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I'm trying to determine the relative contribution of each variable, including the fixed effects, in explaining the overall model. The variance is provided to do this for the random effects, but I'm not sure how to do this for the fixed effects. Any suggestions for how to do this would be very much appreciated.

Linear mixed model fit by REML ['lmerMod']
Formula: time ~ agecat + sex + (1 | Resource) + (1 | Person)
   Data: subdata

REML criterion at convergence: 6699


Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.4931 -0.5373 -0.1770  0.3340 13.4259


Random effects:
 Groups   Name        Variance Std.Dev.
 Person   (Intercept)   7.68    2.771

 Resource (Intercept)  18.73    4.327

 Residual             638.44   25.267

Number of obs: 722, groups:  Person, 42; Resource, 12


Fixed effects:
               Estimate Std. Error t value
(Intercept)     53.5637     2.2043  24.299
agecat(0,11]    10.7435     8.8624   1.212
agecat(11,21]    0.8068     5.7625   0.140
agecat(65,80]    0.9927     2.1830   0.455
agecat(80,130]   1.6798     2.6869   0.625
sexM             6.9659     1.9073   3.652


Correlation of Fixed Effects:
            (Intr) a(0,11 a(11,2 a(65,8 a(80,1
agect(0,11] -0.118

agct(11,21] -0.164  0.037

agct(65,80] -0.357  0.095  0.150

agc(80,130] -0.306  0.077  0.121  0.326

sexM        -0.370 -0.017  0.023 -0.076 -0.017
Cenoc
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1 Answers1

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Fixed effects don't have variance provided, because they are fixed, as they are point estimates, not random variables. You can partition the explained variance by comparing the variances of the random effects $\sigma^2_\alpha, \sigma^2_\gamma, \dots$ to "total variance" understood as the sum of their variances and the residual variance $\sigma^2_\varepsilon$

$$ICC_\alpha = \frac{\sigma^2_\alpha}{\sigma^2_\alpha + \sigma^2_\gamma + ... + \sigma^2_\varepsilon}$$

but that's all. You would need to answer yourself what you mean by "relative contribution" because this is comparing apples to oranges, as fixed and random components play different roles in the model.

Tim
  • 138,066