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I am looking at component wear type problem, where the dependent variable is a percentage of the original wall thickness. I had read on these forums that the use of a beta regression would make sense for this data, assuming I did not have examples with 0% loss or 100% loss in my dataset.

I have the additional challenge that the lower limit of my wall thickness detector is 10%. Values below this are written as a zero. So this would make my data also left-censored at 10%.

Could I please get some general advice on a strategy for modelling this data to account for the left-censoring at 10% and the max value allowed being 100%.

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  • $\begingroup$ Another option is Bayesian analysis. See for example the section on modeling Censored data in the Stan user guide. $\endgroup$
    – dipetkov
    Feb 10 at 15:22

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Semiparametric ordinal regression models such as the proportional odds model handle detection limits automatically, as long as you don’t try to use the model to estimate the mean. You can use it to estimate cumulative probabilities and quantiles. Resources are here.

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  • $\begingroup$ I'd potentially be looking to provide a prediction for a given component of when it is likely to reach a certain %. Would you still recommend this approach in that case? $\endgroup$
    – Meep
    Feb 14 at 3:45
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    $\begingroup$ That is one of the cumulative probabilities I mentioned. You get $\Pr(Y \geq y | X)$ for any $y$. $\endgroup$ Feb 14 at 13:05

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