# Centered vs. non-centered parameterizations

According to Stan Manual (Version 2.18.1, page 33):

Non-centered parameterizations tend to be more efficient in hierarchical models;

However, I’m experimenting with a 3-PL IRT model, very similar to the one proposed by the manual (at the same page) and the centered version is much faster. Moreover, the estimation of the beta parameter is more precise.

In this forest plot the red plots refer to the non-centered model, the blue ones to the centered model. Sampling was done with 4 chains, with 2000 draws.

I was surprised, since I expected the non-centered model were better. In fact, the centered model is easier to interpret (the estimated beta is directly the value for a 50% success probability in the item response curve), thus it is definitely preferable.

I am not a stats experts, thus I wonder if there is something that I’m interpreting wrongly. Thanks in advance.

Check out this forum discussion to see some expert discussion on the topic of centered, non centered, and partially centered parameterizations.

As I understand it, centered actually works better when you have informative data (large N relative to \sigma) for a particular group, while non centered is better for uninformative data (small N relative to \sigma) for a particular group. The thread I linked also discusses trying to center some groups and not others depending on how much data is in each group, but it seems like finding the cut off for N is a difficult task.

Also check out this paper for more in depth analysis of the challenges hierarchical models present for Hamiltonian Monte Carlo.

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In fact, i have a lot of data and limited variability, so I guess your understanding fits well…