[R-sig-ME] Interpreting lmer() interactions with Helmert contrasts
Ken Beath
ken.beath at mq.edu.au
Sat Aug 22 02:18:36 CEST 2015
The first thing to do is to decide if an interaction is really needed.
Applying anova() to the model with interaction should give this. Note that
if there is an interaction it is not possible to conclude anything about
the main effects. The tests that you have performed use Chi-sq statistics
which is not correct for a linear model, it should be F. Playing around
with lme4 I found that wasn't possible except when using a single model.
Testing for removal of combined interaction and main effect is not correct.
If there is an interaction I would suggest using the standard contrasts.
Then you will need to summarise this and there are a few ways in R to do
this. One is svycontrast in the survey package. The result should be a
different effect of time for each word type or vice-versa. This is
something that should be talked over with a statistician.
On 22 August 2015 at 03:39, Dan McCloy <drmccloy at uw.edu> wrote:
> As a word of caution, you seem to have set up your factor coding to make
> interpretation especially tricky. The coding of your "Time1" variable is
> set up so that your factor level of "-1" has a positive coefficient, and
> your factor level of "1" has a negative coefficient. Before doing anything
> else, I recommend you re-run the model after re-setting the contrasts for
> "Time" so that your textual levels have the same sign as their coefficients
> in the model (personally I would go further and re-code the factor as "Pos"
> and "Neg" or some other textual shorthand that cannot be confused with row
> or column numbers of the contrast matrix). I also usually set the row
> names of contrast matrices to be actual names, so that the lmer output
> names the coefficients in a way that is harder for me to mis-interpret
> (e.g., as "TimePos" or "TimeNeg" instead of "Time1"). While you're at it,
> if you're interested in "treatment" vs "no treatment" you might consider
> re-setting the contrasts for the WordType factor as well. You have this:
>
> [,1] [,2]
> 0 0.6666667 0.0 # untrained
> 1 -0.3333333 -0.5 # trained-related
> 2 -0.3333333 0.5 # trained-unrelated
>
> which means that *positive* coefficient estimates for factor 1 mean that
> "untrained" increases RT. Similar comment for related vs. unrelated. I
> would recommend swapping the signs on both factors so that anything that is
> "un-" is negative, like this:
>
> [,1] [,2]
> 0 -0.6666667 0.0 # untrained
> 1 0.3333333 0.5 # trained-related
> 2 0.3333333 -0.5 # trained-unrelated
>
> As far as interpreting the model coefficients for the interactions:
>
> WordType1:Time1 0.0301627 0.0115349 2.61
> WordType2:Time1 -0.0089123 0.0141624 -0.63
>
> This says that comparing cases of "WordType1" (which curently means
> "untrained minus trained" in your experiment) combined with "Time1" (which
> I think means Time=1 or what I'm calling "Pos") has a positive coefficient
> (the combination increases log reaction time, or slows people down)
> relative to what you would expect if "WordType" and "Time" contributed
> independently to reaction time. In other words, I think this means that
> lack of training slows people down more when Time=1 than when Time=-1
> (though the mismatch between signs of the factor levels and contrast
> coefficients for the Time variable make me hesitate as to whether I said
> that last bit backwards).
>
> Hope it helps, and good luck.
> -- dan
>
> Daniel McCloy
> http://dan.mccloy.info/
> Postdoctoral Research Fellow
> Institute for Learning and Brain Sciences
> University of Washington
>
>
> On Fri, Aug 21, 2015 at 6:23 AM, Becky Gilbert <beckyannegilbert at gmail.com
> >
> wrote:
>
> > Hi Paul/List,
> >
> > After thinking about this a bit more, I don't think planned comparisons
> > gives me what I'm looking for. I want to know whether the effect of Time
> > is different for WordType = 0 (level 1) vs the other two levels combined
> -
> > this is WordType contrast 1. I also want to know whether the effect of
> > Time is different for WordType = 1 vs WordType = 2 (i.e. level 2 vs level
> > 3) - this is WordType contrast 2.
> >
> > I think the use of planned comparisons here would defeat the purpose of
> my
> > contrasts, but maybe I'm missing something?
> >
> > Thanks!
> > Becky
> >
> > ____________________________________________
> >
> > Dr Becky Gilbert
> >
> > On 21 August 2015 at 13:46, Becky Gilbert <beckyannegilbert at gmail.com>
> > wrote:
> >
> > > Hi Paul,
> > >
> > > Thanks very much for the suggestion! I tried using lsmeans() to get
> the
> > > pairwise comparisons as you suggested, and the results are below.
> > >
> > > I'm a little confused by the results because the pairwise comparison
> > tests
> > > all show p > .05, but the WordType x Time interaction was significant
> > when
> > > tested via model comparisons...? I think this might be due to the
> Tukey
> > > adjustment for multiple comparisons, but I'm not sure. Specifically
> the
> > > contrast for the two levels of Time at WordType = 2 looks like it might
> > > have been significant before the multiple comparisons correction, thus
> > > accounting for the significance of the interaction term in model
> > > comparisons. Any thoughts?
> > >
> > > Thanks again!
> > > Becky
> > >
> > > $lsmeans
> > > WordType = 0:
> > > Time lsmean SE df lower.CL upper.CL
> > > -1 2.880592 0.02209390 21.58 2.834721 2.926464
> > > 1 2.887315 0.02144245 22.13 2.842860 2.931769
> > >
> > > WordType = 1:
> > > Time lsmean SE df lower.CL upper.CL
> > > -1 2.856211 0.02156603 19.78 2.811193 2.901229
> > > 1 2.888640 0.02089339 20.17 2.845080 2.932200
> > >
> > > WordType = 2:
> > > Time lsmean SE df lower.CL upper.CL
> > > -1 2.852485 0.02181905 20.72 2.807072 2.897898
> > > 1 2.893827 0.02113775 21.12 2.849883 2.937770
> > >
> > > Confidence level used: 0.95
> > >
> > > $contrasts
> > > WordType = 0:
> > > contrast estimate SE df t.ratio p.value
> > > -1 - 1 -0.00672255 0.02078469 19.31 -0.323 0.7498
> > >
> > > WordType = 1:
> > > contrast estimate SE df t.ratio p.value
> > > -1 - 1 -0.03242907 0.02097452 20.02 -1.546 0.1377
> > >
> > > WordType = 2:
> > > contrast estimate SE df t.ratio p.value
> > > -1 - 1 -0.04134141 0.02146707 21.93 -1.926 0.0672
> > >
> > >
> > > ____________________________________________
> > >
> > > Dr Becky Gilbert
> > >
> > > On 21 August 2015 at 12:19, paul debes <paul.debes at utu.fi> wrote:
> > >
> > >> Hi Becky,
> > >>
> > >> Maybe you are interested in pairwise comparisons? The "lsmeans"
> package
> > >> comes in handy.
> > >>
> > >> Try something like this:
> > >>
> > >> library("pbkrtest") # gives you KW-adjusted denDF for tests, but must
> be
> > >> installed
> > >> library("lsmeans")
> > >>
> > >> Model.lmer.means = lsmeans(Model, spec = pairwise ~ WordType|Time)
> > >> Model.lmer.means = summary(Model.lmer.means)
> > >> Model.lmer.means
> > >>
> > >> Maybe you want the contrast conditional on WordType, not Time? Swap it
> > to:
> > >> "spec = pairwise ~ Time|WordType"
> > >>
> > >> Best,
> > >> Paul
> > >>
> > >>
> > >> On Fri, 21 Aug 2015 14:04:07 +0300, Becky Gilbert <
> > >> beckyannegilbert at gmail.com> wrote:
> > >>
> > >> Dear list,
> > >>>
> > >>> I'm wondering if someone could help me interpret an interaction
> between
> > >>> two
> > >>> factors, when one of the factors uses Helmert contrasts?
> > >>>
> > >>> I ran a linear mixed effects model (lmer) with reaction times as the
> > DV,
> > >>> 2
> > >>> fixed factors: Time (2 levels) and Word Type (3 levels), and 2 random
> > >>> factors: Subjects and Items. I used Helmert contrasts for the Word
> > Type
> > >>> factor:
> > >>> - Contrast 1 = level 1 (Untrained) vs levels 2 & 3 (Trained-related
> and
> > >>> Trained-unrelated)
> > >>> - Contrast 2 = level 2 vs. level 3 (Trained-related vs
> > Trained-unrelated)
> > >>> The data, contrasts, model, summary and model comparisons are listed
> at
> > >>> the
> > >>> end of the message.
> > >>>
> > >>> Model comparisons with anova() showed a significant interaction
> between
> > >>> Time and Word Type. However, I don't know how to get the statistics
> > for
> > >>> the interactions between Time and each Word Type contrast.
> > >>>
> > >>> Based on the t-values for coefficients in the model summary, it looks
> > >>> like
> > >>> the significant Word Type x Time interaction is driven by the
> > interaction
> > >>> with the 1st contrast for Word Type (t = 2.61). However I don't
> think
> > >>> that
> > >>> the statistics for the fixed effects coefficients are exactly what
> I'm
> > >>> looking forward (they are sequential tests, right?). And if these
> are
> > >>> the
> > >>> appropriate statistics, I'm aware of the problems with trying to get
> > >>> p-values from these estimates. So is there a way to do likelihood
> > ratio
> > >>> tests for each Word Type contrast, or some other way of interpreting
> > the
> > >>> Word Type x Time interaction?
> > >>>
> > >>> Data structure:
> > >>>
> > >>>> str(rtData)
> > >>>>
> > >>> 'data.frame': 1244 obs. of 11 variables:
> > >>> $ Subject : Factor w/ 16 levels "AB","AS","AW",..: 1 1 1 1 1 1
> 1
> > 1
> > >>> 1
> > >>> 1 ...
> > >>> $ Item : Factor w/ 48 levels "ANT","BANDAGE",..: 3 4 6 12 13
> 14
> > 22
> > >>> 29 30 34 ...
> > >>> $ Response : int 960 1255 651 1043 671 643 743 695 965 589 ...
> > >>> $ Time : Factor w/ 2 levels "-1","1": 1 1 1 1 1 1 1 1 1 1 ...
> > >>> $ WordType : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1
> > ...
> > >>> $ logRT : num 2.98 3.1 2.81 3.02 2.83 ...
> > >>>
> > >>> contrasts(rtData$Time)
> > >>>>
> > >>> [,1]
> > >>> -1 0.5
> > >>> 1 -0.5
> > >>>
> > >>> contrasts(rtData$WordType)
> > >>>>
> > >>> [,1] [,2]
> > >>> 0 0.6666667 0.0
> > >>> 1 -0.3333333 -0.5
> > >>> 2 -0.3333333 0.5
> > >>>
> > >>> Model:
> > >>> lmer(logRT ~ 1 + WordType + Time + WordType:Time +
> > >>> (1 + Time|Subject) +
> > >>> (1|Item),
> > >>> data = rtData)
> > >>>
> > >>> REML criterion at convergence: -2061.2
> > >>> Scaled residuals:
> > >>> Min 1Q Median 3Q Max
> > >>> -2.7228 -0.6588 -0.0872 0.5712 3.7790
> > >>> Random effects:
> > >>> Groups Name Variance Std.Dev. Corr
> > >>> Item (Intercept) 0.000933 0.03054
> > >>> Subject (Intercept) 0.004590 0.06775
> > >>> Time1 0.005591 0.07478 0.05
> > >>> Residual 0.009575 0.09785
> > >>> Number of obs: 1244, groups: Target, 46; Subject, 16
> > >>> Fixed effects:
> > >>> Estimate Std. Error t value
> > >>> (Intercept) 2.8765116 0.0177527 162.03
> > >>> WordType1 0.0111628 0.0110852 1.01
> > >>> WordType2 0.0007306 0.0071519 0.10
> > >>> Time1 -0.0268310 0.0195248 -1.37
> > >>> WordType1:Time1 0.0301627 0.0115349 2.61
> > >>> WordType2:Time1 -0.0089123 0.0141624 -0.63
> > >>>
> > >>> Model comparisons with anova() for main effects and interaction:
> > >>>
> > >>> -full model vs no Word Type x Time interaction
> > >>> Df AIC BIC logLik deviance
> > Chisq
> > >>> Chi Df Pr(>Chisq)
> > >>> rtModelNoInteraction 9 -2077.5 -2031.3 1047.7 -2095.5
> > >>>
> > >>> rtModelFull 11 -2080.5 -2024.1 1051.2 -2102.5 7.0388
> > >>> 2
> > >>> 0.02962 *
> > >>>
> > >>> -full model vs model without Time and interaction
> > >>> Df AIC BIC logLik deviance Chisq Chi
> Df
> > >>> Pr(>Chisq)
> > >>> rtModelNoTime 8 -2077.8 -2036.7 1046.9 -2093.8
> > >>> rtModelFull 11 -2080.5 -2024.1 1051.2 -2102.5 8.7424 3
> > >>> 0.03292 *
> > >>>
> > >>> -full model vs model without Word Type and interaction
> > >>> Df AIC BIC logLik deviance Chisq Chi
> Df
> > >>> Pr(>Chisq)
> > >>> rtModelNoWT 7 -2080.4 -2044.5 1047.2 -2094.4
> > >>> rtModelFull 11 -2080.5 -2024.1 1051.2 -2102.5 8.0875 4
> > >>> 0.08842
> > >>> .
> > >>>
> > >>> Thanks in advance for any advice!
> > >>> Becky
> > >>> ____________________________________________
> > >>>
> > >>> Dr Becky Gilbert
> > >>>
> > >>> [[alternative HTML version deleted]]
> > >>>
> > >>> _______________________________________________
> > >>> R-sig-mixed-models at r-project.org mailing list
> > >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> > >>>
> > >>
> > >>
> > >> --
> > >> Paul Debes
> > >> DFG Research Fellow
> > >> University of Turku
> > >> Department of Biology
> > >> Itäinen Pitkäkatu 4
> > >> 20520 Turku
> > >> Finland
> > >>
> > >
> > >
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
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> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
--
*Ken Beath*
Lecturer
Statistics Department
MACQUARIE UNIVERSITY NSW 2109, Australia
Phone: +61 (0)2 9850 8516
Level 2, AHH
http://stat.mq.edu.au/our_staff/staff_-_alphabetical/staff/beath,_ken/
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