[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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