multi-location latin square design analysis


I have a 5 x 5 Latin square design which is replicated 5 times within each location (same rows and columns in each location). The same design was used in 10 different locations and I was asked to perform a combined location analysis.

I have done it before with other designs, such as RCB or split-plots, using the location and treatment x location as random effects but I have never analyzed latin square designs.
I found information how to analyze a replicated latin square in one location but not in many combined. I have never seen latin square design analysis using a mixed model either.

This is the model with only fixed effects I am considering:

fixed: Y= location + rep(location) + row(location) + column(location) + treatment

Thoughts from anyone who knows how to analyze such a design is greatly appreciated.