… or, as Uncle Ben would say

Mosteller & Tukey (1977). Data Analysis and Regression.

“Encouraging linguists to use linear mixed-effects models is like giving shotguns to toddlers.” Gerry Altmann (see Barr et al., 2013)

“A world of subjectivity” Sarah Depaoli “IF YOU BEAT THE DATA, AT SOME TIME IT WILL SPEAK” data loss - illustrate how proportions loose data by 2/4 … and 30/60 ….etc.

“A world of subjectivity” Sarah Depaoli “… and then you publish and get tenure.” data loss - illustrate how proportions loose data by 2/4 … and 30/60 ….etc.

distinguish between test and control variables LMM response ~ intercept + slope * fixed effect + error distinguish between test and control variables that’s the “model” part of it… we model the world as falling into two categories… things that we do understand, and things that we don’t understand

Test vs. Control Variable Example pitch ~ politen * gender test variable control variable pitch ~ gender Both test and control variables are always fixed effects (because their influence is systematic) Null Model

Test vs. Control Variable Example vowdur ~ VowelType * Repetition test variable control variable vowdur ~ Repetition I’m testing whether polite speech has lower pitch (test variable) … but I’m not really interested in gender. I nevertheless have to control for gender because that co-determines pitch (control variable) Null Model

Test vs. Control Variable Example Response ~ BLACK BOX Critical Effect Control 1 Control 2 Random Effects I’m testing whether polite speech has lower pitch (test variable) … but I’m not really interested in gender. I nevertheless have to control for gender because that co-determines pitch (control variable)

Test vs. Control Variable Example Response ~ BLACK BOX Critical Effect Control 3 Control 2 Random Effects I’m testing whether polite speech has lower pitch (test variable) … but I’m not really interested in gender. I nevertheless have to control for gender because that co-determines pitch (control variable)

Test vs. Control Variable Example Response ~ Critical Effect Control 3 Control 2 Random Effects I’m testing whether polite speech has lower pitch (test variable) … but I’m not really interested in gender. I nevertheless have to control for gender because that co-determines pitch (control variable)

Trade-off #1 Model Simplicity Model Fit How much do you want your models to be simple? How much do you want them to capture the real world? GENERALIZABILITY; The number of data points should vastly exceed the number of fixed effects levels you estimate.

Trade-off #2 Data- driven Theory- driven “Exploratory End” “Confirmatory End” Data- driven Theory- driven Harald Baayen

Roger Mundry (and many others) Trade-off #2 “Exploratory End” “Confirmatory End” Data- driven Theory- driven Roger Mundry (and many others)

Trade-off #2 Big Question: How much do you allow the data to suggest new hypotheses? How much do you depend on a priori theory?

Approach 1: more data-driven Approach 2: more theory-driven e.g., test whether random slopes are needed (maybe not advisable) e.g., test whether interaction for sth. is necessary or not (“o.k.” if the interaction is a control variable) e.g., test whether sth. requires a non-linear or a linear effect (maybe o.k.)

Approach 1: more data-driven Approach 2: more theory-driven THINGS TO WORRY ABOUT: Taken to the extreme, this approach has a very high likelihood of finding any significant result The model selection process is less transparent to outsiders (or, you have to write a LONG LONG stats section) (in Baayen’s defense: he doesn’t go that far)

Approach 1: more data-driven Approach 2: more theory-driven ADVANTAGES: You don’t miss important things in your data Your model might thus be more accurate and “more true to the data”

Approach 1: more data-driven Approach 2: more theory-driven You formulate your model before you look at the data The components of your model are guided by:  Theory + Published Results  General world-knowledge  Research experience Taken to the extreme, you can’t even make a plot before you formulate your model

Approach 1: more data-driven Approach 2: more theory-driven ADVANTAGES: It forces you to think a lot It’s fun! It gives you a lot of responsibility, as a scientist Your estimates are going to be more conservative

Think about model (before you conduct your experiment) Approach 1: more data-driven Approach 2: more theory-driven Think about model (before you conduct your experiment) Test whether control variables interact with test variable, or whether they are needed Build model, evaluate the model’s assumptions Build model that better fits the assumptions

Dialogue with your model You need to know that there’s multiple responses per subject and item! Token Researcher ;-) People might speed up or slow down throughout an experiment. You need to know that each item was repeated two times!

Keep in mind: You have to resolve non-independencies Your random effects structure should be maximal with respect to your experimental design

Protecting your research from yourself: Whatever you do, your model decision should not be based on the significance of your effect

(JEPS Bulletin)

CONFIRM FIRST EXPLORE SECOND Important principle McArdle (2011: 335) John McArdle McArdle (2011: 335) McArdle, J. J. (2011). Some ethical issues in factor analysis. In A.T. Panter & S. K. Sterba (Eds.), Handbook of Ethics in Quantitative Methodology (pp. 313-339). New York, NY: Routledge.

The write-up The success of phonetics as a field depends on the transparency of reporting analyses

Important principle BE HONEST NOT PURE John McArdle

Cool guidelines United Nations Economic Commission for Europe (2009a). Making Data Meaningful Part 1: A guide to writing stories about numbers. New York and Geneva: United Nations. United Nations Economic Commission for Europe (2009b). Making Data Meaningful Part 2: A guide to presenting statistics. New York and Geneva: United Nations. Write a story about the results, not a story about your statistical discovery process However, do specify your model selection choices

“We tested a linear mixed effects model with subjects and items as random effects.” without mentioning the random effects structure, you don’t know what’s going on

= Reproducible Research The write-up should reflect (as adequately as possible) the details of your model… and your model selection procedure precisely because there are so many researcher degrees of freedom… it is important for your audience to know what you did… and to potentially critique you the purpose of reporting your analysis is replicability = Reproducible Research

Rule of thumb: “One needs to provide sufficient information for the reader to be able to recreate the analyses.” Barr et al. (2013) ,,, therefore … it is advisable to keep your model lean Ask yourself: With the information that I provided, could I, myself, replicate the analysis?

How to write up (1) "Phenomenon-oriented write-up" (2) Appendix / Supplementary Materials (even though I think they should be)

Example #1 “We used generalized linear mixed models to test the effect of Gender and Politeness on pitch. Subjects and items were random effects (random intercepts) (Baayen, Davidson & Bates, 2008), with random slopes for subjects and items for the effect Politeness (Barr, Levy, Scheepers & Tily, 2013). We also included a Gender * Politeness interaction into the model and if this interaction was not significant, only included the main effects. /// Q-Q plots and plots of residuals against fitted values revealed no obvious deviations from normality and homoskedasticity. We report p-values based on Likelihood Ratio Tests of the model with the main fixed effect in question (Politeness) against the model without the main fixed effect (null model, including Gender).”

Example #2: "Phenomenon-oriented" “We used generalized linear mixed models to test the association between voice onset time and pitch. The fixed effects quantify the effect of VOT on politeness, as well as the effect of place of articulation, vowel type and gender on politeness. The random effects quantify the by-subject and by-item variability in pitch (random intercepts), as well as the variation of the effect of VOT on pitch for subjects and items (random slopes).”

Mentioning assumptions “Visual inspection of residual plots revealed no obvious deviation from normality and homoskedasticity of errors.” “We checked plots of residuals against fitted values and found no indication that the normality and homoskedasticity assumption were violated.” “… indicated a problem with … We therefore log-transformed the data.”

Results Provide results of likelihood ratio test (i.e., significance etc.) Provide estimates and standard errors in the metric of the model For poisson and logistic regression, additionally provide some exemplary back-transformed values (don’t back-transform the standard errors)

Likelihood Model Output Data: mag Models: magmodel.maineffect: linelength ~ condition + city_status + german_side + gender + magmodel.maineffect: trial_order + (1 + condition * city_status | subjects) + magmodel.maineffect: (1 + condition * city_status | items) magmodel: linelength ~ condition * city_status + german_side + gender + magmodel: trial_order + (1 + condition * city_status | subjects) + magmodel: (1 + condition * city_status | items) Df AIC BIC logLik Chisq Chi Df Pr(>Chisq) magmodel.maineffect 27 7984.5 8121.9 -3965.3 magmodel 28 7893.7 8036.2 -3918.8 92.821 1 < 2.2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Important principle BE HONEST NOT PURE John McArdle

Make your scripts orderly and reproducible

Reproducibility Make your script online available Avoid modifying your data manually ... make a script that records your process red one = in your own self-interest (for later use)

That’s it