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I am interested in modelling a response that is a proportional change in mechanical equipment health before the equipment is turned off, and then when it is brought back online again (so the treatment this in case is both conditions in the offline period and how its brought back online again).

The health measurement is strictly positive, it should have an upper bound of 100 but there are circumstances where it can exceed 100 legitimately. I have four continuous variables that I would like to include as explanatory variables - these relate to the conditions during the downtime and how the equipment is brought back online. We have only take the second health measurement once the equipment is considered safely online.

In this thread - Relative or Absolute Change for Test Statistic it was mentioned that proportional change was analysed traditionally using logarithms. From this thread I don't see the final step of modelling - should I be log transforming my response? And what would the appropriate GLM specification be in that case (family/link)?

I've also seen it recommended that a Beta distribution as the family in the GLM is appropriate for a ratio of two continuous variables (in my case, these are positive continuous variables).

I'm a bit confused as to which approach I should be taking - if anyone could clarify this it would be amazing.

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    $\begingroup$ This is a bit too abstract. Can yu describe yur use case in english? Questions with some interesting context tends to generate higher interest! $\endgroup$ Oct 1, 2021 at 7:57
  • $\begingroup$ I’ve updated to include context, hope that helps! $\endgroup$
    – Meep
    Oct 2, 2021 at 23:07

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In case anyone stumbles on this question - I found some additional relevant sources around the use of log transformations and alternatives to it (gaussian with log link) and potentially gamma distributions for evaluating a multiplicative relationship between response and regressors.

Log-linked Gamma GLM vs log-linked Gaussian GLM vs log-transformed LM

Linear model with log-transformed response vs. generalized linear model with log link

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