Message-ID: <B89C22E3-3DCB-4D4C-9D8C-AE8735D2AB0E@umn.edu>
Date: 2019-07-15T22:21:31Z
From: Noelle G. Beckman
Subject: Question about non-significant interactions
In-Reply-To: <CAJuCY5xNHmpM81qgMWF8YFPnPB32k6yxYC9oTRBwkHMe9SRs1A@mail.gmail.com>
I am currently out of the office until July 5th. I will respond to your email upon my return.
On Jul 10, 2019, at 12:51 AM, Thierry Onkelinx via R-sig-mixed-models <r-sig-mixed-models at r-project.org> wrote:
> Dear Francesco,
>
> To answer your question, you should convert your hypothesis in a set of
> linear contrasts and test those.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> thierry.onkelinx at inbo.be
> Havenlaan 88 bus 73, 1000 Brussel
> www.inbo.be
>
> ///////////////////////////////////////////////////////////////////////////////////////////
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
> ///////////////////////////////////////////////////////////////////////////////////////////
>
> <https://www.inbo.be>
>
>
> Op di 9 jul. 2019 om 23:25 schreef Francesco Romano <fbromano77 at gmail.com>:
>
> ---------- Forwarded message ---------
> From: Francesco Romano <fbromano77 at 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 at 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 at 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 at r-project.org] on
> behalf of Francesco Romano [fbromano77 at gmail.com]
> Sent: July 9, 2019 9:49 AM
> To: r-sig-mixed-models at 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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