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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

• 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

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.

• 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?

• 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…

• Run a cross-tab or a correlation between new variable and the independent variable.

• Is there a relationship?

• Is new variable affecting the IV, the DV, and/or the relationship between the DV and the IV.

• Spurious?

• Specification?

• Antecedent?

• 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

• 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.

• 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.

• 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.

• 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.

• 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 term = Z * X

• Example, if X = Education, Z = Female (1)

• IVs:

• X (weak / insignificant)

• Z (insignificant)

• Z * X (strong, significant)

• 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

• 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)

• 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!

• 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.

• “Direct” effect = effect of X1 is when X2 is zero and vice versa.

• 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.

• 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.

• 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…

• 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

• 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.