# Multilevel modelling multiple binary covariates vs stratification

Readin this document it seems that random intercept + random slope (binary covariate) requires a covariance matrix

for this model

`````` for (i in 1:n) {
mu[i] = a_county[county[i]] + b_floor[county[i]] * vfloor[i] + b_uranium * log_uranium[i];
}
``````

In the manual for post-stratification

we see this formula

``````alpha + beta[age] + ...
``````

which would be also represented by

``````alpha + x_age_strata_1 * beta_1 + x_age_strata_2 * beta_2 + ...
``````

Why does this not require multivariate?

In my case I have repeated measures data of 3 conditions, do I need to use multivariate?

Hi, @stemangiola! You donâ€™t need a prior with covariance. For example, Andrew Gelman and I didnâ€™t use multivariate priors in our Covid sensitivity and specificity paper because we didnâ€™t have the kind of data required to fit it. But Iâ€™d recommend doing it if your data supports it, especially if you donâ€™t have much data and there are strong correlations.

We explain how to code the multivariate priors efficiently following Gelman and Hillâ€™s Red-State/Blue-State example in their original regression book.

Luckily, it doesnâ€™t change the stratification logic at allâ€”MRP still works exactly the same way.

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Thanks @Bob_Carpenter , I kept working on this.

So far for discrete covariates I allow multilevel model without any multivariate prior. Now, I have a design matrix with these columns

tissue_heart (binary) | tissue_blood (binary) | age (continuous)

Does the statement

is valid even if I have now also a continuous covariate? for a model like

`~ 0 + tissue + age + (tissue + age | GROUPING)`

If I get your point is that I might need `prior with covariance` only if tissue and age are very correlated (e.g. a tissue have mostly young and another tissue have mostly old).

thanks!