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Let's say we have this:

 model2 <- lmer(milk.amount~(1|cow), data=milk, REML=FALSE)
 model1 <- lmer(milk.amount~(1|cow), data=milk)
 summary(model2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: milk.amount ~ (1 | cow)
    Data: milk
     AIC      BIC   logLik deviance df.resid 
   186.5    191.6    -90.2    180.5       37 

Scaled residuals: 
     Min      1Q  Median      3Q     Max 
 -2.0244 -0.4104  0.1795  0.6621  1.3879 

Random effects:
 Groups   Name        Variance Std.Dev.
 cow      (Intercept) 6.755    2.599   
 Residual             2.999    1.732   
 Number of obs: 40, groups: cow, 10

Fixed effects:
             Estimate Std. Error t value
 (Intercept)  27.0150     0.8663   31.18

then

summary(model1)
Linear mixed model fit by REML ['lmerMod']

Formula: milk.amount ~ (1 | cow)
   Data: milk
 REML criterion at convergence: 178.9

 Scaled residuals: 
      Min      1Q  Median      3Q     Max 
  -1.9981 -0.4136  0.1775  0.6561  1.4021 

 Random effects:
  Groups   Name        Variance Std.Dev.
  cow      (Intercept) 7.589    2.755   
  Residual             3.000    1.732   
  Number of obs: 40, groups: cow, 10

 Fixed effects:
              Estimate Std. Error t value
  (Intercept)  27.0150     0.9132   29.58

Why model1 (with REML) doesn't show AIC, BIC, logLik, deviance coefficients? Is it possibly due to some kind of software dependency?

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  • $\begingroup$ No software dependency issue. It's defined like that in getLlikAIC, which gets called by summary.merMod. I'd assume there are (theoretical) issues with computing these for a REML fit. (Although AIC(model1) works just fine.) $\endgroup$
    – Roland
    Commented Aug 4, 2014 at 14:19

1 Answer 1

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It's because the likelihood (which deviance, AIC, and BIC are calculated from) is calculated only when using maximum likelihood estimation (i.e., method = "ML"). This is because REML takes into account the degrees of freedom of the fixed effects to estimate the variance components, resulting in less-biased variance estimates compared to those from ML estimation, but an incorrect likelihood value for model comparison.

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