[R-sig-ME] Fitting RT: underdispersion with gamma and identity link
Baud-Bovy Gabriel
b@ud-bovy@g@br|e| @end|ng |rom h@r@|t
Thu Mar 21 14:06:48 CET 2019
Dear all,
I have updated a one-month old post on stakexchange about a GLMM model that I used to fit RT with gamma
distribution.
https://stats.stackexchange.com/questions/391076/how-to-interpret-significant-factors-in-a-glmm-gamma-model-that-appears-to-be-go
I mention this question in the mailing list because there are still things that I don't understand. I have put some info at the end of this email it is probably best to answer me on stakeexchange, where it is also possible to see the plots
(otherwise, I'll cross post the answers).
- The DHARMa residual plot suggests underdispersion and I don't know how to deal with that.
- The results of the model don't make sense. For example, all fixed effect are statistically significant
despite the fact that these factors explain little to nothing when looking at the plots. The random
effects also appear to be needed (statistically significant LRTs) and supported by the data (rePCA)
although I double that it is the case. Note that the model fits without warning.
- I don't understand why the results are statistically significant. Intuitively, I would expect that
estimates to be not statistically significant if there is a lot of unexplained variability.
- Even if gamma distribution is not a perfect model of RT variability (because of underdispersion),
it is a better model than Gaussian noise. I would expect therefore that the result of the model
would be more trustworthy with gamma noise than with gaussian noise.
- I also don't understand the value of residual SD, which seems to be on a different scale
that I would expect.
- As I have mentioned in a previous question to the list, my general goal is to be able to fit RT
with identity link and welcome other suggestion but I would also like to understand what
is happening in this case.
If anybody is interested, I might share the
data privately. Thank you for any help.
Gabriel
>fitRespLat11 <- glmer(resp.lat ~ stake.i.c + dir.c + win.prob.c +
(stake.i.c + dir.c + win.prob.c || su),
data=tmp, family = Gamma(link = "identity"),
control=glmerControl(optimizer = "bobyqa"))
> summary(fitRespLat11)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: Gamma ( identity )
Formula: resp.lat ~ stake.i.c + dir.c + win.prob.c + (stake.i.c + dir.c + win.prob.c || su)
Data: tmp
Control: glmerControl(optimizer = "bobyqa")
AIC BIC logLik deviance df.resid
58026.3 58083.4 -29004.2 58008.3 4160
Scaled residuals:
Min 1Q Median 3Q Max
-1.7918 -0.6890 -0.2162 0.4502 4.8900
Random effects:
Groups Name Variance Std.Dev.
su (Intercept) 5.413e+03 73.576
su.1 stake.i.c 2.008e+03 44.806
su.2 dir.c 2.944e+03 54.260
su.3 win.prob.c 7.514e+04 274.108
Residual 2.172e-01 0.466
Number of obs: 4169, groups: su, 120
Fixed effects:
Estimate Std. Error t value Pr(>|z|)
(Intercept) 612.589 6.290 97.390 < 2e-16 ***
stake.i.c -61.037 6.001 -10.171 < 2e-16 ***
dir.c -33.530 5.481 -6.117 9.52e-10 ***
win.prob.c 34.071 8.262 4.124 3.72e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) stk..c dir.c
stake.i.c -0.089
dir.c -0.014 0.126
win.prob.c 0.191 -0.226 -0.108
> isSingular(fitRespLat11)
[1] FALSE
# Random structure checks
> rePCA(fitRespLat11)
$su
Standard deviations (1, .., p=4):
[1] 588.19493 157.88241 116.43287 96.14736
Rotation (n x k) = (4 x 4):
[,1] [,2] [,3] [,4]
[1,] 0 1 0 0
[2,] 0 0 0 1
[3,] 0 0 1 0
[4,] 1 0 0 0
attr(,"class")
[1] "prcomplist"
> anova(fitRespLat11,fitRespLat12,fitRespLat13,fitRespLat14)
Data: tmp
Models:
fitRespLat14: resp.lat ~ stake.i.c + dir.c + win.prob.c + (1 | su)
fitRespLat13: resp.lat ~ stake.i.c + dir.c + win.prob.c + (stake.i.c || su)
fitRespLat12: resp.lat ~ stake.i.c + dir.c + win.prob.c + (stake.i.c + dir.c || su)
fitRespLat11: resp.lat ~ stake.i.c + dir.c + win.prob.c + (stake.i.c + dir.c + win.prob.c || su)
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
fitRespLat14 6 58203 58241 -29096 58191
fitRespLat13 7 58129 58173 -29057 58115 76.699 1 < 2.2e-16 ***
fitRespLat12 8 58056 58107 -29020 58040 74.820 1 < 2.2e-16 ***
fitRespLat11 9 58026 58083 -29004 58008 31.496 1 1.999e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# See stackexchange link for plots and DHARMa residuals
--
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Gabriel Baud-Bovy web: www.iit.it/people/gabriel-baud-bovy<http://www.iit.it/people/gabriel-baud-bovy>
Italian Institute of Technology email: gabriel.baud-bovy using iit.it<mailto:gabriel.baud-bovy using iit.it>
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