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Items to consider - 3  Multicollinearity  The relationship between IV’s…when IV’s are highly correlated with one another  What to do:  Examine the.

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Presentation on theme: "Items to consider - 3  Multicollinearity  The relationship between IV’s…when IV’s are highly correlated with one another  What to do:  Examine the."— Presentation transcript:

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2 Items to consider - 3  Multicollinearity  The relationship between IV’s…when IV’s are highly correlated with one another  What to do:  Examine the correlation matrix of all IV’s & DV to detect any multicollinearity  Look for r’s between IV’s in excess of 0.70  If detected, it is generally best (or at least most simple) to re-run MLR and eliminate one of the offending IV’s from the model (see model reduction, later) 2 3 1

3 Multicollinearity – what is it?  It’s to do with unique and shared variance of the IV’s with the predictor & themselves  Must establish what unique variance on each predictor (IV) is related to variance on criterion (DV)  Example 1 (graphical):  y – freshman college GPA  predictor 1 – high school GPA  predictor 2 – SAT total score  predictor 3 – attitude toward education 1

4 Multicollinearity – what is it? x1x1 x2x2 y Common variance in y that both predictors 1 and 2 account for variance in y accounted for by predictor 2 after the effect of predictor 1 has been partialled out Circle = variance for a variable; overlap = shared variance (only 2 predictors shown here)

5 Multicollinearity – what is it? x1x1 x2x2 y Circle = variance for a variable; overlap = shared variance (only 2 predictors shown here) Total R 2 =.66 or 66%

6 Multicollinearity – what is it? x1x1 x2x2 y Circle = variance for a variable; overlap = shared variance (only 2 predictors shown here) Total R 2 =.33 or 33% 4

7 Multicollinearity – what is it?  Example 2 (words):  y – freshman college GPA  predictor 1 – high school GPA  predictor 2 – SAT total score  predictor 3 – attitude toward education

8 Multicollinearity – what is it? = variance in college GPA predictable from variance in high school GPA = residual variance in SAT related to variance in college GPA = residual variance in attitude related to variance in college GPA 1

9 Multicollinearity – what is it?  Consider these: X1X2X3 Y X1.5.4 X2.6 X1X2X3 Y X1.2.3 X2.2 X1X2X3 Y.6.7 X1.7.6 X2.8 ACB Which would we expect to have the largest overall R 2, and which would we expect to have the smallest? 1

10 Multicollinearity – what is it?  R 2 will be at least.7 for B & C, but only at least.3 for A  No chance of R 2 for A getting much larger, because intercorrelations of X’s are as large for A as for B & C X1X2X3 Y X1.5.4 X2.6 X1X2X3 Y X1.2.3 X2.2 X1X2X3 Y.6.7 X1.7.6 X2.8 ACB 1 2

11 Multicollinearity – what is it?  R will probably be largest for B  Predictors are correlated with Y  Not much redundancy among predictors  R probably greater in B than C, as C has considerable redundancy in predictors X1X2X3 Y X1.5.4 X2.6 X1X2X3 Y X1.2.3 X2.2 X1X2X3 Y.6.7 X1.7.6 X2.8 ACB 1 2

12 What effect does the big M have?  Can increase SE E of regression coefficients (those with the multicollinearity)  This can lead to insignificant findings for those coefficients  So predictors that may be significant when used in isolation may not be significant when used together  Can also lead to imprecision among regression coefficients (mistakes in estimating the change in Y for a unit change in the IV)  So a model with multicollinearity is misleading, & can have redundancy among the predictors

13 What do we do about the big M?  Many opinions  E.g. O‘Brien (2007) A Caution Regarding Rules of Thumb for Variance Inflation Factors. Quality & Quantity, 41, 5,  Can use “VIF” (variance inflation factor) and “tolerance” values in SPSS (“problem” variables are those with “VIF” < 4)  Can painstakingly examine all possible versions of the model (putting each predictor in 1 st )  We’ll just signal multicollinearity with a r >.70, and enforce removal of at least one of the variables,  and signal possible multicollinearity with a r of between.5 and.7, and suggest examination of the model with and without one of the variables. 1 2

14 The Goal of MLR  The big picture…  What we’re trying to do is create a model predicting a DV that explains as much of the variance in that DV as possible, while at the same time:  Meet the assumptions of MLR  Best manage the other issues – sample size, n of predictors, outliers, multicollinearity, r with dependent variable, significance in model  Be parsimonious (can be very important) 1 2


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