# Sigma vs. Residuals in stan_glmer output?

In the print() output of a multi-level model

stan_glmer
family:       gaussian [identity]
formula:      ec ~ g + (g | chr)
observations: 608
------
(Intercept) 51.434  0.777
gv           3.136  0.813

Auxiliary parameter(s):
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?

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When using the summary function one gets the mean of sigma, the print() function though, gives the median of sigma. So this will probably explain the difference.

It is strange that, under the Error terms the mean of the Residuals are given, with the median of the same parameter, as sigma, under Auxiliary parameters.

Normally, with print() one gets the median values of parameters, with summary() the means. With a multi-level model, it seems both are used.

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