Joint fitting of all countries

[athowes]

Marta mentioned that we could consider fitting all countries with a joint model. I can see that this would have some benefits, including: allowing inclusion of country-level random effects which may be used to control the degree of smoothing between countries (there is between country heterogeneity in the estimates, but not an unreasonable amount in my opinion), allowing for "percentage of variance explained by county-level random effects" to be read directly off the posterior. Downsides could be: takes longer to fit (computation so far is not a limiting factor), would require rewriting code, may be difficult not to over-smooth.

[athowes]

• Common variance for age is sensible
• Common variance for space versus country-specific variance is tricky: open question
• Could try time as a linear trend first, possibly random slope by country

[athowes]

Closing issue #32 and having representing time properly in the model be part of the goal of this issue (where we have sufficiently many surveys to have a "true" temporal random effect, as well as possible survey-type random effects)

[athowes]

Add option to reduce number of countries to make this tractable locally for code checking.

[athowes]

Add interaction models to this.

[athowes]

This is done at a basic level so going to close and make new issues for extra improvements.