Interactions
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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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