# Visualizing model results####
# There are several ways of visualizing the results of a mixed model, all of which
# involve using the coefficients generated by the model. 
# So the first step is to obtain the model coefficients to be able to add them to the figures
coef(M8)
# Now put the coefs into dataframes to make them more easy to manipulate
Lake.coef <- as.data.frame(coef(M8)$Lake)
colnames(Lake.coef) <- c("Intercept","Slope")
Species.coef <- as.data.frame(coef(M8)$Fish_Species)
colnames(Species.coef) <- c("Intercept","Slope")

# Plot 1 - All Data
# Make a plot that includes all the data
plot <- ggplot(aes(Z_Length,Z_TP),data=data)
Plot_AllData <- plot + geom_point() + xlab("Length (mm)") + ylab("Trophic Position") + 
                labs(title="All Data") + fig
# Add a layer that has an abline with the intercept and slope of the relationship between length and 
# trophic position.
# Note that you can obtain the intercept and slope of the fixed factor directly from the model summary
summary(M8)
Plot_AllData + geom_abline(intercept = -0.0009059, slope =0.4222697)