Interactions

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# Interactions - PowerPoint PPT Presentation

Interactions. POL 242 Renan Levine March 13/15, 2007. Recap. Learned how to do bivariate analyses Cross-tabs, measures of association, correlations. Added variables. Learned to do multivariate regression analyses. Learned to interpret coefficients when controlling for all other variables.

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### Interactions

POL 242

Renan Levine

March 13/15, 2007

Recap
• Learned how to do bivariate analyses
• Cross-tabs, measures of association, correlations.
• Learned to do multivariate regression analyses.
• Learned to interpret coefficients when controlling for all other variables.
• Today: What if relationship between one IV (X) and the DV (Y) is different at different levels of another variable?

X

Y

Question:

Will this relationship be the same at all levels of Z???

X

X

Y

Y

Focus on the relationship

When Z = α

Can be positive or negative.

Can be strong, weak or have no effect.

?

When Z = β

NOT what is the effect of Z on Y.

See Pollock p. 86 for a complete set of possible interactions.

Step 1
• Go back to contingency tables or correlations.
• Recode variables if necessary (reduce number of categories).
• Run a different cross-tab (or correlation) for each value of Z
• Look to see if relationship changes.
• Are the measures of association different?
Focus is on X & Y
• The question is:
• Did the relationship between X and Y change at different levels of Z?
• Did the relationship get weaker? stronger?
• Did the sign change or stay the same?
• Focus on the relationship between X & Y
• Not on how Z affects Y until Step 2…
Step 2
• Run a cross-tab or a correlation between new variable and the independent variable.
• Is there a relationship?
Evaluate
• Is new variable affecting the IV, the DV, and/or the relationship between the DV and the IV.
• Spurious?
• Specification?
• Antecedent?
Possible Outcome - I
• Relationship between independent and dependent variables remains unchanged &
• New variable is not related to dependent variable.
• What to do: Eliminate new variable from further analysis UNLESS you anticipate that people will expect this variable to be included and you need to demonstrate it has no effect.
• You can have IVs that are control variables and have no hypothesized effect on the DV
Possible Outcome - IIA
• Relationship between independent and dependent variables remains unchanged BUT
• New variable is related to dependent variable.
• What to do: Consider adding new variable to regression.
Possible Outcomes IIB
• Relationship between independent variable and dependent variable is slightly changed and remains consistent across categories of control.
• Both IV and the 3rd variable are related to DV.
• What to do: Consider including IV and 3rd variable in future analyses.
• Might consider running separate regressions for each category of 3rd variable if you are very interested in that relationship.
• Probably no reason to do anything special.
Possible Outcomes - III
• When you add a third variable…
• Relationship between independent and dependent variables virtually disappears.
• Independent variable is not related to dependent variable OR
• There is a sequence: independent variable affects third variable which affects DV.
• Recall example: Race, income and the vote in the US
• New variable replaces IV in the regression.
Possible Outcomes IV
• Relationship between independent and dependent variables changes (Specification) BUT
• New variable is not related to dependent variable.
• What to do:
• Run separate regressions for each level of new variable (only works when new variable has few categories – like Francophobes/Anglophones).
• Add new variables to regression and create interaction term between new variable and IV.
Specification
• Z specifies relationship of x and y.
• Example: when z=1, x has a strong, positive relationship with y, but when z=0, x has a weak, negative relationship with y.’
Interaction
• Interaction term = Z * X
• Example, if X = Education, Z = Female (1)
• IVs:
• X (weak / insignificant)
• Z (insignificant)
• Z * X (strong, significant)
Possible Outcomes V
• Relationship between independent and dependent variables changes “markedly” like when relationship between IV and DV changes sign across categories of control variable.
• The relationship is interactive; the control variable specifies the relationship between DV and IV.
• What to do:
• Include IV & new variable in all future analyses.
• Add variable and interaction term
Interaction
• Treat Z as another independent variable, X2.
• X1 and X2 do not have an additive effect on Y. Form is not Y=a+bX1+bX2
• Relationship is interactive. Y=a+bX1+bX2+b(X1*X2)
Interaction Terms
• Example:
• X1= Attitude towards abortion
• Y= Opinion towards feminists
• X2= Political Knowledge
• In the U.S., those with high levels of knowledge equate feminism and feminists with pro-choice stances. Relationship is much weaker at low levels of political knowledge.
• So, we need to interact political knowledge with attitudes towards abortion to best explain attitudes towards
• OpinionFeminists=AttitudeAbortion+PolKnowledge+PolKnowledge*AttitudeAbortion
• Note: you always include the “direct” effect of both interaction terms in equation too!
Problems and Opportunities
• You can interact more than two variables.
• Interaction can be Interval/Ordinal*Interval/Ordinal OR Interval/Ordinal*Dummy OR Dummy*Dummy
• But every time you run an interaction, you risk multicollinearity since the interaction term is necessarily related to direct effects of the variables that are interacting.
Tricky interpretation
• “Direct” effect = effect of X1 is when X2 is zero and vice versa.
Example – Gender & Language
• Three dummy variables:
• Gender (1=Women, 0=Men)
• Language (1=French, 0=English)
• Gender*Language (Interaction)
• Interpret direct effect of Gender as effect of English speaking women compared to English speaking men.
• Since 0=English and 0=Men, reference category is always English speaking men.
• Interpret direct effect of Language as effect of French speaking men compared to English speaking men.
• Interaction is understood as effect of French speaking women compared to English speaking men.
Example – Age & Religiosity
• Three variables:
• Age (ordinal, young->old recoded into cohort groups)
• Religiosity (ordinal, high=regular church-goer)
• Gender*Language (Interaction)
• Interpret direct effect of Age as effect of increasing age for non-religious people.
• Reference category is always non-religious young.
• Interpret direct effect of Religiosity as effect of religion on youngest group.
• Interaction is understood as effect of increasing both Age and Religiosity, in other words, what is effect of older, religious people compared to non-religious young.
Another possible option
• When one variable is dichotomous it is often easier to just run separate regressions for each category of the control variable.
• So, one regression for francophones, and one for anglophones. Or one for men, and one for women…
To – Do:
• Lab 7 – but can also be done with correlations (for interval level data or ordinal data with many categories)
• Foundation for worksheet
• Lab 9B – Interactions
• Put an interaction variable in the equation OR
• Run multiple regressions on different parts of the data
Announcements
• Turnitin.com; 2653464 Pwd = Tables
• Thursday: 2653473, Pwd = spring
• Quiz results
• Next week may be a little different than what is on the syllabus
• Encouraged to speak to me and the TAs about papers OR whether you are best off taking the test.