Question on Contextual Effects

Dear Jithin Sam,

I think that with only 20 states with roughly 20 different values for each
contextual variable, that number (i.e., 20) is probably your relevant
sample size. And if I remember that correctly, the rule of thumb is that
you need 20 data points for each parameter in a linear model, so I guess
this applies here to. So I would say much more than 1 contextual variable
is probably not advisable in one model. You can of course run multiple
models each with different contextual variables, but a joint model sounds
somewhat questionable.

I know that sounds crazy given your enormous amount of data, but the only
thing this many data allows you to do, is to estimate the probability of a
success (i.e., the binomial parameter) in each state very precisely. But
then your main interest is in the inference performed at the state level so
it has to be seen in that context.

Please note that this explanation ignores the fact that estimating
parameters in a binomial model is usually more complicated than in a linear
model.

Please note that I am not a statistician, so I am happy to be corrected by
someone more knowledgeable. But in my experience with such models, the
number of levels at the highest level seems to be the relevant number in
such cases.

Best,
Henrik



Am Di., 30. Juli 2019 um 14:59 Uhr schrieb Varghese, Jithin Sam <
jithin.sam.varghese at emory.edu>:

Hi everyone,

We are working on a project to model 3 separate cross-sectional surveys
(i.e., 3 independent samples). Each survey has the following hierarchical
data structure:
L3 - states (~20)
L2 -villages  (~X)
L1 - Individuals (~55,000 total)

We are interested in estimating the association between  a contextual
variable measured at the state-level (normally distributed) and an outcome
measured at the individual-level (dichotomous) in the pooled data set.  Is
there any guidance on the advisable number of contextual variables that
could be accommodated in the logistic MLM model?

Thanks a lot for the help in advance.

Regards,
Jithin Sam Varghese
Emory University

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