# Error model representations for RUV

**URL:** <https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423>\
**Category:** How-to\
**Created:** [July 14, 2026, 6:03pm UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423 "2026-07-14T18:03:30Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![tesh\_sutha99](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/tesh_sutha99/32/815_2.png) [@tesh\_sutha99](https://discourse.pumas.ai/u/tesh_sutha99)\
**Post date:** [July 14, 2026, 6:03pm UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423/1 "2026-07-14T18:03:30Z")

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Hello Team,  
I have couple of questions regarding error model representations.

Is dv ~ @. Normal(cp, cp \* σ) same as dv ~ @.Normal(cp, cp\*exp(σ))?  
An exponential error model is represented as dv ~ @. LogNormal(log(cp), σ), how is it different from proportional error model under FOCE

Can expoennalso be represented as dv ~ @. Normal(cp, exp(σ)) in Pumas ?

I would apprciate if you could help me understand how these representations differ under FOCE approximation.  
Thank you in advance.

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**Author:** ![vijay](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/vijay/32/96_2.png) [@vijay](https://discourse.pumas.ai/u/vijay)\
**Post date:** [July 18, 2026, 6:56am UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423/2 "2026-07-18T06:56:34Z")

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Sorry, for the late response. Did you try ask.pumas.ai for this?

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**Author:** ![tesh\_sutha99](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/tesh_sutha99/32/815_2.png) [@tesh\_sutha99](https://discourse.pumas.ai/u/tesh_sutha99)\
**Post date:** [July 19, 2026, 1:07pm UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423/3 "2026-07-19T13:07:16Z")

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Thank you so much for your response, Vijay. Yes.  
To summarize what it says  
dv ~@.`Normal(cp, cp*σ)` and dv ~@.`Normal(cp, cp*exp(σ))` are the same _model but with different representations_. The first is the proportional error model: the observation is Normal, centered at `cp`, with an SD that scales with `cp`, so it mimics multiplicative error but being Normal, it stays symmetric and can go negative, unlike the true exponential/LogNormal model.

`dv ~ @.Normal(cp, cp*exp(σ))` only reparameterizes the CV through a log link so `σ` can range freely while the CV stays positive. The model is still proportional, just `σ = log(CV)` instead of the CV directly.

y ~ @.`Normal(cp, exp(σ))` is additive on the natural scale, a constant-SD Normal, where `exp` only keeps the SD positive. The exponential error model is the multiplicative one, `Y = cp·exp(ε)`, which yields strictly positive, right-skewed observations and is written in Pumas as `dv ~ @. LogNormal(log(cp), σ)`.  
This is my understanding. Would appreciate to get more inputs to get more clarity.

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**Author:** ![andreasnoack](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/andreasnoack/32/22_2.png) [@andreasnoack](https://discourse.pumas.ai/u/andreasnoack)\
**Post date:** [July 27, 2026, 2:52pm UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423/4 "2026-07-27T14:52:36Z")

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Your summary here is correct. Notice, though, that it is simpler to just restrict `σ` to be positive in the `@param` block and wrapping it in `exp` in the model definition.

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<div class="post-metadata">

**Author:** ![tesh\_sutha99](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/tesh_sutha99/32/815_2.png) [@tesh\_sutha99](https://discourse.pumas.ai/u/tesh_sutha99)\
**Post date:** [July 28, 2026, 1:56pm UTC](https://discourse.pumas.ai/t/error-model-representations-for-ruv/1423/5 "2026-07-28T13:56:27Z")

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Got it. Thank you so much.