I have randomly broken down a very large dataset into 20 equal-sized blocks.

I have fit a logistic model with random effects on each block with R (lme4).

Say my model is simply:

```
lmer(y ~ X + Y + (1|city/ID), family = binomial, REML=FALSE))
y = a + b·X + c·Y + random term
```

This gives me the intercept and each coefficient, and their standard errors and p-values on each block.

I have the output as a data.frame (or data.table) with one row per block and one column per coefficient and std.errors and p-values, but I can change it.

Now I would like to combine all the results to get a "global" or "averaged" model.

For example, for the coefficients "b":

- I calculate the global b as the weighted average of all b
_{i}. - I calculate the standard error or p-value of the global b.

How can I get that standard error of the coefficients? Any solution with a formula or an R package function would be great.

How do I combine the standard errors to get a global standard error and then compute a p-value?

I think it's a kind of meta-analysis.