Solved – How to report a linear mixed-effects model equation

mixed modelrandom-effects-model

I have run a linear mixed-effects model, with one fixed effect (dd) and a random slope and intercept term for individual (fInd) and would like to know how to report the results? In particular, I would like to display the model equation, but I am having trouble working out what to do with the random effects part. Below is my model output using the lme() function in R. The optimal random effects structure was chosen using likelihood ratio tests for models fitted with REML as suggested in Zuur et al (2009):

Model = lme(dtim ~ dd, random= ~1 + dd|fInd, data=df, method="REML")        

Linear mixed-effects model fit by REML
 Data: df 
       AIC      BIC    logLik
  93024.49 93064.13 -46502.43

Random effects:
 Formula: ~1 + dd | fInd
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev    Corr  
(Intercept) 0.5231033 (Intr)             
dd          0.2154805 -0.47 
Residual    2.6134946       

Fixed effects: dtim ~ dd 
                 Value  Std.Error    DF  t-value p-value
(Intercept) -0.5721233 0.12394717 17600 -3.46132       0
dd           2.2663854 0.04906525 17600 42.14376       0
 Correlation: 
       (Intr)
dd     -0.489

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max 
-7.0603118 -0.4650351 -0.1982975  0.2412834 14.1304020

If I was displaying the model equation from a linear model without random terms I would write the equation as so:

dtim = 2.266 * dd – 0.572

How would one then include notation to symbolise the random effects terms or are model outputs not reported in this way with mixed-effects models? Any advise would be much appreciated.

Best Answer

You can report that equation as stated, and add that the coefficient of dd varies from individual to individual with a standard deviation of .215. And also that the individuals' intercepts vary with an SD of .523, and that the SD of error not accounted for by individuals is 2.613. This information is in the summary table of random effects.

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