In the print() output of a multi-level model
stan_glmer family: gaussian [identity] formula: ec ~ g + (g | chr) observations: 608 ------ Median MAD_SD (Intercept) 51.434 0.777 gv 3.136 0.813 Auxiliary parameter(s): Median MAD_SD sigma 5.499 0.159 Error terms: Groups Name Std.Dev. Corr chr (Intercept) 1.772 gv 1.746 -0.34 Residual 5.503 Num. levels: chr 5
I have the \sigma^2_y of 5.503 as the Residuals and the \sigma^2_\alpha and \sigma^2_\beta, all given under Error terms. This sigma though is slightly different here, 5.499 but in some other models it is the same, to at least the third or fourth decimal.
In this tutorial the difference between residuals en sigma is not explained.
Could somebody explain the difference between the two?