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Understanding Causation: Definitions and Statistical Models

wynter-fitzgerald avatar
wynter-fitzgerald
6 diapositives · 253 Views · Nov 29, 2014

This document explores the concept of causation through an analytical framework. It begins with a thorough definition of causation, highlighting its four critical characteristics: co-variation, a valid time frame, non-spuriousness, and theoretical grounding. It then delves into the statistical elaboration model which involves elimination and specification of spurious relationships. The document presents both non-quantitative and quantitative statistical examples, guiding the reader step-by-step through the processes of constructing cross-tabulation tables, calculating measures of association, and drawing conclusions from correlations.

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  1. Cause (Part I) - Elaboration Topics I. The Definition of Causation II. The Statistical Elaboration Model III. Non-quantitative Statistical Example IV. Quantitative Statistical Example

  2. Cause (Part I) - Elaboration I. The Definition of Causation - Four Characteristics A. Co-variation B. Over a valid time frame C. Of a non-spuriousnature D. That is grounded in theory

  3. Cause (Part I) - Elaboration II. The Statistical Elaboration Model A. Elimination B. Specification Spuriousness X e.g. the effectof fire size (Z) on the relationship between # of firemen (X) and damage (Y) 1. Antecedent Z Y 2. Intervening X Y e.g. the effectof education (Z) on the relationship between age (X) and income (Y) Z

  4. Cause (Part I) - Elaboration III. Non-quantitative Statistical Example Step 1 – Construct the zero order cross-tabulation table. The Marginal (Zero-Order) Table Step 2 – Calculate the zero order measure of association. e.g. Lambda = 40/40 – 30/40 = .25 or Phi = (25-20)2/20 + (15-20)2/20 + (15-20)2/20 + (25-20)2/20 = square root of 5/80 = .25

  5. Cause (Part I) - Elaboration Step 3 – Construct the first order partial tables. The Marginal Table Partial Table for Young Partial Table for Old = + Step 4 – Calculate the partial measures of association Total Young Old Lambda .25 .00 1.00 Step 5 – Form the conclusion Since the partials have changed from the marginal measure, one getting stronger and the other disappearing, we would say that we have specified the zero order relationship as probably intervening (i.e. we are born into a sex, grow older and as a result, join a political party).

  6. .55 – (.6) (.4) Cause (Part I) - Elaboration IV. Quantitative Statistical Example Step 1 – Construct the zero order Pearson’s correlations (r). Assume rxy= .55 where x = divorce rates and y = suicide rates. Further, assume that unemployment rates (z) is our control variable and that rxz = .60 and ryz= .40 Step 2 – Calculate the partial correlation (rxy.z) = = .42 Therefore, Z accounts for (.30-.18) or 12% of Y and (.12/.30) or 40% of the relationship between X&Y Before z (rxy)2 = .30 Step 3 – Draw conclusions After z (rxy.z)2 = .18