Interpreting lmer() interactions with Helmert contrasts

contrasts(rtData$Time)

contrasts(rtData$WordType)

(say variable A), when that variable is in a model involving an interaction
with another variable (say variable B) will test the interaction term A:B
and the main effect A.  The full model has A + B + A:B and the reduced
model has only B.  Thus a proper omnibus test for the usefulness of A in
the model will involve the interaction A:B and the main effect A.  This
test really should be done before testing A:B for proper multiple
comparisons control.

-----Original Message-----
From: R-sig-mixed-models [mailto:

r-sig-mixed-models-bounces at r-project.org]

On Behalf Of Ken Beath
Sent: August-21-15 5:19 PM
To: Dan McCloy
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Interpreting lmer() interactions with Helmert
contrasts

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.

In the case of a significant interaction, the conclusion is that the
change in one of the main effects depends on the level of the other main
effect.  Both main effects are statistically significant, but a single
value for each main effect will not adequately summarize the degree of
response.  One can make conclusions about the main effects, but the
conclusions are more complex than a single estimate for each main effect.

The tests that you have performed use Chi-sq statistics
which is not correct for a linear model, it should be F.

For linear mixed effects models, F tests are not possible.  The Chi-square
tests presented are likelihood ratio chi-square tests comparing the
likelihoods of the full model (under the alternative hypothesis) and the
reduced model (under the null hypothesis).  The anova() method for lmer
objects automagically refits the two models using maximum likelihood (as
opposed to restricted maximum likelihood) and performs the likelihood ratio
chi-square test.  The degrees of freedom of that test equal the number of
parameters posited to be zero under the reduced (null hypothesis) model as
compared to the full (alternative hypothesis) model.

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.

An omnibus test for the statistical significance of a variable of interest
(say variable A), when that variable is in a model involving an interaction
with another variable (say variable B) will test the interaction term A:B
and the main effect A.  The full model has A + B + A:B and the reduced
model has only B.  Thus a proper omnibus test for the usefulness of A in
the model will involve the interaction A:B and the main effect A.  This
test really should be done before testing A:B for proper multiple
comparisons control.



Steven McKinney, Ph.D.

Statistician
Molecular Oncology and Breast Cancer Program
British Columbia Cancer Research Centre

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

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

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

--
Paul Debes
DFG Research Fellow
University of Turku
Department of Biology
It?inen Pitk?katu 4
20520 Turku
Finland

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--

*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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