Negative binomial GLMM model/variables selection based in marginal R2 and conditional R2

:

Dear R-Mixed-Models Members,

 ?????? ?????? I've like to chose my negative binomial GLMM better
model/variables based in marginal R2 (variance explained by the fixed
factor(s)) and conditional R2 (variance explained by both the fixed and
random factors), but some times I have a great dissimilarities in this
values, if I have gain in the conditional R2, my marginal R2 is poor and
vice-versa (I make a little exercise by changes in the position on fixed
and random effects in the models). In my example:

*A) Model 1 - Inf_Leaves ~ Inf_YST + Age_months + (1 | Trat) - balance
values between marginal and conditional R2*

R2m R2c

delta 0.4282151 0.5203953

lognormal 0.5090799 0.6186677

trigamma 0.3153259 0.3832049


Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']

Family: Negative Binomial(0.9207)?? ( log )

Formula: Inf_Leaves ~ Inf_YST + Age_months + (1 | Trat)

 ???? Data: d3

 ???????? AIC?????????? BIC???? logLik deviance df.resid

 ????4500.6???? 4521.9?? -2245.3???? 4490.6?????????? 519

Scaled residuals:

Min?????????? 1Q?? Median?????????? 3Q???????? Max

-0.9413 -0.7254 -0.4113?? 0.5294?? 7.2853

Random effects:

Groups Name?????????????? Variance Std.Dev.

Trat???? (Intercept) 0.2176 ????0.4664

Number of obs: 524, groups:?? Trat, 4

Fixed effects:

 ?????????????????????????? Estimate Std. Error z value Pr(>|z|)

(Intercept)?? 0.2847245?? 0.2913635???? 0.977 0.328

Inf_YST???????? -0.0016482?? 0.0003483?? -4.732 2.22e-06 ***

Age_months???? 0.3144764?? 0.0183616?? 17.127?? < 2e-16 ***

---

Signif. codes:?? 0 ???***??? 0.001 ???**??? 0.01 ???*??? 0.05 ???.??? 0.1
??? ??? 1

Correlation of Fixed Effects:

 ???????????????????? (Intr) In_YST

Inf_YST???????? 0.171

Age_months -0.558 -0.532

convergence code: 0

Model failed to converge with max|grad| = 0.00631137 (tol = 0.001,
component 1)

Model is nearly unidentifiable: very large eigenvalue

- Rescale variables?

Model is nearly unidentifiable: large eigenvalue ratio

- Rescale variables?


*B) Model 2 -?? Inf_Leaves ~ Inf_YST + Trat + (1 | Age_months) - a better
conditional but poor marginal R2*

R2m R2c

delta???????? 0.1626844 0.7257397

lognormal 0.1725712 0.7698453

trigamma?? 0.1489258 0.6643626


Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']

Family: Negative Binomial(1.8431)?? ( log )

Formula: Inf_Leaves ~ Inf_YST + Trat + (1 | Age_months)

 ???? Data: d3

 ???????? AIC?????????? BIC logLik deviance df.resid

 ????4121.5???? 4151.4 -2053.8???? 4107.5?????????? 517

Scaled residuals:

Min?????????? 1Q?? Median?????????? 3Q???????? Max

-1.2776 -0.6703 -0.1486?? 0.3279?? 5.4019

Random effects:

Groups Name?????????????? Variance Std.Dev.

Age_months (Intercept) 1.172?????? 1.083

Number of obs: 524, groups:?? Age_months, 4

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept)???????????????? 3.4859551 0.5492043???? 6.347 2.19e-10 ***

Inf_YST???????????????????????? 0.0005702 0.0002864???? 1.991???? 0.0465 *

TratC1-Insecticide -1.1081610 0.1012478 -10.945?? < 2e-16 ***

TratC2-Control???????? -0.7859302 0.1058146?? -7.427 1.11e-13 ***

TratC2-Insecticide -1.3833545 0.1041882 -13.277?? < 2e-16 ***

---

Signif. codes:?? 0 ???***??? 0.001 ???**??? 0.01 ???*??? 0.05 ???.??? 0.1
??? ??? 1

Correlation of Fixed Effects:

 ?????????????????????? (Intr) In_YST TrC1-I TrC2-C

Inf_YST???????? -0.122

TrtC1-Insct -0.103 0.189

TrtC2-Cntrl -0.104 0.265?? 0.436

TrtC2-Insct -0.097 0.221?? 0.424?? 0.504

convergence code: 0

Model failed to converge with max|grad| = 0.00398879 (tol = 0.001,
component 1)

Model is nearly unidentifiable: very large eigenvalue

- Rescale variables?

Model is nearly unidentifiable: large eigenvalue ratio

- Rescale variables?


And my questions are:

1) Marginal R2 is a good metric for identify a bad fixed effect choose
in my models B? Despite a better conditional R2 comparing of conditional
R2 in my model A.

2) If I'm sure about my fixed and random effects, it is better a final
model with high values in both R2 or I choose based in the high value in
conditional R2?


Thanks in advanced,


Alexandre


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Alexandre dos Santos
Prote????o Florestal
IFMT - Instituto Federal de Educa????o, Ci??ncia e Tecnologia de Mato
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