About creating pseudo-levels

[cesarroga]

I've got a question that I think it may be a too noob one, but I'm more or less new in the world of multilevel analysis.

I have data about cases of a disease that include sex, age and small area code. I also have date at small area level including socio-economic index, and population by sex and by age groups. I was trying to estimate a multilevel logistic regression model based on proportion (assuming binomial distribution). The question is wether I can, and how, introduce pseudo-levels in order to adjust for age and sex.

I think it may be like this:
I use the data that is registered as "women younger than 16", "women between 16-64", and son on, to set denominators. So, I get age group and sex specific denominators for the level 1 units. Each level 1 unit is included then in a pseudo unit for level 2. The codes for level 1 and level 2 are the same. Then, I include level 2 units in level 3 units that are the small area, so every small area will have 6 units (2 sexes * 3 age groups). Then I can include sex and age group confounders (as level 2 variables).

Is this correct?
Thanks in advance

[billb]

Hi Cesarroga,
You should be able to code logistic regression examples where the denominator is not 1 so that you can then model the 6 proportions as 6 couplets (y,n) one per row in the dataset and nest these within small areas. In MLwiN you would have as you say the same levels as level 1 and level 2 with then small areas at level 3. You would need to sort the data so that all 6 proportions are in consecutive rows for each small area so that it can identify the hierachy. Then level 1 would capture binomial variation and level 2 additive overdispersion.
Hope that helps,
Bill.

[cesarroga]

Hi billb! Thank you very much.
I did that and I think I got some interesting results. But know I have some doubts about how to interpret these results.
Specifically, I don't know how to interpret the variance of the (pseudo)level 2 residuals (linked to the random intercept). Do they resemble the variability between small areas that the model somehow does not impute to the level 3? Or do they resemble the variability in how sex and group age may affect the outcome, since this level 2 is an "artifact" created from a fragmentation based on sex and age within each small area?
I tend to interpret this variance more like the second way. It is because when I get from the null model to a modell that only includes sex and group age as explanatory variables, the level 2 variance is reduced by a lot (from 1.977 to 0.949), but actually the level 3 variance increases from 0.432 to 0.511. Somehow I think that sex and age group as explanatory variables "explain" the difference between these pseudogroups that, in fact, are defined as <16age men, <16age women, and so on. So, the value of 0.949 for the variance of the level 2 residuals would be the variability between these groups within each level 3 unit that is not fully explained by sex and age group as explanatory variables.
Is this thinking correct?

Thank you so much in advance.

[billb]

Hi Cesarroga,
I can recommend my paper on this https://rss.onlinelibrary.wiley.com/doi ... 04.00365.x which looks at partitioning variation in a logistic model with overdispersion and has a similar example of counts for different categories.
Best wishes,
Bill.

[grippingfossil]

Hi Cesarroga,
I can recommend my paper on this https://rss.onlinelibrary.wiley.com/doi ... 04.00365.x geometry dash world
which looks at partitioning variation in a logistic model with overdispersion and has a similar example of counts for different categories.
Best wishes,
Bill.

I'm unsure of how to interpret the variance of the random intercept-linked (pseudo)level 2 residuals. Do they mirror the localized variability that the model, for some reason, does not attribute to level 3?