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.
Updated slides on GLM, GLMM, plyr, etc. available
Some of you asked for the slides to the Mixed effect regression class I taught at the 2013 LSA Summer Institute in Ann Arbor, MI. The class covered some Generalized Linear Model, Generalized Linear Mixed Models, extensions beyond the linear model, simulation-based approaches to assessing the validity (or power) of your analysis, data summarization and visualization, and reporting of results. The class included slides from Maureen Gillespie, Dave Kleinschmidt, and Judith Degen (see above link). Dave even came by to Ann Arbor and gave his lecture on the awesome power of plyr (and reshape etc.), which I recommend. You might also just browse through them to get an idea of some new libraries (such as Stargazer for quick and nice looking latex tables). There’s also a small example to work through for time series analysis (for beginners).
Almost all slides were created in knitr and latex (very conveniently integrated into RStudio — I know some purists hate it, but comm’on), so that the code on the slides is the code that generated the output on the slides. Feedback welcome.
Is my analysis problematic? A simulation-based example
This post is in reply to a recent question on in ling-R-lang by Meredith Tamminga. Meredith was wondering whether an analysis she had in mind for her project was circular, causing the pattern of results predicted by the hypothesis that she was interested in testing. I felt her question (described below in more detail) was an interesting example that might best be answered with some simulations. Reasoning through an analysis can, of course, help a lot in understanding (or better, as in Meredith’s case, anticipating) problems with the interpretation of the results. Not all too infrequently, however, I find that intuition fails or isn’t sufficiently conclusive. In those cases, simulations can be a powerful tool in understanding your analysis. So, I decided to give it a go and use this as an example of how one might approach this type of question.
Effects of phonological overlap on fluency, speech rate, and word order in unscripted sentence production
The last two papers based on Katrina Furth’s and Caitie Hilliard’s work back when they were at Rochester just came out in the Journal of Experimental Psychology: Learning, Memory, and Cognition and the journal Frontiers in Psychology.
The JEP:LMC paper investigates how lemma selection (i.e., word choice) is affected by phonological overlap. We find evidence for a (weak) bias against sequences of phonologically onset overlapping words. That is, when speakers have a choice, they seem to prefer sentences like “Hannah gave the hammer to the boy”, rather than “Hannah handed the hammer to the boy”. This suggests very early effects of phonology on lexical production, which seem to be incompatible with strictly serial models of word production.
Jaeger, T. F., Furth, K., and Hilliard, C. 2012. Phonological overlap affects lexical selection during sentence production. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(5), 1439-1449. [doi: 10.1037/a0027862]
The Frontiers paper investigates Read the rest of this entry »
New R library for multilevel modeling
This might be of interest to many of you. MLwiN, a software package for multilevel modeling developed at Bristol that includes functions beyond those present in, e.g., lmer, now has an interface for R (kinda like WinBugs, etc.), so that you can continue to use R while taking advantage of the powerful tools in MLwiN. The package is called R2MLwiN. For more details, see below.
Dear all,
We are pleased to announce a new R package, R2MLwiN (Zhang et al. 2012)
that allows R users access to the functionality within MLwiN directly from
within the R package. This package has been developed as part of the e-STAT
ESRC digital social research programme grant along with the Stat-JR package.
See <http://www.bristol.ac.uk/cmm/software/r2mlwin/> for more details
including examples taken from the book MCMC Estimation in MLwiN.Feedback gratefully received by either me or Zhengzheng Zhang (Z.Zhang@bristol.ac.uk).
Best wishes,
Bill Browne.
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 »
New R resource for ordinary and multilevel regression modeling
Here’ s what I received from the Center of Multilevel Modeling at Bristol (I haven’t checked it out yet; registration seems to be free but required):
The Centre for Multilevel Modelling is very pleased to announce the addition of R practicals to our free on-line multilevel modelling course. These give detailed instructions of how to carry out a range of analyses in R, starting from multiple regression and progressing through to multilevel modelling of continuous and binary data using the lmer and glmer functions. MLwiN and Stata versions of these practicals are already available. You will need to log on or register onto the course to view these practicals. Read More... http://www.cmm.bris.ac.uk/lemma/course/view.php?id=13
R code for Jaeger, Graff, Croft and Pontillo (2011): Mixed effect models for genetic and areal dependencies in linguistic typology: Commentary on Atkinson
- Jaeger, Graff, Croft, and Pontillo. 2011. Mixed effect models for genetic and areal dependencies in linguistic typology: Commentary on Atkinson. Linguistic Typology 15(2), 281–319. [if you’re not subscribed to Linguistic Typology, check out this pre-final draft or contact me for an offprint].
More on random slopes and what it means if your effect is not longer significant after the inclusion of random slopes
I thought the following snippet from a somewhat edited email I recently wrote in reply to a question about random slopes and what it means that an effect becomes insignificant might be helpful to some. I also took it as an opportunity to updated the procedure I described at https://hlplab.wordpress.com/2009/05/14/random-effect-structure/. As always, comments are welcome. What I am writing below are just suggestions.
[…] an insignificant effect in an (1 + factor|subj) model means that, after controlling for random by-subject variation in the slope/effect of factor, you find no (by-convention-significant) evidence for the effect. Like you suggest, this is due to the fact that there is between-subject variability in the slope that is sufficiently large to let us call into question the hypothesis that the ‘overall’ slope is significantly different from zero.
[…] So, what’s the rule of thumb here? If you run any of the standard simple designs (2×2, 2×3, 2x2x2,etc.) and you have the psychologist’s luxury of plenty of data (24+item, 24+ subject […]), the full random effect structure is something you should entertain as your starting point. That’s in Clark’s spirit. That’s what F1 and F2 were meant for. […] All of these approaches do not just capture random intercept differences by subject and item. They also aim to capture random slope differences.
[…] here’s what I’d recommend during tutorials now because it often saves time for psycholinguistic data. I am only writing down the random effects but, of course, I am assuming there are fixed effects, too, and that your design factors will remain in the model. Let’s look at a 2×2 design: 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.
Mixed model’s and Simpson’s paradox
For a paper I am currently working on, I started to think about Simpson’s paradox, which wikipedia succinctly defines as
“a paradox in which a correlation (trend) present in different groups is reversed when the groups are combined. This result is often encountered in social-science […]”
The wikipedia page also gives a nice visual illustration. Here’s my own version of it. The plot shows 15 groups, each with 20 data points. The groups happen to order along the x-axis (“Pseudo distance from origin”) in a way that suggests a negative trend of the Pseudo distance from origin against the outcome (“Pseudo normalized phonological diversity”). However, this trend does not hold within groups. As a matter of fact, in this particular sample, most groups show the opposite of the global trend (10 out of 15 within-group slopes are clearly positive). If this data set is analyzed by an ordinary linear regression (which does not have access to the grouping structure), the result will be a significant negative slope for the Pseudo distance from origin. So, I got curious: what about linear mixed models?
Diagnosing collinearity in mixed models from lme4
I’ve just uploaded files containing some useful functions to a public git repository. You can see the files directly without worrying about git at all by visiting regression-utils.R (direct download) and mer-utils.R (direct download). Read the rest of this entry »
Annotated example analysis using mixed models
Jessica Nelson (Learning Research and Development Center, University of Pittsburgh) uploaded a step-by-step example analysis using mixed models to her blog. Each step is nicely annotated and Jessica also discusses some common problems she encountered while trying to analyze her data using mixed models. I think this is a nice example for anyone trying to learn to use mixed models. It goes through all/most of the steps outlined in Victor Kuperman and my WOMM tutorial (click on the graph to see it full size):
Tutorial on Regression and Mixed Models at Penn State
Last week (02/3-5/10), I had the pleasure to give the inaugural 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 »
HLP/Jaeger lab blog 