[HN Gopher] An Introduction to Hierarchical Modeling
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       An Introduction to Hierarchical Modeling
        
       Author : andyxor
       Score  : 82 points
       Date   : 2021-03-02 07:50 UTC (2 days ago)
        
 (HTM) web link (mfviz.com)
 (TXT) w3m dump (mfviz.com)
        
       | [deleted]
        
       | antipaul wrote:
       | How might this be combined with a training/testing data splitting
       | paradigm, or even using an ML model?
        
         | causalmodels wrote:
         | Probabilistic machine learning is still machine learning. If
         | you're referring to one of the popular tensor frameworks,
         | pretty much all of them have probabilistic features or add-ons
         | [1][2][3]. There are also frameworks developed specifically for
         | this kind of work [4][5].
         | 
         | This [6] is a more in depth look at hierarchical / multi-level
         | modeling. The prediction section [7] specifically goes over
         | cross validation and inference.
         | 
         | [1]
         | https://www.tensorflow.org/probability/examples/Multilevel_M...
         | [2] https://pyro.ai/examples/forecasting_iii.html [3]
         | http://edwardlib.org/ [4] https://mc-stan.org/ [5]
         | https://docs.pymc.io/ [6]
         | https://docs.pymc.io/notebooks/multilevel_modeling.html [7]
         | https://docs.pymc.io/notebooks/multilevel_modeling.html#Pred...
        
       | gegtik wrote:
       | I don't quite understand what's hierarchical about this example.
       | seems like a few different mutually exclusive segments that can
       | then be independently analysed?
        
         | ZephyrBlu wrote:
         | It's hierarchical because of the nature of the data, not
         | because of the model itself.
        
       | abeppu wrote:
       | Though the visualization is cool here, I think this is actually
       | not a good example. The final "hierarchical" model presented
       | doesn't say anything about a relation between the coefficients
       | for the different departments, so one can view this as really
       | just having separate models, one for each department.
       | 
       | To me, the point of a hierarchical model is that one can assume
       | relationships between these parameters (e.g. suppose that they
       | are from the same distribution). Then when one department has
       | very few data points, some of the information in your beliefs
       | about the parameters for that department come from what you
       | learned in other departments. E.g. the base salary is likely to
       | be similar to base salaries of other departments.
        
       | antipaul wrote:
       | What if you simply add department and department*salary
       | interaction terms to a standard regression model?
        
         | aseerdbnarng wrote:
         | You'll run out of data pretty quickly.
         | 
         | https://statmodeling.stat.columbia.edu/2018/03/15/need-16-ti...
        
         | wodenokoto wrote:
         | Then for any given data point, salary for all other departments
         | will be zero (dep1 _salery = dep2_ salary = ... = 0) so data
         | for each department will become separate and you will in effect
         | have i number of different models, although they all share the
         | same bias term / intersect.
        
           | plouffy wrote:
           | You could argue that a hierarchical model is already multiple
           | models. If each department has a dummy variable then they
           | wouldn't share the same intersect. The only difference is how
           | you interpret that intercept. The department intercept would
           | now not be the salary of an individual with 0 experience, but
           | the difference between the salary of an individual with 0
           | experience in a department compared to the all other
           | employees with 0 experience.
        
       | ZephyrBlu wrote:
       | I love the visualization and animation, but I think it should be
       | specified that this is Linear Hierarchical Modelling.
       | 
       | I was expecting something bayesian-related given that bayesian
       | statistics lends itself to hierarchical models quite nicely.
        
       | plouffy wrote:
       | Very cool animation.
        
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