I'm writing a paper regarding the inter and intra reliability of various musculoskeletal screening tests. The outcome variables consist of binary, ordinal and continuous variables. I have used the following reliability coefficients and their confidence intervals for analysis of the respective types of variables:

Continuous data: ICC, CI and SEM

Binary: Gwet's AC1 and CI

Ordinal: Gwet's AC2 and CI

As the formulae for SEM (agreement/precision measure) takes ICC (reliability measure) into consideration it is obvious that it has to be reported with the corresponding ICC.

Is there an agreement measure such as SEM that has to be reported with the reliability coefficients that is not ICC? Perhaps just typical standard error?