[R-sig-eco] car::Anova type III for glmer: are very high chi square values a sign of overfitting?

[Guillaume Adeux]

Hello everyone,

My experimental lay out is a split split plot experiment
(block/tillage/nitrogen/cover crop type) replicated on 4 blocks. 2
pseudoreplications were carried out within the experimental units (hence
the last level of nesting) each of the two years.

I am analyzing the effect of these factors (tillage*nitrogen*cover crop
type) on weed biomass.

Up until now, the following model was working just fine:
mod=glmer(dry_bio_weeds_m2+0.001~*block+year+tillage*nitrogen*cover crop*
+(1|block:tillage)+(1|block:tillage:N)+(1|block:tillage:N:CC)+(1|block:year)+(1|block:year:tillage)+(1|block:year:tillage:N)+(1|block:year:tillage:N:CC),family=gaussian(link="sqrt"),control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=2e5)),data=biomassCC)

However, I also wanted to take into account the variability of cover crop
biomass production because I expect that the relationship between weed and
cover crop biomass is not the same depending on cover crop type (Brassica
vs. Legume) :
mod1=glmer(dry_bio_weeds_m2+0.001~*block+year+dry_bio_cover_m2*tillage*nitrogen*cover
crop*+(1|block:tillage)+(1|block:tillage:N)+(1|block:tillage:N:CC)+(1|block:year)+(1|block:year:tillage)+(1|block:year:tillage:N)+(1|block:year:tillage:N:CC),family=gaussian(link="sqrt"),control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=2e5)),data=biomassCC_wo_C)
# the control = baresoil was taken out

For each combination of cover crop type, nitrogen level and tillage, 16
observations of cover crop biomass (i.e. dry_bio_cover_m2) are available (4
blocks x 2 points per experimental unit x 2 years). It seems reasonable (at
least to me) to test these slopes. I usually obtain p. values with
monet::test_terms or afex::mixed() but it produces non sensical denominator
d.f. with this model (first sign of overfitting?). However, mod1 shows a 10
point AIC drop compared to a model that would not include
"dry_bio_cover_m2".

To investigate further, I headed toward car::Anova(model, type="III") and
obtained the following table:

Analysis of Deviance Table (Type III Wald chisquare tests)

Response: dry_bio_weeds_m2 + 0.001
                                                              Chisq Df
Pr(>Chisq)
(Intercept)                                   5.3317e+02  1  < 2.2e-16 ***
block                                           8.0032e+00  3  0.0459463 *
year                                             2.7720e-01  1  0.5985096

dry_bio_cover_m2                      *7.8745e+04*  1  < 2.2e-16 ***
tillage                                          1.3815e+01  1  0.0002017
***
N                                                 8.4024e+01  3  < 2.2e-16
***
CC                                              2.7821e+01  2  9.095e-07 ***
dry_bio_cover_m2:tillage           2.6228e+01  1  3.034e-07 ***
dry_bio_cover_m2:N                  *1.3953e+05*  3  < 2.2e-16 ***
tillage:N                                      1.3281e+01  3  0.0040657 **
dry_bio_cover_m2:CC               4.2261e+01  2  6.654e-10 ***
tillage:CC                                   1.3697e+01  2  0.0010613 **
N:CC                                          4.1353e+01  6  2.467e-07 ***
dry_bio_cover_m2:tillage:N       1.7634e+01  3  0.0005234 ***
dry_bio_cover_m2:tillage:CC    7.5090e-01  2  0.6869748
dry_bio_cover_m2:N:CC           4.7310e+01  6  1.623e-08 ***
tillage:N:CC                               1.7857e+01  6  0.0065986 **
dry_bio_cover_m2:tillage:N:CC 3.7262e+01  6  1.565e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I am no statistician but some of the Chi square values seem particularly
huge (*7.8745e+04 and **1.3953e+05)*. The output plots however seem to back
this up....

Could anyone give me their feedback?

Thank you very much.

Guillaume ADEUX

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