# Centered vs. non-centered parameterizations

**URL:** <https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344>\
**Category:** Modeling\
**Tags:** performance\
**Created:** [January 19, 2019, 10:42am UTC](https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344 "2019-01-19T10:42:32Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![mmonga](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mmonga/32/3923_2.png) [@mmonga](https://discourse.mc-stan.org/u/mmonga)\
**Post date:** [January 19, 2019, 10:42am UTC](https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344/1 "2019-01-19T10:42:32Z")

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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.

 ![index](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/9/99c15bed44799908d8fd4c03e9b0fd6a36234d8a.png)

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.

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**Author:** ![ScottAlder](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/scottalder/32/3322_2.png) [@ScottAlder](https://discourse.mc-stan.org/u/ScottAlder)\
**Post date:** [January 19, 2019, 4:53pm UTC](https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344/2 "2019-01-19T16:53:46Z")

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Check out [this forum discussion](https://discourse.mc-stan.org/t/partial-non-centered-parametrizations-in-stan/7104) 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](https://arxiv.org/abs/1312.0906) for more in depth analysis of the challenges hierarchical models present for Hamiltonian Monte Carlo.

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**Author:** ![mmonga](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mmonga/32/3923_2.png) [@mmonga](https://discourse.mc-stan.org/u/mmonga)\
**Post date:** [January 19, 2019, 5:15pm UTC](https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344/3 "2019-01-19T17:15:45Z")

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

Thank you for your reading suggestions.

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**Author:** ![andre.pfeuffer](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andre.pfeuffer](https://discourse.mc-stan.org/u/andre.pfeuffer)\
**Post date:** [January 20, 2019, 4:29am UTC](https://discourse.mc-stan.org/t/centered-vs-non-centered-parameterizations/7344/4 "2019-01-20T04:29:39Z")

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May I ask: How about divergences according to Centered and non-centered parm.?