Ao ajudar alguém com suas análises, eu me deparei com uma pergunta sobre a diferença entre os testes t e os testes F para modelos lineares mistos no lme4 para R, conforme fornecido pelo lmerTest. Estou ciente dos problemas com o cálculo de qualquer tipo de valor-p para modelos lineares mistos (como eu entendo, principalmente devido ao fato de que a definição dos graus de liberdade é problemática), bem como dos problemas com a interpretação dos principais efeitos em a presença de interações significativas (com base no princípio da marginalidade).
Resumidamente, os dados são de um experimento com duas condições (congruência VERDADEIRA / FALSA), medidas em seis conjuntos de sensores que podem ser descritos como uma combinação de dois fatores: anterioridade (anterior / posterior) e lateralidade (esquerda / central / direita) .
Como pode ser visto no resumo resumido abaixo, os testes t não mostram um efeito significativo de congruência (p = 0,12), enquanto a saída anova mostra um efeito muito significativo de congruência (p = 2,8e-10). Como a congruência possui apenas dois níveis, isso não pode ser o resultado do teste F realizando um teste abrangente em vários níveis do fator fixo. Portanto, não tenho certeza do que causa o resultado muito significativo na saída da anova. Isso se deve ao fato de haver fortes interações envolvendo congruência que, é claro, dependem da inclusão do efeito principal na parametrização do modelo?
Procurei uma resposta anterior a esta pergunta no CrossValidated, mas não consegui encontrar nada relevante, exceto possivelmente a primeira resposta a essa pergunta . No entanto, se isso fornece uma resposta real, está implícito na matemática, e estou procurando uma resposta conceitual que possa explicar à pessoa que estou tentando ajudar.
> final.mod<-lmer(uV~1+factor(congruity)*factor(laterality)*factor(anteriority)+(1|sent.id)+(1|Subject),data=selected.data)
> summary(final.mod)
Linear mixed model fit by REML
t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: uV ~ 1 + factor(congruity) * factor(laterality) * factor(anteriority) + (1 | sent.id) + (1 | Subject)
Data: selected.data
REML criterion at convergence: 348903.5
Scaled residuals:
Min 1Q Median 3Q Max
-7.0440 -0.6002 0.0069 0.6038 11.3912
Random effects:
Groups Name Variance Std.Dev.
sent.id (Intercept) 1.773 1.332
Subject (Intercept) 2.548 1.596
Residual 111.396 10.554
Number of obs: 46176, groups: sent.id, 41; Subject, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.768e-03 3.973e-01 7.900e+01 0.012 0.9905
factor(congruity)TRUE 3.758e-01 2.410e-01 4.611e+04 1.559 0.1189
factor(laterality)left 7.154e-02 2.430e-01 4.610e+04 0.294 0.7685
factor(laterality)right -2.003e-01 2.430e-01 4.610e+04 -0.824 0.4098
factor(anteriority)posterior -4.203e-02 2.430e-01 4.610e+04 -0.173 0.8627
factor(congruity)TRUE:factor(laterality)left -1.013e-01 3.404e-01 4.610e+04 -0.298 0.7660
factor(congruity)TRUE:factor(laterality)right 7.233e-02 3.404e-01 4.610e+04 0.213 0.8317
factor(congruity)TRUE:factor(anteriority)posterior 6.162e-01 3.404e-01 4.610e+04 1.810 0.0702 .
factor(laterality)left:factor(anteriority)posterior 2.568e-01 3.437e-01 4.610e+04 0.747 0.4549
factor(laterality)right:factor(anteriority)posterior 1.763e-01 3.437e-01 4.610e+04 0.513 0.6080
factor(congruity)TRUE:factor(laterality)left:factor(anteriority)posterior -5.162e-02 4.813e-01 4.610e+04 -0.107 0.9146
factor(congruity)TRUE:factor(laterality)right:factor(anteriority)posterior -2.420e-01 4.813e-01 4.610e+04 -0.503 0.6152
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) fc()TRUE fctr(ltrlty)l fctr(ltrlty)r fctr(n) fctr(cngrty)TRUE:fctr(ltrlty)l fctr(cngrty)TRUE:fctr(ltrlty)r
fctr(c)TRUE -0.310
fctr(ltrlty)l -0.306 0.504
fctr(ltrlty)r -0.306 0.504 0.500
fctr(ntrrt) -0.306 0.504 0.500 0.500
fctr(cngrty)TRUE:fctr(ltrlty)l 0.218 -0.706 -0.714 -0.357 -0.357
fctr(cngrty)TRUE:fctr(ltrlty)r 0.218 -0.706 -0.357 -0.714 -0.357 0.500
fctr(cngrty)TRUE:fctr(n) 0.218 -0.706 -0.357 -0.357 -0.714 0.500 0.500
fctr(ltrlty)l:() 0.216 -0.357 -0.707 -0.354 -0.707 0.505 0.252
fctr(ltrlty)r:() 0.216 -0.357 -0.354 -0.707 -0.707 0.252 0.505
fctr(cngrty)TRUE:fctr(ltrlty)l:() -0.154 0.499 0.505 0.252 0.505 -0.707 -0.354
fctr(cngrty)TRUE:fctr(ltrlty)r:() -0.154 0.499 0.252 0.505 0.505 -0.354 -0.707
fctr(cngrty)TRUE:fctr(n) fctr(ltrlty)l:() fctr(ltrlty)r:() fctr(cngrty)TRUE:fctr(ltrlty)l:()
fctr(c)TRUE
fctr(ltrlty)l
fctr(ltrlty)r
fctr(ntrrt)
fctr(cngrty)TRUE:fctr(ltrlty)l
fctr(cngrty)TRUE:fctr(ltrlty)r
fctr(cngrty)TRUE:fctr(n)
fctr(ltrlty)l:() 0.505
fctr(ltrlty)r:() 0.505 0.500
fctr(cngrty)TRUE:fctr(ltrlty)l:() -0.707 -0.714 -0.357
fctr(cngrty)TRUE:fctr(ltrlty)r:() -0.707 -0.357 -0.714 0.500
> anova(final.mod)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
factor(congruity) 4439.1 4439.1 1 46142 39.850 2.768e-10 ***
factor(laterality) 572.9 286.5 2 46095 2.572 0.076430 .
factor(anteriority) 1508.1 1508.1 1 46095 13.538 0.000234 ***
factor(congruity):factor(laterality) 31.6 15.8 2 46095 0.142 0.867581
factor(congruity):factor(anteriority) 775.1 775.1 1 46095 6.958 0.008349 **
factor(laterality):factor(anteriority) 111.9 56.0 2 46095 0.502 0.605126
factor(congruity):factor(laterality):factor(anteriority) 31.2 15.6 2 46095 0.140 0.869183
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Em resposta à pergunta de @ Aurelie:
> congruity.mod<-lmer(uV~1+factor(congruity)+(1|sent.id)+(1|Subject),data=selected.data)
> summary(congruity.mod)
Linear mixed model fit by REML
t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: uV ~ 1 + factor(congruity) + (1 | sent.id) + (1 | Subject)
Data: selected.data
REML criterion at convergence: 494077.2
Scaled residuals:
Min 1Q Median 3Q Max
-10.1673 -0.5790 -0.0097 0.5818 12.6088
Random effects:
Groups Name Variance Std.Dev.
sent.id (Intercept) 4.568 2.137
Subject (Intercept) 6.132 2.476
Residual 178.137 13.347
Number of obs: 61568, groups: sent.id, 41; Subject, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.6055 0.5671 57.0000 1.068 0.29
factor(congruity)FALSE -0.7105 0.1084 61535.0000 -6.558 5.51e-11 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr)
fctr()FALSE -0.093
> anova(congruity.mod)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
factor(congruity) 7660.5 7660.5 1 61535 43.004 5.507e-11 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> laterality.mod<-lmer(uV~1+factor(laterality)+(1|sent.id)+(1|Subject),data=selected.data)
> summary(laterality.mod)
Linear mixed model fit by REML
t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: uV ~ 1 + factor(laterality) + (1 | sent.id) + (1 | Subject)
Data: selected.data
REML criterion at convergence: 372848.2
Scaled residuals:
Min 1Q Median 3Q Max
-9.7033 -0.5981 -0.0076 0.6006 12.2265
Random effects:
Groups Name Variance Std.Dev.
sent.id (Intercept) 5.568 2.360
Subject (Intercept) 6.777 2.603
Residual 186.966 13.674
Number of obs: 46176, groups: sent.id, 41; Subject, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.8128 0.6115 61.0000 1.329 0.18877
factor(laterality)left -0.4260 0.1559 46105.0000 -2.733 0.00628 **
factor(laterality)right -0.6709 0.1559 46105.0000 -4.304 1.68e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) fctr(ltrlty)l
fctr(ltrlty)l -0.127
fctr(ltrlty)r -0.127 0.500
> anova(laterality.mod)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
factor(laterality) 3548.2 1774.1 2 46105 9.4889 7.584e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> anteriority.mod<-lmer(uV~1+factor(anteriority)+(1|sent.id)+(1|Subject),data=selected.data)
> summary(anteriority.mod)
Linear mixed model fit by REML
t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: uV ~ 1 + factor(anteriority) + (1 | sent.id) + (1 | Subject)
Data: selected.data
REML criterion at convergence: 372738.6
Scaled residuals:
Min 1Q Median 3Q Max
-9.6668 -0.5986 -0.0032 0.6017 12.2711
Random effects:
Groups Name Variance Std.Dev.
sent.id (Intercept) 5.569 2.360
Subject (Intercept) 6.777 2.603
Residual 186.525 13.657
Number of obs: 46176, groups: sent.id, 41; Subject, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.2693 0.6081 59.0000 -0.443 0.66
factor(anteriority)posterior 1.4328 0.1271 46105.0000 11.272 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr)
fctr(ntrrt) -0.105
> anova(anteriority.mod)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
factor(anteriority) 23700 23700 1 46106 127.06 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Atualização: Depois de atualizar os contrastes com base na resposta de @ Henrik:
> options(contrasts=c("contr.sum","contr.poly"))
> final.mod<-lmer(uV~1+factor(congruity)*factor(laterality)*factor(anteriority)+(1|sent.id)+(1|Subject),data=selected.data)
> summary(final.mod)
Linear mixed model fit by REML
t-tests use Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: uV ~ 1 + factor(congruity) * factor(laterality) * factor(anteriority) + (1 | sent.id) + (1 | Subject)
Data: selected.data
REML criterion at convergence: 372689.8
Scaled residuals:
Min 1Q Median 3Q Max
-9.6772 -0.5979 -0.0016 0.5977 12.3439
Random effects:
Groups Name Variance Std.Dev.
sent.id (Intercept) 5.556 2.357
Subject (Intercept) 6.752 2.599
Residual 186.232 13.647
Number of obs: 46176, groups: sent.id, 41; Subject, 30
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.355e-01 6.039e-01 5.800e+01 0.721 0.4737
factor(congruity)1 4.501e-01 6.396e-02 4.613e+04 7.037 1.99e-12 ***
factor(laterality)1 3.628e-01 8.983e-02 4.610e+04 4.039 5.38e-05 ***
factor(laterality)2 -5.732e-02 8.983e-02 4.610e+04 -0.638 0.5234
factor(anteriority)1 -7.183e-01 6.352e-02 4.610e+04 -11.308 < 2e-16 ***
factor(congruity)1:factor(laterality)1 1.433e-01 8.983e-02 4.610e+04 1.596 0.1106
factor(congruity)1:factor(laterality)2 -1.535e-01 8.983e-02 4.610e+04 -1.709 0.0875 .
factor(congruity)1:factor(anteriority)1 9.442e-02 6.352e-02 4.610e+04 1.487 0.1371
factor(laterality)1:factor(anteriority)1 2.282e-01 8.983e-02 4.610e+04 2.540 0.0111 *
factor(laterality)2:factor(anteriority)1 -2.121e-01 8.983e-02 4.610e+04 -2.362 0.0182 *
factor(congruity)1:factor(laterality)1:factor(anteriority)1 -7.802e-03 8.983e-02 4.610e+04 -0.087 0.9308
factor(congruity)1:factor(laterality)2:factor(anteriority)1 -1.141e-02 8.983e-02 4.610e+04 -0.127 0.8989
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) fctr(c)1 fctr(l)1 fct()2 fctr(n)1 fctr(cngrty)1:fctr(l)1 fc()1:()2 fctr(cngrty)1:fctr(n)1
fctr(cngr)1 -0.003
fctr(ltrl)1 0.000 0.000
fctr(ltrl)2 0.000 0.000 -0.500
fctr(ntrr)1 0.000 0.000 0.000 0.000
fctr(cngrty)1:fctr(l)1 0.000 0.000 -0.020 0.010 0.000
fctr()1:()2 0.000 0.000 0.010 -0.020 0.000 -0.500
fctr(cngrty)1:fctr(n)1 0.000 0.000 0.000 0.000 -0.020 0.000 0.000
fctr(l)1:()1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
fctr()2:()1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
f()1:()1:() 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
f()1:()2:() 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
fctr(l)1:()1 f()2:( f()1:()1:
fctr(cngr)1
fctr(ltrl)1
fctr(ltrl)2
fctr(ntrr)1
fctr(cngrty)1:fctr(l)1
fctr()1:()2
fctr(cngrty)1:fctr(n)1
fctr(l)1:()1
fctr()2:()1 -0.500
f()1:()1:() -0.020 0.010
f()1:()2:() 0.010 -0.020 -0.500
> anova(final.mod)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
factor(congruity) 9221.9 9221.9 1 46129 49.518 1.993e-12 ***
factor(laterality) 3511.5 1755.7 2 46095 9.428 8.062e-05 ***
factor(anteriority) 23814.0 23814.0 1 46095 127.873 < 2.2e-16 ***
factor(congruity):factor(laterality) 680.3 340.1 2 46095 1.826 0.16101
factor(congruity):factor(anteriority) 411.5 411.5 1 46095 2.210 0.13714
factor(laterality):factor(anteriority) 1497.4 748.7 2 46095 4.020 0.01796 *
factor(congruity):factor(laterality):factor(anteriority) 8.6 4.3 2 46095 0.023 0.97713
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
anova()
esummary()
delmerMod
?Respostas:
Os testes do tipo III requerem codificação correta para que efeitos de ordem inferior sejam significativos, especificamente contrastes ortogonais. O padrão R
contr.treatment
não é ortogonal, mas existem outros contrastes (por exemplo,contr.sum
). No seu código, parece que você usou não alterou os padrões, portanto, seus resultados são os chamados efeitos principais simples. Discutimos isso em nosso capítulo que será lançado em breve aqui , mas outras referências são fáceis de encontrar .Para usar os contrastes corretos, execute o seguinte antes de ajustar um modelo misto em R:
Um código mais fácil de lembrar é usar
set_sum_contrasts()
no meuafex
pacote:Atualize sua pergunta se isso não resolver o seu problema (de preferência com dados para recriar o problema).
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