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This question might have been answered somewhere else but I could not find it.

Hi all. My research is about investigating whether a certain policy increases the speed of construction of housing units or has no effect. Since market factors play role in duration, I need to structure it in panel format and I am in desperate need for panel data tools (Fixed effects, clustering etc.)

I was thinking to use Probability Linear Models (PLM) for estimation that its results are much easier to explain as well as the ability to use panel data settings. Also there are new methods to produce better estimates which you can find here.

However, I could not find a source that explains how I can estimate a survival model using PLM or Least Square methods. All I could find was Additive Hazard models, which are a bit problematic because of time-variant covariates and the difficulty in reporting results as well as statistical inference.

I want to know do you have any suggestions or do you any sources that could help me with this settings?

In short, how can I estimate a survival model in panel format using linear regression.

Thank you all for your time!

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    $\begingroup$ It's not clear that a linear probability model will help you. The reference you cite uses that only as a first step in a linear discriminant model (LDM) approach to efficient imputation on a large scale--which involves logistic regression as a final step, anyway. For evaluating the LDM approach, it says: "Standard logit should be the gold standard. LDM can't do any better than conventional logit..." Please edit your question to say more about the specific problems you face, as there are many tools available for refining time-to-event analysis both in continuous and in discrete time scales. $\endgroup$
    – EdM
    Dec 7, 2021 at 14:47
  • $\begingroup$ Thank you @EdM for your comment. I modified the question as you advised.My main issue is finding a way to estimate survival model using Linear regression. LDM is just helping with producing estimates for further analysis. $\endgroup$ Dec 8, 2021 at 13:26
  • $\begingroup$ I mean, once you estimated your discrete time model you can use the Allison procedure to get the instant hazards, and then based on those calculate the cumulative hazards. (That gets you point estimates, I don't know about standard errors though for those survival curves.) $\endgroup$
    – Andy W
    Dec 8, 2021 at 13:36

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A discrete-time survival model suitable for panel data with time-varying covariates is essentially a set of binomial regressions for the included time periods. See Willett and Singer, for example. So if you really want to use a linear probability model for each of those binomial regressions there's nothing to stop you, as @AndyW implies in a comment.

The reason why you aren't finding pre-built software to do linear probability model fitting in this context is that standard logistic regression or other binomial modeling that restricts probabilities to [0,1] (e.g., probit regression, complementary log-log link) is superior for the binomial modeling. It's hard to imagine a situation in which a linear probability model would be superior, particularly for "statistical inference." You claim that its "results are much easier to explain," but how do you explain predictions of negative probabilities from a linear probability model?

Particularly if you are intending to publish your results, stick with established statistical approaches.

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