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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. Added variables. Learned to do multivariate regression analyses. Learned to interpret coefficients when controlling for all other variables.

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interactions

Interactions

POL 242

Renan Levine

March 13/15, 2007

recap
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.
  • Today: What if relationship between one IV (X) and the DV (Y) is different at different levels of another variable?
start with a basic bivariate relationship
Start with a basic bivariate relationship

X

Y

Question:

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

focus on the relationship

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
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
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
Step 2
  • Run a cross-tab or a correlation between new variable and the independent variable.
  • Is there a relationship?
evaluate
Evaluate
  • Is new variable affecting the IV, the DV, and/or the relationship between the DV and the IV.
    • Spurious?
    • Specification?
    • Antecedent?
  • Reference your qualitative research!
possible outcome i
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
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
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
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
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
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
  • Interaction term = Z * X
  • Example, if X = Education, Z = Female (1)
    • IVs:
      • X (weak / insignificant)
      • Z (insignificant)
      • Z * X (strong, significant)
possible outcomes v
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
interaction1
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
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
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
Tricky interpretation
  • “Direct” effect = effect of X1 is when X2 is zero and vice versa.
example gender language
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
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
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
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
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.
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