[R-sig-ME] Question about non-significant interactions

Fox, John j|ox @end|ng |rom mcm@@ter@c@
Tue Jul 9 23:03:34 CEST 2019

Dear Francesco,

I didn't entirely follow your question and I expect that to answer it, it would be necessary to know more about what your research entails. As you imply, this seems to be more a statistics question than an R question. It's also not clear to me what function you used to fit the mixed-effects logistic regression.

But I did notice that you're apparently using Anova() for type-III tests with the default contr.treatment() coding for factors. The main-effect tests that result are not sensible. As it says in ?Anova:

Be careful of type-III tests: For a traditional multifactor ANOVA model with interactions, for example, these tests will normally only be sensible when using contrasts that, for different terms, are orthogonal in the row-basis of the model, such as those produced by contr.sum, contr.poly, or contr.helmert, but not by the default contr.treatment. In a model that contains factors, numeric covariates, and interactions, main-effect tests for factors will be for differences over the origin. In contrast (pun intended), type-II tests are invariant with respect to (full-rank) contrast coding. If you don't understand this issue, then you probably shouldn't use Anova for type-III tests."

I hope that this is of some help,
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario
Canada L8S 4M4
web: socserv.mcmaster.ca/jfox

From: R-sig-mixed-models [r-sig-mixed-models-bounces using r-project.org] on behalf of Francesco Romano [fbromano77 using gmail.com]
Sent: July 9, 2019 9:49 AM
To: r-sig-mixed-models using r-project.org
Subject: [R-sig-ME] Question about non-significant interactions

Dear all,

I have more of a theoretical than practical question for you. The model I
am using has two IVs, group (3 levels) and task (2 levels), and a
categorical DV (correct versus incorrect), hence logistic regression.
Random effects for subjects and items, as well as slopes for group by item
and task by subject.

I am interested in the effect of belonging any of three groups, the levels
of the group IV, in order to test some a priori predictions. The bayesian
wrapper is to help the model converge.

Here is the output:

> summary(paper2analysis1)
Cov prior  : item ~ wishart(df = 5.5, scale = Inf, posterior.scale = cov,
common.scale = TRUE)
           : Participant ~ wishart(df = 4.5, scale = Inf, posterior.scale =
cov, common.scale = TRUE)
Prior dev  : 6.9466

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['bglmerMod']
 Family: binomial  ( logit )
Formula: correctness ~ task * group + (1 + task | Participant) + (1 +
 group | item)
   Data: data
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid
  3857.8   3957.2  -1913.9   3827.8     5570

Scaled residuals:
    Min      1Q  Median      3Q     Max
-2.0196 -0.3744 -0.2312 -0.1368  6.9534

Random effects:
 Groups      Name        Variance Std.Dev. Corr
 item        (Intercept) 1.1266   1.0614
             groupL2     0.1311   0.3620   -0.12
             groupNS     0.2029   0.4504   -0.31  0.17
 Participant (Intercept) 0.7582   0.8708
             taskpriming 1.2163   1.1029   -0.77
Number of obs: 5585, groups:  item, 219; Participant, 46

Fixed effects:
                    Estimate Std. Error z value Pr(>|z|)
(Intercept)         -2.49187    0.28318  -8.800  < 2e-16 ***
taskpriming          1.30911    0.37367   3.503 0.000459 ***
groupL2             -0.04042    0.38322  -0.105 0.916005
groupNS             -1.01144    0.36607  -2.763 0.005727 **
taskpriming:groupL2  0.04305    0.48693   0.088 0.929544
taskpriming:groupNS -0.04942    0.46034  -0.107 0.914506
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) tskprm gropL2 gropNS tsk:L2
taskpriming -0.733
groupL2     -0.660  0.482
groupNS     -0.693  0.507  0.509
tskprmng:L2  0.499 -0.632 -0.755 -0.386
tskprmng:NS  0.530 -0.676 -0.390 -0.750  0.508

The model was then subjected to car::Anova for ANOVA type III analysis with
the following output:

> car::Anova(paper2analysis1, type = "III")
Analysis of Deviance Table (Type III Wald chisquare tests)

Response: correctness
              Chisq Df Pr(>Chisq)
(Intercept) 77.4344  1  < 2.2e-16 ***
task        12.2737  1  0.0004594 ***
group        9.9237  2  0.0070000 **
task:group   0.0391  2  0.9806462
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I am not sure how to interpret the non-significant interaction in this
case. Does this mean that, although simple effects exist at group level
within one particular task or at task level within one particular group, I
lack sufficient power to conclude those effects are real? If I look at the
simple effects, I do indeed find such effects but am not sure how to
interpret them against the lack of a main interaction. At a practical
level, the interaction, rather than the main effects, is the most important
part of the analysis.

Thank you in advance for any advice.




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