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University of Toronto Mississauga
John Kervin

SOC 222 -- MEASURING the SOCIAL WORLD Session #12 -- NESTED REGRESSION CONTEXT of TODAY’S SESSION • “Statistics and Data Analysis” What is Data Analysis? Statistics is about two questions: 1. Is there a relationship 2. Does that relationship also exist in the population • Art of finding true relationships and true causes (something you can do with) o Looking at causal processes, ruling out alternative explanations 1. causal processes 2. alternative explanations • controlling statistically Today’s Objectives: Know… 1. How statistical control is achieved 2. The difference between experimental and statistical control 3. How to build successive regression models 4. The different kinds of effects when a third variable is added Terms to Know causal process alternative explanation statistical control causal diagram Venn diagram independent effects spurious effects indirect effects interaction effects experimental control statistical control unique effect CAUSAL PROCESSES add a second independent variable, T • Like X, it (T) is a potential cause • Check covariance, and then check for effect size and significance Causal Diagrams and Venn Diagrams Causal Diagrams • Use arrows to show the causal connections among variables • Simplest causal diagram is X Y • Time is part of it, and it goes from left to right • Time is one of the three requirements, so say something causes something else (has to come before) • The causal diagram is a short way to say two things: 1. Variation in x is associated with variation in y (vary together in some systematic way) 2. X comes before y Venn Diagrams Each circle represents the variation in a variable Venn diagram do not indicate causal ordering • Indicate co-variation by overlapping or not overlapping (don’t show systematic change) No covariation (no relationship): X Y Covariation (a relationship): X Y Covariation (a strong relationship) X Y ADDING a SECOND IV: “T” • Hardly throw in another dependent variable, restrict it to 1 dependent variable 1. Independent effects X Y T X Y T • X and T both covary with (affect) Y • Each has a direct effect on Y • They are independent of one another • Regression check: • The bivariate results for X don’t change when T is added to the regression as a second IV 2. Spurious effect T Y X T X Y • T affects (covaries with) both X and Y • Thus both X and Y will vary together, as a result of changes in T • As T increases, both X and Y increase • This makes it seem that X and y are directly related when they aren’t • Thus the X-Y relationship is spurious (third variable that is causing both X & Y ) • Regression check: controlling for T, removes X-Y relationship • T precedes X in time • When T is added to the regression, the bivariate results for X-Y disappear • Controlling for T removes the X-Y relationship 3. Indirect effect; seems X-Y directly related, when they are not (indirectly causes Y) X Y T T X Y • X affects T • T, in turn, affects Y • Thus Y will vary when X varies • This makes it seem that X and Y are directly related when they aren’t • Thus the X-Y relationship is indirect • X does cause Y, but indirectly, through T • Regression check: • X precedes T in time • When T is added to the regression, the bivariate results for X-Y disappear (because we are controlling the T in the middle) • Note: • This is similar to the spurious effect • Only difference: • Spurious effect: T comes before X • Indirect effect: T comes after X 4. Interaction effect: T affects the relationship between X & Y (X-Y depends on T) X Y T T 1 X Y T 2 X Y • The X-Y relationship changes • Depending on the value of T (usually category variable) • T is usually a category variable (e.g., sex, religion) • Regression check: separate regression for each category for T (ex, each religious group) and then see the X-Y relationship • Run separate regressions for each category of T • The bivariate X-Y relationship varies as T changes • Note: • T does not have to covary with either X or Y • All it has to do is just changes the X-Y relationship Practice Suggestion • Practice with the Student data set REGRESSION and CONTROLLING (don’t all
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