3/29/2017

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Today’s schedule

• 8:15 to 9:30 am, catch‐up

• 9:30 am nuts and bolts

• 9:30 to 10:30 am, lab 3 details

• 10:30 to 11:30, projects

Information for final hwk #4 problem

Retribution

Predictors t value

Control ‐.05 <1

Responsibility .17 2.07*

Anger .30 4.04***

Sympathy ‐.30 ‐3.68***

Stability ‐.01 <1

Expectancy ‐.10 ‐1.33

R2 .27

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Hypothesis testing…

H0: β1 = 0 (no linear relationship)H1: β1 0 (linear relationship does exist)

)ˆ.(.

0ˆ

es

Tn-2=

What predicts SSU students’ interest in leaving? 

Predictors B SE β R2 Adj.

R2

Constant 2.16 .15 ‐

Experience discrimination ‐.01 .01 ‐.02

Observe discrimination .01 .01 .04

Faculty climate ‐.61* .06 ‐.36* 13.5% 13.2%

Note. N=837. * p<.0001

Predicted interest = 2.16 +‐(.01) (experience discrimination) + (.01) (observe discrimination + (‐.61) (faculty climate) + error

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Controversies

• Controversy about how to judge the relative importance of each predictor variable in predicting the dependent variable

• As add or subtract variables, weights change

• Consider both the r’s and the β’s• Experience discrimination and interest in

leaving• r(838)=.19, p<.001• =-.01, ns

Functions of multivariate analysis:• Control for confounders (third variables, spurious correlations)

• Improve predictions

• Test mediation (why?) or moderation (when?) hypotheses

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Multivariate regression pitfalls

1. Multi‐collinearity

2. Residual confounding

3. Overfitting

1. Multicollinearity 

Multicollinearity arises when two variables that measure the same thing or similar things (e.g., weight and BMI) are both included in a multiple regression model; they can cancel each other out and destroy your model. 

Center predictors if include interactions in regression equation (reduces correlations between interactions and predictors)

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2. Residual confounding

• You cannot completely wipe out confounding simply by adjusting for variables in multiple regression unless variables are measured with zero error (which is usually impossible).

• Example: meat eating and mortality

Men who eat a lot of meat are unhealthier for many reasons!

Sinha R, Cross AJ, Graubard BI, Leitzmann MF, Schatzkin A. Meat intake and mortality: a prospective study of over half a millionpeople. Arch Intern Med 2009;169:562-71

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3. Overfitting

• In multivariate modeling, you can get highly significant but meaningless results if you put too many predictors in the model.

• The model is fit perfectly to the quirks of your particular sample, but has no predictive ability in a new sample.  

• Importance of theory (!) and replication

Basic Research

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The Mediational Model – why or how? 

Why the Interest in Mediation?

• Enables us to answer hypotheses of “how” and “why”

• Understand the mechanism

• theoretical concerns

• cost and efficiency concerns

• Find more proximal endpoints for interventions

• Understand why the intervention did not work

• finding the missing link 

• compensatory processes (suppressor effects)

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An example

ObserveDiscrimination

Want to leave SSU

Poor faculty climate

c (c1)

ab

Four Step Approach

• Step 1: X  Y (test path c)

• Step 2: X M (test path a)

• Step 3: M (and X) Y (test path b)

• Step 4: X (and M)  Y (test path c′)

Note that Steps 3 and 4 use the same regression equation.

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Total and Partial Mediation

• Total Mediation

•Meet steps 1, 2, and 3 and find that c′ equal zero

• Partial Mediation

•Meet steps 1, 2, and 3 and find that c′ is smaller in absolute value than c

(New School)

Shift focus to whether indirect effect is statistically reliable (or different from zero)

Decomposition of EffectsTotal Effect = Direct Effect + Indirect Effect

c = c′ + ab

The Indirect Effect or ab provides one number that summarizes the amount of mediation. 

Note that 

ab = c ‐ c′

That is, the indirect effect exactly equals the amount of the reduction in the total effect (c) after the mediator is introduced.

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Strategies to Test ab = 0•Sobel test•Bootstrapping

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Bootstrapping• “Nonparametric” way of computing a sampling distribution.

• Re‐sampling (with replacement)

• Many trials (computationally intensive)

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Results of Bootstrapping95% Percentile Confidence Interval:

Lower     Upper.5325       5.0341

(Done using the Hayes & Preacher macro from http://www.afhayes.com/spss‐sas‐and‐mplus‐macros‐and‐code.html.)

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BOOTSTRAP RESULTS FOR INDIRECT EFFECTS

Indirect Effects of IV on DV through Proposed Mediators (ab paths)Data Boot Bias SE

TOTAL .0044 .0044 .0000 .0014full_fac .0044 .0044 .0000 .0014

Bias Corrected and Accelerated Confidence IntervalsLower Upper

TOTAL .0016 .0075full_fac .0016 .0075

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Level of Confidence for Confidence Intervals:95

Number of Bootstrap Resamples:1000

The indirect effect from discrimination observations via perceptions of university climate to interest in leaving the university was statistically reliable (standardized indirect effect = ‐.004, 95% CI from ‐.002 to .007).