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Currently, the dispersion parameter for families with one isn't taken into account when calculating the deviance for GLMMs. For example, in Julia we have:
julia> lexdec_glmm_gamma
Generalized Linear Mixed Model fit by maximum likelihood (nAGQ = 1)
rt_raw ~ 1 + Class + NativeLanguage + Class & NativeLanguage + (1 | Subject) + (1 | Word)
Distribution: Gamma{Float64}
Link: IdentityLink()
Deviance: 91.9052
Variance components:
Column Variance Std.Dev.
Word (Intercept) 0.0000 0.00000
Subject (Intercept) 1508.7803 38.84302
Number of obs: 1659; levels of grouping factors: 79, 21
Fixed-effects parameters:
──────────────────────────────────────────────────────────────────────────────
Estimate Std.Error z value P(>|z|)
──────────────────────────────────────────────────────────────────────────────
(Intercept) 563.552 6.69785 84.1393 <1e-99
Class: plant 6.43673 9.20547 0.699229 0.4844
NativeLanguage: Other 114.543 11.2587 10.1737 <1e-23
Class: plant & NativeLanguage: Other -29.3668 15.495 -1.89524 0.0581
──────────────────────────────────────────────────────────────────────────────
julia> loglikelihood(lexdec_glmm_gamma)
ERROR: MethodError: no method matching Gamma{Float64}(::Float64)
Closest candidates are:
Gamma{Float64}(::Any, ::Any) where T at /home/XXX/.julia/packages/Distributions/Vcqls/src/univariate/continuous/gamma.jl:30
Stacktrace:
[1] loglikelihood(::GeneralizedLinearMixedModel{Float64}) at /home/XXX/Work/MixedModels.jl/src/generalizedlinearmixedmodel.jl:301
[2] top-level scope at none:0
But in R we have:
R> summary(lexdec_glmm_gamma)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: Gamma ( identity )
Formula: rt_raw ~ 1 + Class * NativeLanguage + (1 | Subject) + (1 | Word)
Data: lexdec
AIC BIC logLik deviance df.resid
20339.4 20377.3 -10162.7 20325.4 1652
Scaled residuals:
Min 1Q Median 3Q Max
-1.7910 -0.5810 -0.1798 0.3265 8.2691
Random effects:
Groups Name Variance Std.Dev.
Word (Intercept) 1.533e+03 39.1482
Subject (Intercept) 1.915e+03 43.7595
Residual 4.142e-02 0.2035
Number of obs: 1659, groups: Word, 79; Subject, 21
Fixed effects:
Estimate Std. Error t value Pr(>|z|)
(Intercept) 588.839 11.955 49.255 <2e-16 ***
Classplant 4.894 11.218 0.436 0.6627
NativeLanguageOther 115.619 13.578 8.515 <2e-16 ***
Classplant:NativeLanguageOther -28.138 9.379 -3.000 0.0027 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Clsspl NtvLnO
Classplant -0.109
NtvLnggOthr -0.044 -0.071
Clsspln:NLO 0.039 -0.085 0.034
R> deviance(lexdec_glmm_gamma)
[1] 52.56222
R> -2 * logLik(lexdec_glmm_gamma)
'log Lik.' 20325.38 (df=7)
See also lme4/lme4#375.
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