Oh, another benefit of including trial-by-trial data is that you can increase the signal-to-noise ratio for the effects of interest by covarying out temporal/sequential effects that typically are of less interest; for example, response hand, time since last response (if targets are temporally uncertain), etc. You can also quantify things are are indeed of interest but that may not have been possible to measure in traditional anova: I like to add block-number and trial-number-within-block to look at the effects of practice and fatigue, respectively (you could even let block/trial interact with the other effects of interest to see if/how those effects are affected by practice & fatigue). Lately I've been exploring adding the previous trial's RT as a covariate; if you ever look at the correlation between current and previous trial RT, it's typically quite large and likely driven by things like vigilance cycles that may not be of interest. On this theme, a colleague mentioned an alternative approach he's seen folks adopt whereby you first do a PCA that includes several trials back of RTs, then include the first component as a covariate in the mixed model; I'm still not sure what this achieves over-and-above the more straightforward case of simply using the previous trial's RT, but it certainly sounds sexy :Op Mike
On Sat, Jul 31, 2010 at 10:07 PM, Mike Lawrence <Mike.Lawrence at dal.ca> wrote:
I'm still learning mixed effects modelling myself, but one thing pops out at me: In your formulae, you have the variable "meanRT"; I presume this reflects the fact that you aggregated your data to means within conditions prior to submitting it to lmer? If so, you have done yourself a disservice; lmer can analyze the raw, trial-by-trial data and you'll find that you can achieve higher power by providing it will all the data. Now, a problem arises whereby RT data are ?typically positively skewed and violate the normality assumption; I feel there is still a gap in the literature on how to deal with this (because there are plenty of examples where this skew has been found to be affected by experimental manipulations differentially from central tendency), but a reciprocal transform at least seems to do well at normalizing the residuals (Kliegl, Masson & Richter, 2009, compare various transforms). So, where "a" is your trial-by-trial data, I suggest you try: a$rrt = 1/a$rt fit1 = lmer( ? ?formula = rrt ~ (angle+laterality+condition:laterality)+(1|subject) ? ?, data = a ) and let us know if you still get wonky results. As a side note, l *think* that the difference between the two models you posted was that the second permitted the effects to vary Ss-by-Ss, which may be plausible but I assume costs power. As I understand it, unless you are really interested in individual differences in the effect (eg. for correlations, etc), it's better to avoid letting effects vary Ss-by-Ss. (Again, I'm still getting to grips with mixed effects modelling, so I may be entirely incorrect on these points!). On Sat, Jul 31, 2010 at 8:41 AM, nuala brady <nuala.brady at ucd.ie> wrote:
Dear lmer?people & Dr Bates ?I ?am a cognitive psychologist who needs to leave the ?world of ANOVA?and move to lmer. I am looking for advice on coding ?random effects in lmer. ??My experiment is: 30 subjects judge the laterality?of a hand (i.e.. say whether it is a left or right hand) presented onscreen?which varies in its ?(A) Laterality?(2 levels, right/left) and ?(B) Orientation (8 levels, 0 to 315 degs?in steps of 45 degs) while holding their own hands in one of 3 postures ?(C) Postures (3 levels, coded as both, minusRight?& minusLeft). ?The dependent variable is reaction time (RT). ?Laterality, Orientation & Posture are fixed effects (all ?coded as categorical variables), the random effects come from the ?subjects i.e., ?all 30 subjects respond in all possible combinations of the ?experimental variables and we need to generalise from them to the ?population ... ?My expectation (based on theory & previous studies) is that there will be a sig. main effect of angle, of laterality?& possibly a condition by laterality?interaction; ?and graphing shows this. ?The traditional way to analyse such data ?in psychology, where we typically look at all main effects & possible ?interactions as a first pass,? is via a repeated measures ?(or within-subjects) ANOVA?and the ?code in R is ?aov(RT~Laterality*Angle*Posture+Error(subject/(Laterality*Angle*Posture)),data=RTdata) ?moving to lmer, simplifying the model to just look at effects I am interested in, and specifying the random effects as shown in many examples online as follows: ?model2a<-lmer(meanRT~(angle+laterality+condition:laterality)+(1|subject),data=RTdata) ?I receive the output shown below as OUTPUT 1. Looking at the table of fixed effects I note that the Std. Err. within a specific explanatory variable (e.g, Angle) is constant across all levels of that variable. Obviously I am on the wrong track as this is not an assumption I want to? make. One of the reasons I am moving from ANOVA?to lmer?is because variance is not constant across the levels of some factors (both angle & laterality) as seen from graph, by running levene's?test etc ?Rerunning as: ?model2<-lmer(meanRT~(angle+laterality+condition:laterality)+(angle|subject)+(laterality|subject)+(condition:laterality|subject),data=RTdata) ?(...and?quite honestly, I am generalizing here from how one might specify error in aov....) ?I receive the output shown below as OUTPUT 2. Scrolling?down to the fixed effects, the Std., Errs are looking a lot better to me, BUT I am unsure whether I am using the ?syntax?correctly ?can anyone advise?? I ?appreciate this may be a very basic question, but I have not found many ?examples in my reading except for nested designs (which do not apply here, as least in my understanding of 'nested designs' ), and crossed random effects (which seem more complex than I need, having more than 1 source of random effects) ?thanks in advance, - Nuala ?ps - in case the description of the experiment is not clear, I copy data for s1 (aine) at the very end of the email - this pattern will repeat for s2 to s30 ?OUTPUT 1: summary(model2a) ?Linear mixed model fit by REML ?Formula: meanRT ~ (angle + laterality + condition:laterality) + (1 | subject) ??? Data: data ??? AIC?? BIC logLik deviance REMLdev ??20620 20699 -10295??? 20700?? 20590 ?Random effects: ??Groups?? Name??????? Variance Std.Dev. ??subject? (Intercept) 124335?? 352.61 ??Residual????????????? 94809?? 307.91 ?Number of obs: 1440, groups: subject, 30 ?Fixed effects: ???????????????????????????????????? Estimate Std. Error t value ?(Intercept)????????????????????????? 1218.82????? 70.70? 17.240 ?angle45??????????????????????????????? 13.49????? 32.46?? 0.416 ?angle90?????????????????????????????? 217.20????? 32.46?? 6.692 ?angle135????????????????????????????? 499.11????? 32.46? 15.378 ?angle180????????????????????????????? 961.80????? 32.46? 29.633 ?angle225????????????????????????????? 471.60????? 32.46? 14.530 ?angle270????????????????????????????? 228.82????? 32.46?? 7.050 ?angle315?????????????????????????????? 62.12????? 32.46?? 1.914 ?lateralityright????????????????????? -122.60????? 28.11? -4.362 ?lateralityleft:conditionminusLeft????? 14.23????? 28.11?? 0.506 ?lateralityright:conditionminusLeft??? -27.28????? 28.11? -0.971 ?lateralityleft:conditionminusRight??? -33.77????? 28.11? -1.201 ?lateralityright:conditionminusRight??? 35.94????? 28.11?? 1.279 ?OUTPUT 2: summary(model2) ? Linear mixed model fit by REML ?Formula: meanRT ~ (angle + laterality + condition:laterality) + (angle | subject) + (laterality | subject) + (condition:laterality |subject) ??? Data: data ??? AIC?? BIC logLik deviance REMLdev ??19918 20345? -9878??? 19867?? 19756 ?Random effects: ??Groups?? Name??????????????????????????????? Variance?? Std.Dev.?? Corr ??subject? (Intercept)???????????????????????? 3.5601e+04 188.681267 ?????????? angle45???????????????????????????? 3.5488e+01?? 5.957191? 1.000 ?????????? angle90???????????????????????????? 1.9515e+04 139.697353? 1.000 ?????????? angle135??????????????????????????? 7.8349e+04 279.909544? 0.704 ?????????? angle180??????????????????????????? 3.3373e+05 577.689525? 0.390 ?????????? angle225??????????????????????????? 7.1096e+04 266.638569? 0.462 ?????????? angle270??????????????????????????? 1.7412e+04 131.954987? 0.695 ?????????? angle315??????????????????????????? 7.1155e+03? 84.353226? 0.759 ??subject? (Intercept)???????????????????????? 2.5444e-04?? 0.015951 ?????????? lateralityright???????????????????? 5.2171e-05?? 0.007223 -1.000 ??subject? (Intercept)???????????????????????? 1.4016e+04 118.388702 ?????????? conditionboth:lateralityleft??????? 1.2554e+04 112.046691? 0.327 ?????????? conditionminusLeft:lateralityleft?? 3.0653e+04 175.080964? 0.257 ?????????? conditionminusRight:lateralityleft? 1.6837e+04 129.758438 -0.019 ?????????? conditionboth:lateralityright?????? 1.0627e+04 103.089657 -0.340 ?????????? conditionminusLeft:lateralityright? 9.6021e+03? 97.990531 -0.822 ?????????? conditionminusRight:lateralityright 1.0345e+04 101.711720 -0.453 ??Residual???????????????????????????????????? 4.2251e+04 205.549629 ?? 1.000 ?? 0.704? 0.704 ?? 0.390? 0.390? 0.847 ?? 0.462? 0.462? 0.837? 0.889 ?? 0.695? 0.695? 0.711? 0.609? 0.867 ?? 0.759? 0.759? 0.324 -0.042? 0.021? 0.317 ?? 0.424 ?? 0.196? 0.569 ?? 0.428 -0.431 -0.555 ??-0.112 -0.364 -0.475? 0.730 ??-0.451 -0.211? 0.622 -0.400 -0.094 ?Number of obs: 1440, groups: subject, 30 ?Fixed effects: ???????????????????????????????????? Estimate Std. Error t value ?(Intercept)????????????????????????? 1218.82????? 52.37? 23.273 ?angle45??????????????????????????????? 13.49????? 21.69?? 0.622 ?angle90?????????????????????????????? 217.20????? 33.47?? 6.490 ?angle135????????????????????????????? 499.11????? 55.51?? 8.992 ?angle180????????????????????????????? 961.80???? 107.67?? 8.933 ?angle225????????????????????????????? 471.60????? 53.29?? 8.850 ?angle270????????????????????????????? 228.82????? 32.40?? 7.062 ?angle315?????????????????????????????? 62.12????? 26.58?? 2.337 ?lateralityright????????????????????? -122.60????? 28.20? -4.348 ?lateralityleft:conditionminusLeft????? 14.23????? 35.18?? 0.404 ?lateralityright:conditionminusLeft??? -27.28????? 23.13? -1.180 ?lateralityleft:conditionminusRight??? -33.77????? 33.79? -0.999 ?lateralityright:conditionminusRight??? 35.94????? 36.48?? 0.985 ?Example data for 1 subject ?data[1:48,1:5] - RT is actially mean RT of 18 trails ??? subject laterality? posture angle??? RT ?1???? aine?????? left?????? both???? 0? 844.8000 ?2???? aine?????? left?????? both??? 45? 796.4706 ?3???? aine?????? left?????? both??? 90 1007.5722 ?4???? aine?????? left?????? both?? 135 1214.7556 ?5???? aine?????? left?????? both?? 180 1249.9625 ?6???? aine?????? left?????? both?? 225 1305.0500 ?7???? aine?????? left?????? both?? 270 1043.8000 ?8???? aine?????? left?????? both?? 315? 814.6833 ?9???? aine?????? left? minusLeft???? 0? 817.3778 ?10??? aine?????? left? minusLeft??? 45? 951.0588 ?11??? aine?????? left? minusLeft??? 90 1044.5706 ?12??? aine?????? left? minusLeft?? 135 1345.5625 ?13??? aine?????? left? minusLeft?? 180 1482.8333 ?14??? aine?????? left? minusLeft?? 225 1331.3588 ?15??? aine?????? left? minusLeft?? 270? 985.1000 ?16??? aine?????? left? minusLeft?? 315? 995.2563 ?17??? aine?????? left minusRight???? 0? 986.8556 ?18??? aine?????? left minusRight??? 45? 903.2176 ?19??? aine?????? left minusRight??? 90? 947.8059 ?20??? aine?????? left minusRight?? 135 1453.8750 ?21??? aine?????? left minusRight?? 180 1698.8278 ?22??? aine?????? left minusRight?? 225 1337.1200 ?23??? aine?????? left minusRight?? 270 1109.2467 ?24??? aine?????? left minusRight?? 315? 929.0412 ?25??? aine????? right?????? both???? 0? 913.5944 ?26??? aine????? right?????? both??? 45? 930.5056 ?27??? aine????? right?????? both??? 90 1093.9167 ?28??? aine????? right?????? both?? 135 1275.9647 ?29??? aine????? right?????? both?? 180 1489.1750 ?30??? aine????? right?????? both?? 225 1188.1333 ?31??? aine????? right?????? both?? 270 1054.7778 ?32??? aine????? right?????? both?? 315? 904.8722 ?33??? aine????? right? minusLeft???? 0? 888.9375 ?34??? aine????? right? minusLeft??? 45? 915.0706 ?35??? aine????? right? minusLeft??? 90 1060.3167 ?36??? aine????? right? minusLeft?? 135 1240.0867 ?37??? aine????? right? minusLeft?? 180 1772.4611 ?38??? aine????? right? minusLeft?? 225 1168.5625 ?39??? aine????? right? minusLeft?? 270 1093.1889 ?40??? aine????? right? minusLeft?? 315? 842.2667 ?41??? aine????? right minusRight???? 0? 971.3944 ?42??? aine????? right minusRight??? 45? 974.3333 ?43??? aine????? right minusRight??? 90 1064.9833 ?44??? aine????? right minusRight?? 135 1389.0059 ?45??? aine????? right minusRight?? 180 1575.9000 ?46??? aine????? right minusRight?? 225 1322.6444 ?47??? aine????? right minusRight?? 270 1053.7389 ?48??? aine????? right minusRight?? 315 1077.0529 ?Nuala Brady ?School of Psychology ?University College Dublin ?Belfield, D4 ?IRELAND ?+353 (0)1 716 8247 ?nuala.brady at ucd.ie ? ? ? ?[[alternative HTML version deleted]]
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-- Mike Lawrence Graduate Student Department of Psychology Dalhousie University Looking to arrange a meeting? Check my public calendar: http://tr.im/mikes_public_calendar ~ Certainty is folly... I think. ~
Mike Lawrence Graduate Student Department of Psychology Dalhousie University Looking to arrange a meeting? Check my public calendar: http://tr.im/mikes_public_calendar ~ Certainty is folly... I think. ~