[R-sig-ME] Fwd: Question about non-significant interactions
Francesco Romano
|brom@no77 @end|ng |rom gm@||@com
Tue Jul 9 23:24:41 CEST 2019
---------- Forwarded message ---------
From: Francesco Romano <fbromano77 using gmail.com>
Date: Tue, Jul 9, 2019 at 11:24 PM
Subject: Re: [R-sig-ME] Question about non-significant interactions
To: Fox, John <jfox using mcmaster.ca>
Dear John,
Thanks for the reply. One of my research entails examining the relationship
between 3 groups of speakers, the 3 levels of the group categorical
variable previously mentioned, and two tasks. One prediction is that one
group will perform better than other groups on one test but not the other.
I fit a maximal model using the bglmr function as shown previously, then
used car::Anova to determine main effects. My understanding from previous
interaction with you precisely here on r-sig-me is that the function works
as a form of shortcut to the traditional way of model-fitting/ reduction
via the function anova() comparing models, eliminating terms one at a time.
I hope this is clearer now and yes, the question is more of a statistical
one than an R one, even though I suspect the mixed-effect aspect of the
regression may be relevant to answering it.
Frank
Tue, Jul 9, 2019 at 11:03 PM Fox, John <jfox using mcmaster.ca> wrote:
> 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:
>
> "Warning
> 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
> -----------------------------
> 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.
>
> Francesco
>
>
>
>
>
> Best,
>
> Frank
>
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>
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