8. Interactions: Categorical*Categorical Flashcards
What is a categorical*categorical interaction?
A difference in differences between groups across levels of a second factor
When visualising a categorical*categorical interaction, what does it mean if lines are parallel?
There is no interaction
When visualising a categorical*categorical interaction, what does it mean if lines are not parallel but not crossing?
Ordinal interaction
When visualising a categorical*categorical interaction, what does it mean if lines are not parallel but are crossing?
Disordinal interaction
What is the value of beta 0 in a categorical*categorical interaction?
Value of y when x + z are 0
What is the value of beta 1 in a 2x2 categorical interaction?
Difference between x and z =0
What is the value of beta 2 in a 2x2 categorical interaction?
Difference between levels of z when x = 0
What is the value of beta 3 in a 2x2 categorical interaction?
Difference between x across levels of z
How do you visualise categorical*categorical interactions?
Via cat plot
What do we do if there are more 2x2 variables?
Need additional interaction terms
In the hospital example, a 3 x 2 interaction, what was the model and how were the coefficients interpreted?
yijk = b0 + b1D1 + b2D2 + b3D3 + b4D13 + B5D23
b0 = mean of treatment a in hospital 1
b1 = Difference between TA and TB in H1
b2 = Difference between TA and TC in H1
b3 = Difference of TA in hosp 1 and 2
b4 = Difference between TA and TB in H1 and H2
b5 = Difference between TA and TC in H1 and H2
What is the rule on number of interaction terms?
(r-1) * (c - 1)
Row = Number of levels in first categorical variable
Column = Number of levels in second categorical variable
Why are three way interactions not as common?
Requires a lot of data to interpret as effects are often small
Extends issue of power
Only test if strong and theoretical reason to
