1. Psychology 202b Advanced Psychological Statistics, II February 3, 2011

2. Overview Multivariate data simulation Added variable plots (review) Partial correlation The problem of collinearity Regression diagnostics: –Review of assumption checking –Outliers –Influence and leverage

3. What does “control” mean? Controlling or holding constant Partial relationships and the added variable plot

4. Collinearity The problem of collinearity Formal definition: –Two predictors X 1 and X 2 are collinear if there exist constants c 1, c 2, and c 0 such that c 1 X 1 + c 2 X 2 = c 0. –More generally, a set of k predictors is collinear if c 1 X 1 + c 2 X 2 + … + c k X k = c 0. Collinearity is not synonymous with correlation among the predictors.

5. Why is collinearity a problem? Hocking and Pendelton’s picket fence. Implication: when a set of predictors is approximately collinear, estimation becomes unstable and standard errors become large.

6. Diagnosing collinearity Correlations may be diagnostic if the data are multivariate normal. The condition number: An alternative form removes column means from X. Other options eliminate the intercept column or use a correlation metric.