Topics of Interest

Because I just don't always have time to fully develop a post on everthing I come across, here are a few shorties:

Pauls Allison has done some great posts recently related to logistic regression and model assessment.

With regard to the pseudo R^2, see this post as well as the article associated with a new proposed alternative:

Tjur, T. (2009) “Coefficients of determination in logistic regression models—A new proposal: The coefficient of discrimination.” The American Statistician 63: 366-372.

(I've written about the pseudo R-square before here.) 

His most recent post discusses the Hosmer-Lemeshaw test. In the futrue I'd like to expand more on this, but he's critical of the test because it is sensitive to strata size. I am too, and I've also seen many criticisms related to its sensitivity to large sample sizes. I'll come back and expand more on that later, or do a separate post, but for now I'm just looking forward to his next article in which Paul is going to discuss some recent advancements and alternatives to the HL test.

Symbol Pallete

These can be used to cut and paste in blogger for blog posts:

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω . . . . . Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω

∂ ∫ ∏ ∑ . . . . . ← → ↓ ↑ ↔ . . . . . ± − · × ÷ √ . . . . . ¼ ½ ¾ ⅛ ⅜ ⅝ ⅞

∞ ° ² ³ ⁿ Å . . . . . ~ ≈ ≠ ≡ ≤ ≥ « » . . . . . † ‼


More:

Source: http://xahlee.blogspot.com/2010/06/math-symbols-in-unicode.html

Some Greeks: α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς τ υ φ χ ψ ω
superscript: ⁰ ⁱ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ⁿ
subscript: ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₒ ₓ ₔ
Roots: √ ∛ ∜
Sets: ℕ ℤ ℚ ℝ ℂ
Constants: ℯ ℵ ⅇ ⅈ ⅉ ∅ ∞ ⧜ ⧝ ⧞
Basic binary operators: × ÷ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊜ ⊝ ⊞ ⊟ ⊠ ⊡ − ∕ ∗ ∘ ∙ ⋅ ⋆
Sets
element of: ∈ ∋ ∉ ∌ ⋶ ⋽ ⋲ ⋺ ⋳ ⋻
misc: ∊ ∍ ⋷ ⋾ ⋴ ⋼ ⋵ ⋸ ⋹ ⫙ ⟒
binary relation of sets: ⊂ ⊃ ⊆ ⊇ ⊈ ⊉ ⊊ ⊋ ⊄ ⊅ ⫅ ⫆ ⫋ ⫌ ⫃ ⫄ ⫇ ⫈ ⫉ ⫊ ⟃ ⟄ ⫏ ⫐ ⫑ ⫒ ⫓ ⫔ ⫕ ⫖ ⫗ ⫘ ⋐ ⋑ ⟈ ⟉
Union: ∪ ⩁ ⩂ ⩅ ⩌ ⩏ ⩐
Intersection: ∩ ⩀ ⩃ ⩄ ⩍ ⩎
Binary operator on sets: ∖ ⩆ ⩇ ⩈ ⩉ ⩊ ⩋ ⪽ ⪾ ⪿ ⫀ ⫁ ⫂ ⋒ ⋓
N-nary operator on sets: ⋂ ⋃ ⊌ ⊍ ⊎
Joins: ⨝ ⟕ ⟖ ⟗
Order
Precede and succeed: ≺ ≻ ≼ ≽ ≾ ≿ ⊀ ⊁ ⋞ ⋟ ⋠ ⋡ ⋨ ⋩ ⪯ ⪰ ⪱ ⪲ ⪳ ⪴ ⪵ ⪶ ⪷ ⪸ ⪹ ⪺ ⪻ ⪼
less and greater: ≮ ≯ ≤ ≥ ≰ ≱ ⪇ ⪈ ≦ ≧ ≨ ≩
less and greater 2: ⋜ ⋝ ⪙ ⪚ ≶ ≷ ≸ ≹ ⋚ ⋛ ⪋ ⪌ ⪑ ⪒ ⪓ ⪔
with approx: ⪅ ⪆ ⪉ ⪊
less and greater with equivalence: ≲ ≳ ⋦ ⋧ ≴ ≵
less and greater with similarity: ⪝ ⪞ ⪟ ⪠ ⪍ ⪎ ⪏ ⪐
less and greater slanted: ⩽ ⩾ ⫹ ⫺ ⪕ ⪖ ⪛ ⪜
less and greater misc: ⪣ ⪤ ⪥ ⪦ ⪧ ⪨ ⪩ ⪪ ⪫ ⪬ ⪭ ⪮ ⪡ ⪢ ⫷ ⫸ ⩹ ⩺ ⩻ ⩼ ≬ ≪ ≫ ⋘ ⋙
Order relation with dot: ⋖ ⋗ ⩿ ⪀ ⪗ ⪘ ⪁ ⪂ ⪃ ⪄
Equality, Identity, Equivalence, Approx, Congruence
equality: ≝ ≞ ≟ ≠ ∹ ≎ ≏ ≐ ≑ ≒ ≓ ≔ ≕ ≖ ≗ ≘ ≙ ≚ ≛ ≜ ⩬ ⩭ ⩮ ⩱ ⩲ ⩦ ⩴ ⩵ ⩶ ⩷
Identity: ≡ ≢ ⩧
Equivalence: ≍ ≭ ≣ ⩸
Approx equality: ≁ ≂ ≃ ≄ ⋍ ≅ ≆ ≇ ≈ ≉ ≊ ≋ ≌ ⩯ ⩰
Misc equality: ∻
Misc relations: ⊏ ⊐ ⊑ ⊒ ⊓ ⊔ ⋢ ⋣ ⋤ ⋥ ⊲ ⊳ ⊴ ⊵ ⋪ ⋫ ⋬ ⋭ ⫴ ⫵
Logic
Logic: ¬ ⫬ ⫭ ⊨ ⊭ ∀ ∁ ∃ ∄ ∴ ∵ ⊦ ⊬ ⊧ ⊩ ⊮ ⊫ ⊯ ⊪ ⊰ ⊱
Logic binary: ∧ ∨ ⊻ ⊼ ⊽ ⋎ ⋏ ⟑ ⟇ ⩑ ⩒ ⩓ ⩔ ⩕ ⩖ ⩗ ⩘ ⩙ ⩚ ⩛ ⩜ ⩝ ⩞ ⩟ ⩠ ⩢ ⩣ ⨇ ⨈
Logic n-nary: ⋀ ⋁
n-nary operators: ∑ ⨀ ⨁ ⨂ ⨃ ⨄ ⨅ ⨆ ∏ ∐ ∔
Geometry
Geometry: ∣ ∤ ⫮ ⌅ ⌆ ℓ ⫛
Ratio and proportion: ∝ ∶ ∷ ∺
Parallel and perpendicular: ∥ ∦ ⫲ ⫳ ⋕ ⟂ ⫡
Right angle: ∟ ⊾ ⦜ ⦝ ⊿
Angles: ∠ ∡ ⦛ ⦞ ⦟ ⦢ ⦣ ⦤ ⦥ ⦦ ⦧ ⦨ ⦩ ⦪ ⦫ ⦬ ⦭ ⦮ ⦯ ⦓ ⦔ ⦕ ⦖ ⟀
Spherical angle: ∢ ⦠ ⦡
...
Pairs: ⌈ ⌉ ⌊ ⌋ ⦋ ⦌ ⟦ ⟧ ⦍ ⦎ ⦏ ⦐
pairs 2: ⟮ ⟯ ⟨ ⟩ ⟪ ⟫ ⦃ ⦄ ⦅ ⦆ ⦇ ⦈ ⦉ ⦊ ⟬ ⟭ ⦗ ⦘ ⦑ ⦒ ⧼ ⧽
integrals: ∫ ∬ ∭ ∮ ∯ ∰ ∱ ∲ ∳ ⨋ ⨌ ⨍ ⨎ ⨏ ⨐ ⨑ ⨒ ⨓ ⨔ ⨕ ⨖ ⨗ ⨘ ⨙ ⨚ ⨛ ⨜
Derivative: ∂ ′ ″ ‴ ∆
vector: ⨯ ∇ ⊹
Misc indicators: ∎ ± ∓ ⋮ ⋯ ⋰ ⋱
Misc symbols: ∿
Tacks: ⊣ ⊢ ⊥ ⊤ ⟘ ⟙ ⟛ ⟝ ⟞ ⟟ ⫧ ⫨ ⫩ ⫪ ⫫ ⫞ ⫟ ⫠
Turnstiles: ⫢ ⫣ ⫤ ⫥ ⟚
Z notation: ⦁ ⦂ ⩤ ⩥ ⨟ ⨠ ⨡ ⨾
Tilde Operators: ∼ ∽ ⩪ ⩫ ⩳
Misc Operators: ⋄ ⫶ ⫼ ⫾
Misc products: ≀ ⨿ ⨼ ⨽ ⧢ ⋉ ⋊ ⋋ ⋌
Plus variations: ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨭ ⨮
Solidus: ⫻ ⫽
minus sign variations: ∸ ⨩ ⨪ ⨫ ⨬
maps: ⊶ ⊷ ⊸ ⟜ ⧟

Introduction

From wikipedia:

"Heuristic (pronounced /hjʉˈrɪstɨk/, from the Greek "Εὑρίσκω" for "find" or "discover")

A heuristic method is used to come to a solution rapidly that is hoped to be close to the best possible answer, or 'optimal solution'.

A heuristic is a "rule of thumb", an educated guess, an intuitive judgment or simply common sense. A heuristic is a general way of solving a problem"

The purpose of this blog is to provide brief heuristics to help me (and perhaps others) understand topics in econometrics and quantitative methods more concretely.

In graduate school, I completed several courses in statistics and quantitative methods including econometrics, mathematical statistics, experimental design, mathematical economics, biometrics, and statistics based courses in population genetics and plant breeding (my interest in graduate school focused on the environmental and economic ramifications of agricultural biotechnology). In my current employment, I'm constantly learning and applying new data mining algorithms and statistical techniques.

This blog is one way for me to quickly summarize and catalog the key elements of the techniques that I have used in the past, as well as new ones I encounter. While many of these concepts may transcend the range of topics normally thought of as 'econometrics,' most economists would find some of them very useful in their work. As a heuristic guide, some details may be compromised from time to time to illustrate essential themes. (just as with models from economics, sometimes it is necessary to abstract from ancillary details to better elucidate core concepts).

I often make use of R code to illustrate many topics I find interesting in data mining and applied econometrics. I often find that coding allows me to get my hands dirty and forces me to understand with much more precision and greater detail exactly what's going on under the hood with regard to many statistical techniques and algorithms. 

I follow a 'recipe' for blogging very similar to stats blogger Jeremy Kun:

1) Identify a topic that sounds fascinating or something that I would like to master in greater detail

Or

Encounter a problem on the job that requires greater knowledge or detail of some technique I've never used or one that I'm familiar with but never applied professionally, or a topic that I would like to adopt for a classroom application in one of the courses I teach.

2) Research the literature related to the technique (often including journals such as the Journal of Applied Econometrics, Review of Economics and Statistics, Econometrica, The American Statistician, Journal of Applied Statistics, as well as numerous blogs and websites related to data mining and statistical programming)   

4) Write a blog post that provides the theoretical background related to the topic of use and demonstrates its application in a simple way.

5) Update the post with related links and concepts, or new insights that I develop as I become more familiar with or apply the technique professionally.