Opportunities and loose ends

(4). Opportunities and loose ends

(i). Changes and causes [CONTENT to be added]

(ii). Spatial analyses

***Analyzing spatial (or areal, regional) data adds more statistical and causal challenges. The mere ‘average’ (or E, expectation) value of a variable, say the mean (across all county residents) county life expectancy across all the US counties cannot be computed simply with the arithmetic average. The reason can be ‘seen’ if one considers a roulette, or horizontal ‘wheel of fortune’, where the numbers are ordered consecutively, 1,2,3, etc. If a ‘fair’ roulette is jimmied or altered, by adding a weight underneath to tilt the wheel slightly, the number above the added weight will be favored: the probabilities of getting each number are not equal anymore[i], but they are related: the numbers next to this ‘luckiest’ number have 2nd highest probabilities, 3rd highest, and so on, walking away from it. This same type of neighboring-similarity is what makes spatial data more complex: the formulas for the average, for the conditional average, and for the size of the effect of predictors need to be adjusted; one demonstration is here FamilyPractice, and a demo here Tinyurl.com/BLOGSTATS3 (Youtube @ Tinyurl.com/INTRSTATS3 but there is also a ‘hands on’ Excel workbook showing how and why things differ, using the 49 contiguous US states as example @ Tinyurl.com/SPATIALSSM ). Briefly, say CT’s (average, across all residents) Life Expectancy (LifeExpectancy.CT) is impacted by its neighbors’ values, (see Figure):

LifeExpectancyMA & NY & RI -> LifeExpectancyCT; similarly,

%PovertyMA & NY & RI -> %PovertyCT;

and this is even before trying to find the Effect.%Poverty -> LifeExpectancy!

(ii). New/modern emerging statistical tools: and NO! I have not read these, neither do I follow these publications regularly, someone else does, however: Cam Mcintosh, who shares his knowledge on SEMNET.

  1. Revolutionary: Carlos Cinelli’s Pearl vs. ‘Rubin’ (SCM-RCM) equivalence demonstration Semnet 1 and Semnet 2
  2. The E value [2, 3] – with R code
  3. Fair inference: ‘some covariates or treatments are “sensitive,” in the sense of having potential of creating discrimination’ [4, 5]; Elias Bareinboim [5]
  4. Graphical Hierarchy of Interventions: see Shpister & Tchetgen [6]
  5. Personalized Individual effects [7] [8] & [9] + [10] [11] [12] [13] [14] [15]
  6. Attrition/missingness [16]
  7. Interventional effects [17] standardized expectations of potential outcomes
  8. Planned precision vs. planned power [18]
  9. Evidence strength for causality [3]
  10. Single world interventions [19]
  11. Mediation Analysis with Attributable Fractions [20]– with R code
  12. LiNGAM [21-27] + 12.1 Bayesian estimation of causal direction in acyclic structural equation models [28]
  13. Information Geometric Causal Inference Criterion (IGCIC) [29, 30] &Applied: Gaussian process model and ICCIC [31]
  14. Causal Generative Neural Networks (CGNN) [32]
  15. Multivariate additive noise model (MANM) [33]
  16. Causal inference on discrete data via estimating distance correlations [34]
  17. Causal Inference by Stochastic Complexity [35] & [36]
  18. Nonparametric Quantile-Based Causal Discovery
  19. Direction of dependence [37] [38] [39] [40]; Cam McIntosh SEMNET
  20. Direction Dependence Analysis
  21. Higher order moments (skew) to derive directionality ; e.g. in mediation [41]
  22. Population Health Model (POHEM) [42], & Micro-simulation [43], & DAG-informed regression modelling [44]
  23. Lag as moderator for synthesizing longitudinal data [45]
  24. More of Cam McIntosh SEMNET or TXT
  25. More of Cam Nonparametric Simultaneous Equations e.g.
  26. In other fields: physics [46]; paleontology [47];
  27. In relation to chaos/nonlinear dynamical systems[48-55] ;
  28. Microrandomized trials [56, 57] and Contextual Bandit Algorithm [58, 59]
  29. Power priors [60-71]
  30. Convergent cross mapping [72]
  31. Bayesian networks applied in medicine [73] & [74-91]
  32. Dynamical systems analyses www

        *** This concludes the 4 step walk-through in the ‘research methods’/statistics introduction centered on causality. There is of course much more to cover/investigate, but in this age of AI, every one of us tends to become an equally good teacher’, with proper questioning and nuanced interpreting of AI’s response.

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        Footnotes:

        [i] Note that the games of chance were the main data exercise for many mathematicians (and many others, called ‘natural philosophers’ back in the day) who advanced the science of ‘numbers’. The classic history of statistics by Stigler  [1] is a fascinating read; mentioning e.g. De Moivre’s Doctrine of Chances (1738): ‘For example, if De Moivre or someone else of his era knew that of 346 men of age fifty, only 142 survived to age seventy, 10 he might ask, “How much credence can I give to the ratio 142/346 as an estimate of the chance of surviving from fifty to seventy? What, for example, is the probability this number is below 1/2?” ‘ p. 86.