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To say I'm new to statistics is an understatement- I've finally gotten a mixed model to work for me, but I'm unsure as to how I interpret the result. A little background: the data I'm analyzing is relative incidence of a disease in 6 cities from 2012-2016, with binary dummy variables representing whether an outbreak occurred in that city for the specified year. Here's my result:

Linear mixed model fit by REML ['lmerMod']
Formula: Peaks ~ Defol + (1 | City)
   Data: dat.all

REML criterion at convergence: 168.4

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.60287 -0.65942  0.04343  0.68181  1.63883 

Random effects:
 Groups   Name        Variance Std.Dev.
 City     (Intercept) 11.32    3.365   
 Residual             34.77    5.896   
Number of obs: 27, groups:  City, 6

Fixed effects:
            Estimate Std. Error t value
(Intercept)    6.589      4.413   1.493
Defol          1.040      3.528   0.295

Correlation of Fixed Effects:
      (Intr)
Defol -0.913

What exactly does the correlation mean? Also, what exactly is meant by the fixed effects intercept? Thank you so much in advance!

Sven Hohenstein
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Phillip Allen Avery
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1 Answers1

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What exactly does the correlation mean?

That question has been asked before, and is answered here.

Also, what exactly is meant by the fixed effects intercept?

First, it means that it is the average intercept; all of the cities vary in their intercept (as specified by the 1 in the (1|City) argument), but the average intercept is 6.59. The standard deviation of these intercepts is 3.37, so about 68% of the intercepts lie between 6.59±3.37.

Second, what does the intercept mean? It is the predicted value of the dependent variable when all of the other independent variables are zero. So if you want your intercept to be meaningful, consider rescaling your independent variable such that the zero value is meaningful. For example, if the predictor was measured on a scale of 1 to 7, then the intercept (when the IV = 0) isn't really meaningful because it isn't actually a value in the scale.

Mark White
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