[R-sig-ME] Hierarchical regression with partially nested variables

[David Duffy]

On Fri, 26 Jul 2013, Fabio Valeri wrote:

> Dear group,
>
> I would like to do a logistic regression of vaccination coverage of, for
> example, HPV. Let's assume that we have 50 states (S). 30 states have an
> urban part and a country part (urbanity variable U). The other 20 have
> only a country area. 10 of the states have population areas where
> individuals speaks only Spanish and other areas only English (L). The
> linguistic region correlates only slightly with urbanity. For example:
>
> The situation is that U is nested in S but not each S has both levels of
> U. This is also the case for the linguistic variable: L is nested in S
> but not each S has both levels of L. If U would be nested completely in
> S and L completely in S, the model would look like (in R-terminology for
> lmer):
>  y ~ (1|S) +(1|S/U) + (1|S/L)
> where y: 0/1 vaccinated

It's commonly pointed out on this list that nesting is a crossed 
interaction model with appropriate coding of the lower level. If there is 
significant heterogeneity of the effect of U across different S, then this 
needs to be modelled, even if evidence is only coming from a subset of 
informative S.  Re two levels - one commonly uses GLMMs to meta-analyse 
RCTs, with a binomial outcome, two treatment arms and multiple centres or 
trials.  If there is heterogeneity of odds ratios across centres (eg in a 
fixed effects model), then "the" standard approach is a random 
slopes model for treatment effect. I am guessing this is closer to what 
you will actually need from your analysis.


| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v