I also gave two 3h-lectures on regression and mixed models. The slides for Day 1 introduce linear regression, generalized linear models, and generalized linear mixed models. I am using example analyses of real psycholinguistic data sets from Harald Baayen’s *languageR* library (freely available through the free stats package *R*). The slides for Day 2 go through problems and solutions for regression models. For more information have a look at the online lectures available via the HLP lab wiki. I’ve uploaded the pdf slides and an R script. There also might be a pod cast available at some point. Feedback welcome. I’ll be giving a similar workshop at McGill in May, so watch for more materials.

I had an intensive and fun visit, meeting with researchers from Psychology, Communication and Disorders, Linguistics, Spanish, German, etc. I learned a lot about bilingualism (not only though) and a bit about anticipatory motor planning. So thanks to everyone there who helped to organize the visit, especially Jorge Valdes and Jee Sook Park. And thanks to Judith Kroll for the awesome cake (see below). Goes without saying that it was a pleasure meeting the unofficial mayor of State College, too ;). See you all at CUNY! Read the rest of this entry »

### R-code for visual model summaries: linear mixed models

Here is some code to summarize the coefficients of a linear mixed model that produces nice graphs like the following one (well, the curved arrows were added in powerpoint): [click to see a larger version]

But first some background about the example model: Read the rest of this entry »