lmer model interaction with 1 intercept and 1 random effect I am very new to statistical analysis, but I am trying to understand the mixed-effect model.
The data that I have is the mass volume of different rats across different days. Each rat has different time points where they took the measurement of that volume. There are 20 rats with volume measurements and two groups; ten rats came from Chile and ten from England.
I would like to assess if there is an effect on inter variability of the rats and check how the growth is behaving (if it is slower on the rats in Chile and faster in England or vice-versa) :
m1 < - lmer(lVolume ~ Country * Day + (1 | Rat))

Linear mixed model fit by REML ['lmerMod']
Formula: lVolume ~ Country * Day + (1 | Rat) 

REML criterion at convergence: 117.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.6272 -0.3786  0.0727  0.5431  1.8786 

Random effects:
 Groups    Name        Variance Std.Dev.
 Rat       (Intercept) 0.23205  0.4817  
 Residual              0.07364  0.2714  
Number of obs: 145, groups:  Rat, 20

Fixed effects:
                       Estimate Std. Error t value
(Intercept)            1.905378   0.256483   7.429
CountryEngland         1.374471   0.321670   4.273
Day                    0.040673   0.001894  21.474
CountryEngland:Day    -0.005562   0.002354  -2.363

Correlation of Fixed Effects:
             (Intr) CtyEngland Day   
CtyEngland   -0.797                    
Day          -0.794  0.633             
CEngland:     0.638 -0.723       -0.805

But I am really confused about how to interpret these values.
Does the 0.23205 that came from the random effect on rats mean that there is significance inter population variability that affects the growth?
What does it mean the values on the fixed effect values?
In addition, I plotted the model:
plot_model(m1, show.values = TRUE, value.offset = .3)


Do the values mean significance in terms of the fixed or random effect or perhaps both?


Could I have some feedback for this, please?
Thanks.

Firstly, you may be able to make more sense of your model, at least the fixed effects, by plotting predicted values rather than coefficients. The plot_model function you use can do this.
Interpreting the fixed effects:

*

*The intercept is the average volume of Chilean rats at baseline (day 0).

*The coefficient CountryEngland says that, at baseline (day 0), rats from England have on average 1.37 units greater mass than rats from Chile.

*The coefficient for Day tells you that Chilean rats, on average, increase their volume by 0.04 units per day.

*Lastly, the CountryEngland:Day interaction coefficient tells you that the effect of Day (the rate of change of Volume) is on average -0.005 units lower amongst English rats compared to Chilean rats.

Interpreting the random effects is a little more complicated. The standard deviation of the random effect Rat, 0.48, tells you how much between-rat variation there is in Volume, after accounting for your predictors. In other words, conditional on your predictors, you would expect most (68%) rats to be within around $\pm$ 0.48 units of volume.
The statistical significance of this variation I don't think is really relevant - but consider that the standard deviation of the 'between-rat' variation (0.48) is considerably larger than the 'within-rat' variation (0.27), suggesting most variation in Volume is at the between-rat level.
Note that your model can also be extended by allowing the rate of change in Volume to vary between rats. This would introduce a random effect of Day:
m1 < - lmer(lVolume ~ Country * Day + (1 + Day | Rat))

This way, you will also be able to estimate the amount of variation in the rate of change of volume between rats. Whether or not that's valuable for your experiment I don't know.
