4 ms·

When I was at CMU a decade ago I took 36-401 and 36-402 (then taught by Shalizi) and they were both very good statistical classes and they forced me to learn ba

When I was at CMU a decade ago I took 36-401 and 36-402 (then taught by Shalizi) and they were both very good statistical classes and they forced me to learn base R, for better or for worse. A big weakness of linear regression that I had to learn the hard way is that the academic assumptions for valid interpretation of the coefficients are easy to construct for small educational datasets but rarely applicable to messy real world data.

deleted 2y ago
[deleted]
aquafox 2y ago
It depends. The most important assumption is independence of the observations. If that is not given, you have to either account for correlated responses using a mixed-effects model or mean-aggregate those responses (computing the mean decreases the variance but also reduces the number of data points and those two cancel each other out in calculating the t-statistic of the Wald test). With regard to other assumptions, e.g. normality of the residuals, linear models can often deal with some degree of violation against those. But I agree that it's always good to understand the influence of those violations, e.g. by using simulations and making p-value histograms of null-data.
bdjsiqoocwk 2y ago
The flip side is with messy real world data you just need a model that's ok enough, rather than being concerned whether the p-value is this or that.
- minimaxir 2y ago
  At that point, if you don't care about interpretable coefficients, you might as well use gradient-boosted trees or a full neural network instead.
  - borroka 2y ago
    It depends on the "severity" of the violation of assumptions--you can also use GAMs to add flexible nonlinear relationships--and the amount of data you are working with. Statistical modeling is a nuanced job.
    - minimaxir 2y ago
      I tried to argue that while at CMU and it didn't go well.
      - borroka 2y ago
        They may not know at CMU that the vast majority of applied, trained-on-data statistical models that help run the modern world seriously violate one or more of the model's assumptions.

deleted 2y ago

[deleted]

aquafox 2y ago

It depends. The most important assumption is independence of the observations. If that is not given, you have to either account for correlated responses using a mixed-effects model or mean-aggregate those responses (computing the mean decreases the variance but also reduces the number of data points and those two cancel each other out in calculating the t-statistic of the Wald test). With regard to other assumptions, e.g. normality of the residuals, linear models can often deal with some degree of violation against those. But I agree that it's always good to understand the influence of those violations, e.g. by using simulations and making p-value histograms of null-data.

bdjsiqoocwk 2y ago

The flip side is with messy real world data you just need a model that's ok enough, rather than being concerned whether the p-value is this or that.

minimaxir 2y ago
At that point, if you don't care about interpretable coefficients, you might as well use gradient-boosted trees or a full neural network instead.
- borroka 2y ago
  It depends on the "severity" of the violation of assumptions--you can also use GAMs to add flexible nonlinear relationships--and the amount of data you are working with. Statistical modeling is a nuanced job.
  - minimaxir 2y ago
    I tried to argue that while at CMU and it didn't go well.
    - borroka 2y ago
      They may not know at CMU that the vast majority of applied, trained-on-data statistical models that help run the modern world seriously violate one or more of the model's assumptions.