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 Grosso
Campus C??ceres
Caixa Postal 244
Avenida dos Ramires, s/n
Bairro: Distrito Industrial
C??ceres - MT CEP: 78.200-000
Fone: (+55) 65 99686-6970 (VIVO) (+55) 65 3221-2674 (FIXO)
alexandre.santos at cas.ifmt.edu.br
Lattes: http://lattes.cnpq.br/1360403201088680
OrcID: orcid.org/0000-0001-8232-6722
Researchgate: www.researchgate.net/profile/Alexandre_Santos10
LinkedIn: br.linkedin.com/in/alexandre-dos-santos-87961635
Mendeley:www.mendeley.com/profiles/alexandre-dos-santos6/
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