# Random effects caused by covariate

**URL:** <https://discourse.pumas.ai/t/random-effects-caused-by-covariate/567>\
**Category:** How-to\
**Created:** [December 7, 2021, 4:21pm UTC](https://discourse.pumas.ai/t/random-effects-caused-by-covariate/567 "2021-12-07T16:21:51Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![ArnoStrouwen](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/arnostrouwen/32/185_2.png) [@ArnoStrouwen](https://discourse.pumas.ai/u/ArnoStrouwen)\
**Post date:** [December 7, 2021, 4:21pm UTC](https://discourse.pumas.ai/t/random-effects-caused-by-covariate/567/1 "2021-12-07T16:21:52Z")

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I have 10 machines that each gather 10 time series.  
From fitting the same fixed effects model to each time series individually, I have noticed that there is both substantial within- and between machine variance of the estimated model parameters, (and the within machine variance seems to also vary between machines.)

I now want to fit a random effects model to all time series together. How can I express that the model parameters from one time series are correlated with the model parameters from the time series gathered by the same machine?

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**Author:** ![patrick](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/patrick/32/206_2.png) [@patrick](https://discourse.pumas.ai/u/patrick)\
**Post date:** [March 7, 2022, 8:19pm UTC](https://discourse.pumas.ai/t/random-effects-caused-by-covariate/567/2 "2022-03-07T20:19:48Z")

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> [@ArnoStrouwen](#):
>
> parameters

Hi Arno,

I had not seen your question. If it’s still releavnt, can you maybe describe your question in more detail? Correlation can be introduced by having a common component within a machine, but that coulld just be a normal random effect, so I’m not sure that’s what you’re asking.

Any chance you could put it in (pseudo-)math terms?

Best,  
Patrick