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Mosteller & Tukey (1977). Data Analysis and Regression. “Encouraging linguists to use linear mixedeffects models is like giving shotguns to toddlers.” (see Barr et al., 2013) Gerry Altmann “A world of subjectivity” Sarah Depaoli “IF YOU BEAT THE DATA, AT SOME TIME IT WILL SPEAK” “A world of subjectivity” Sarah Depaoli “… and then you publish and get tenure.” LMM response ~ intercept + slope * fixed effect + error distinguish between test and control variables Test vs. Control Variable Example test variable Null Model control variable Test vs. Control Variable Example test variable Null Model control variable Test vs. Control Variable Example Response ~ Critical Effect BLACK BOX Control 1 Control 2 Random Effects Test vs. Control Variable Example Response ~ Critical Effect BLACK BOX Control 3 Control 2 Random Effects Test vs. Control Variable Example Response ~ Critical Effect Control 3 Control 2 Random Effects Trade-off #1 Model Simplicity Model Fit Trade-off #2 “Exploratory End” Datadriven “Confirmatory End” Theorydriven Harald Baayen Trade-off #2 “Exploratory End” Datadriven “Confirmatory End” Theorydriven 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 • 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 2: more theorydriven Approach 1: more data-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) Approach 2: more theorydriven Approach 1: more data-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 2: more theorydriven Approach 1: more data-driven Approach 2: more theorydriven • 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 theorydriven 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 Approach 1: more data-driven Approach 2: more theorydriven Think about model (before you conduct your experiment) Test whether control variables interact with test variable, or whether Build model, evaluate the they are needed model’s assumptions Build model that better fits the assumptions Dialogue with your model People might speed up or slow down throughout an experiment. You need to know that each item was repeated two times! You need to know that there’s multiple responses per subject and item! Token Researcher ;-) 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) Important principle CONFIRM FIRST EXPLORE SECOND 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 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. “We tested a linear mixed effects model with subjects and items as random effects.” The write-up should reflect (as adequately as possible) the details of your model… and your model selection procedure = 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) 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 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 byitem 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 o Provide results of likelihood ratio test (i.e., significance etc.) o Provide estimates and standard errors in the metric of the model o For poisson and logistic regression, additionally provide some exemplary backtransformed 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 That’s it