How to interpret the Rasch reliability? I am tasked to model a set of questionnaires in order to investigate about the food insecurity in the region where my project takes place. Using the Rasch model, I was able to conduct the protocol provided by the FAO organisation and the values respect the ranges of validity. However, I will be charged of communicating my results with my team, and I am a bit confused on how to explain to them in a simple way the Rasch reliabilty.
Would appreciate the help.
You can check here for more details about the FIES protocol :
https://www.fao.org/3/ca9318en/ca9318en.pdf
 A: Rasch model is one of several models in the family of Item Response Theory psychometric models. You can find how reliability is defined for those models in the Reliability in IRT Style thread:

In Classical Test Theory observed test scores $X$ could be defined as:
$$X = T + E$$
where $T$ are the true scores and $E$ is an error of measurement. This
means that their variance is:
$$\sigma^2_X = \sigma^2_T + \sigma^2_E$$
In this case, reliability could be defined as:
$$ \rho_{xx'} = \frac{\sigma^2_T}{\sigma^2_X} = \frac{\sigma^2_X -
 \sigma^2_E}{\sigma^2_X} = 1 - \frac{ \sigma^2_E }{ \sigma^2_X } $$
In classical test theory $\sigma^2_E$ error variance and $\sigma^2_X$
observed score variance.

The same applies to the Rasch model as discussed here or in the paper by Patricia Martinkova (2007).
The explanation is pretty simple: we can decompose the observed scores $X$ into the true (unobservable) scores $T$ and error of measurement $E$, $X = T + E$, in such a case the reliability can be defined as the ratio of the variance of the true scores divided by the variance of the observed data $\sigma^2_T / \sigma^2_X$, that tells us how much variability of the data is explained by the true scores. A perfectly reliable test would explain everything and give reliability of 1, while a completely unreliable would explain nothing and give reliability of 0. This is consistent with the general definition of reliability

"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. [...]"

