Residuals in random effects covariance parameter estimates

[#1]

Hi, 

I ran a mixed-effects linear model and in the random effects covariance parameter estimates, the residual (as part of the % of total) that doesn't account for the variation explained by fixed effects? And if it doesn't, how can I find the variation explained by my fixed effects?

Thanks! 

[#2]

Hi @blip555555,

Welcome in the Community !

Random and fixed effects play a different role in the analysis and in your model. Fixed effects have an impact on mean response (intercept), whereas random effects have an impact on random error (variance). You can read this section to learn more about Random Effect Models. and Example of Estimating Random Effect Parameters (jmp.com)

The variation explained by all your effects (fixed + random) can be found with the R²/R² adjusted values of your model.

The type of factor (random vs. fixed) is decided before the experiments, depending on the goal of the analysis, the assumptions about the levels representativity of this factor and the inference space, and the physical/experimental possibility to change them in a reproducible way. You can read more in closely related disccusions :

Prediction equation for randomly chosen factors 

Random vs Fixed Blocking Factor in DOE 

Random Effect vs Fixed Effects influence on Total model Rsq 

Hope this response will help you,

[#3]

Dear Victor, 

Thank you for your helpful reply. However, I can't see R-squared values in the mixed model report. All I can see in terms of how well the model explains the works are AICc, BIC and -2 log likelihood. Is there a way to specify an R-squared output?

Thanks again!

Assunta 

[#4 · Accepted solution]

Hi @blip555555,

As answered on your latest post When to use Standard Least Square personality using the attrobute 'random' instead of Mixed Model pe..., if your covariance structure is set on "Residual" (implying no covariance between observations, so the errors are independent), you can fit your model using Standard Least Squares personality and get access to R² and R² adjusted.

Hope this answer will help you,