For the non-scots, could someone explain what a "model" is, please
Originally as stated in the provided link "Model Lodging Housing" was an attempt to provide reasonable standard housing for the homeless. The association which started this called itself the Model Lodging Association intending that their housing would become the de facto standard for such provision.
As the years went on the term was shortened to Model and became a generic term for any lodging provided for the homeless - regardless of the standards.
In the vast majority of cases the accomodation provided was in a dormitory style and was provided on a first come first served basis. Despite this, overcrowding and the hygiene problems that go with it was always a problem and "models" gained the reputation of being only a small step above the workhouse. Some, ran by organisations such as the Salvation Army, tried to maintain standards and to provide a decent level of care.