Linear Regression. Learning from experimental psychologist Shu-Hong Zhu.
Channel: Math 4 Wisdom
Date: 2023-02-22

Experimental psychologist Shu-Hong Zhu shares with me and John Harland his insights into linear regression. 

I want to learn about the generalized linear model, which is a generalization of linear regression.  The generalized linear model encompasses the natural exponential families with quadratic variance function, which accord with orthogonal Sheffer polynomials.  I am exploring how the fivefold classification might express the fivefold cognitive framework for decision-making, whereby "every effect has had its cause; but not every cause has had its effect; and so there is a critical point for deciding".  This is why I asked Shu-Hong to teach me about linear regression from his intuitive point of view.

See also: "Linear Regression: Learning from John Harland". John is a functional analyst and teaches math and statistics.
https://www.youtube.com/watch?v=xmqa4RwdlJQ

1:00 Introducing Shu-Hong Zhu. His advisor was Norman H. Anderson (1925-2022), from whom he learned Integrated information theory. Shu-Hong currently works in public health, tobacco control.

4:00 David Freedman, "From Association to Causation: Some Remarks on the History of Statistics"'. In applying linear regression, a key question is: What conceptual model do you have in mind?

5:00 Linear regression has value for checking correlation, for exploratory analysis.  Norman H. Anderson, "Empirical Direction in Design and Analysis" champions the Experimental pyramid: 1) Conceptual framework, 2) Phenomena, 3) Behavior, 4) Measurement, 5) Design, 6) Statistical inference.

7:00 Are the conditions being met? Is the behavior linear? The key variable may be missing. Norman Anderson's example of the bombers and cloud cover.

10:00 Problem: simply calculating what we happen to measure. No conceptual model can mean that we lack a crucial variable.
12:00 Abuses: Too many variables, thus not enough subjects, thus empty cells.

13:30 Linear regression can provide some confirmation, as part of a convergence of evidence.
14:00 Randomization controls the unmeasured. Distribution of key variables equals out.

15:30 Levels of control 1) Factorial design. 2) Randomization. 3) Linear regression.  Factorial design gives most control. Isolate contribution of factors. Calculate interaction. 
19:00 Example of tobacco-control, comparing the effect of behavioral intervention and pharmacological intervention. Often there is no additive effect.

21:00 AK: When are categories comparable?
22:00 Example: Beta-carotene and lung cancer.
25:00 Example: Colonoscopy. Lack of causal model. Per-protocol analysis.
34:00 AK: Negative result is sobering.

35:00 JH: Statistics applied to education. Is math expertise truly helpful?! 
37:00 JH: Challenges with human subjects. Disproportionate impact. Lower success among groups. Example: First generation college students. Unfounded inferences. Creeping inferences. 
40:00 JH: What role should data play? Cultural changes happen personally. Art advances nonobjectively. Great teaching is an art form.
43:00 Multiple interpretations. A problem becomes the acceptability of interpretations. Can choose easy, misleading interpretations. 
44:30 AK: A category may become unhelpful for interventions. JH: A missing variable can be the zipcode.
46:00 We may lack the relevant locus for intervention. Causality suggests a relevant intervention.

47:00 AK: My study of quantum physics with John Harland led to the fivefold classification of orthogonal Sheffer polynomials, the generalized model, the Natural exponential families with quadratic variance function (NEF-QVF), and thus an interest in linear regression. At the SEM-NET mailing list for Structural equation modeling I learned of Judea Pearl's "The Book of Why" and I exchanged letters with Keith Markus. 
49:00 AK: I was surprised by the focus on latent variables. I sense a lack of conflict between latent variables. Can they ever yield a scientific theory?
50:30 Example: Acupuncture (following Chinese medicine) vs. Acupuncture (violating those principles) vs. Drug. Acupuncture outperformed drug but following or violating the theoretical principles made no difference.  JH: Control group?

56:30 AK: Paul Humphreys, "The Chances of Explanation" starts with axioms. Is axiomatic thinking scientific? Are cognitive frameworks preferable?
59:00 Cognitive frameworks seem more suitable for modeling physics rather than human behavior. We need cleverly designed experimental studies. Descriptive linear regression models can only point the way.

Do you have intuition about linear regression or any of the topics we covered?  Please let us know!

My name is Andrius Kulikauskas and I host "Math 4 Wisdom".

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