In the estimation results, se_mean, n_eff, and Rhat are "NaN", why?

General
1

In the output of estimation, the "se_mean"s of Cholesky_Omega[1,1] and Cholesky_Omega[1,2] are “NaN”.

Also, the "n_eff"s and "Rhat"s are also “NaN”.

I’m wondering what these values imply?

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2

Those quantities are only defined if there is variability across samples in the value of the parameter. I think the element at [1,1] should be expected to be constant at 1, but I’m not sure why you’re getting a constant value at [1,2] as well.

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3

Oh wait, yeah, [1,2] will always be zero.

4

So this is reflects that things are not smart enough to either omit the constants from the output or discern that when dealing with a cholesky factor variable those diagnostics shouldn’t be applied to the elements expected to be constant.

5

So, that is not a problem because the elements in the first row of Cholesky factor(a 2 by 2 matrix) are fixed.

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6

The value of element in position 1,1 is constrained to be 1 because in Cholesky factor the length of each row should be 1. Since the Chokesky factor I defined is a 2 by 2 matrix, the element 1,1 must be 1.(Sine the element 1,2 is constrained to be 0, making it a lower triangular matrix.)

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7

Correct.