[R-sig-ME] help in coding random effects in lmer
Mike Lawrence
Mike.Lawrence at dal.ca
Sun Aug 1 15:23:26 CEST 2010
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. ~
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