13_Interaction_ANSWERS
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University of Pittsburgh *
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0036
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Medicine
Date
Dec 6, 2023
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docx
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Uploaded by MateComputerTapir16
1
Linear Regression – Interactions
In this homework you will be learning about interactions. The data is fake, not from the GSS.
There are two sets of variables.
Set 1:
IV1: HrsTherapy1 – Number of Hours of Therapy per Month
IV2: Medicine1 – Whether someone is receiving an antidepressant (1) or not (0)
DV: Mood1 – higher is a better mood
Set 2:
IV1: HrsTherapy2 – Number of Hours of Therapy per Month
IV2: Medicine2 – How much antidepressant someone is receiving from 0 to 4 mg
DV: Mood2 – higher is a better mood
All of the variables should be set at continuous, except Medicine1 which is binary.
First, run the linear regression Mood1~ HrsTherapy1 + Medicine1
Based on the regression results, do you think that therapy is helpful?
It has a significant positive influence
**See Estimate 4.22 which is significant in the table
It has no significant influence
It has a significant negative influence
Based on the regression results, do you think that the medicine is helpful?
It has a significant positive influence
**See Estimate 22.27 which is significant in table
It has no significant influence
It has a significant negative influence
2
Now, you are going to test for an interaction. Before doing so, it would be nice to visualize the
data and see if there is any evidence of an interaction.
To do this, click on the + Modules button at the top right of jamovi -> jamovi library ->Flexplot
and install flexplot. Once you have done this, there should be an icon called Flexplot under
Analyses next to Factor.
Click on Flexolot, and add Mood1 (continuous) as the Outcome Variable and HrsTherapy
(continuous) and Medicine1 (Nominal) as Predictor variables. For the Fitted Line, select
Regression.
From looking at the figure, do you think that there is an effect of HrsTherapy1 on Mood 1 within
the no medicine (0) group?
Positive influence of HrsTherapy1 on Mood1 within the no medicine (0) group
***In the
figure above, the slope for the red line is positive. You might not be entirely sure if it is
significant from looking at it.
No influence of HrsTherapy1 on Mood1 within the no medicine (0) group
3
Negative influence of HrsTherapy1 on Mood1 within the no medicine (0) group
From looking at the figure, do you think that there is a difference in slopes for the no medicine
(0) group vs. the medicine (1) group? A difference of slopes would show up in the regression in
the interaction term.
Medicine group has more positive slope than no medicine
** In the figure above, the
slope for the green line (Medicine) is more positive than the slope for the red (no
medicine) group.
No difference
Medicine group has a more negative slope than no medicine
From looking at the figure, do you think that the Medicine group has better or worse mood than
the no-medicine group
when HrsTherapy1 is zero.
Stated another way, when someone does
not receive any therapy, do you think that the medicine makes a difference? (This will also
appear as the Medicine1 line in the regression.)
Medicine group has more positive mood when HrsTherapy1 = 0
No difference
** In reality, there is not a significant difference. See in the figure below
where I made the red circle. At this point, the lines for the two groups are overlapping –
that is what the grey ‘confidence band’ around the lines mean. You can see that the two
lines actually cross near 1, and near 0 they are still largely overlapping.
Medicine group has more negative mood when HrsTherapy1 = 0
Now, run a regression to test for an interaction. Run the linear regression Mood1~ HrsTherapy1
+ Medicine1 + HrsTherapy1*Medicine1
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4
Note, sometimes this is also abbreviated as Mood1~ HrsTherapy1*Medicine1
The way to run this model is, after entering Mood1 as the DV, and HrsTherapy1 and Medicine1
as Covariates, click on Model Builder, and then click on both HrsTherapy1 and Medicine1 while
holding down shift, and then move them both into Block 1. So it should appear as
HrsTherapy1*Medicine1.
When you run the regression there should be 4 rows: Intercept, HrsTherapy1, Medicine1,
HrsTherapy1*Medicine1.
Is the HrsTherapy1 regression term significantly positive or negative? Note, this row tests
whether HrsTherapy1 is significant for the no medicine (Medicine1 = 0) group.
Positive influence of HrsTherapy1 on Mood1 within the no medicine (0) group
**See
estimate 1.55 which is significant
No influence of HrsTherapy1 on Mood1 within the no medicine (0) group
Negative influence of HrsTherapy1 on Mood1 within the no medicine (0) group
Is there a significant interaction? Note, if this is positive, it means that the slope of HrsTherapy1
is more positive for the Medicine (1) group than the no-medicine (0) group.
Medicine group has more positive slope than no medicine
**see estimate of 6.04 which
is positive and significant
No difference
Medicine group has a more negative slope than no medicine
Is the Medicine1 regression term significant? This tests whether more medicine is associated
with better mood
when HrsTherapy1 is zero.
Stated another way, when someone does not
receive any therapy, does the medicine makes a difference?
Medicine group has more positive mood when HrsTherapy1 = 0
No difference
**see estimate -5.88 which is not
significant. This corresponds again to
the red circle in the figure above.
Medicine group has more negative mood when HrsTherapy1 = 0
5
Here is a summary of key points about interactions in regressions:
First, if you don’t test for an interaction, like in the first regression that you ran, you would not
know if there are or aren’t different slopes.
Second, when you test for an interaction, the slope for the main IV (HrsTherapy1) in the
regression is the slope when the other variable (Medicine1) is zero.
Third, the interaction term is the difference in slopes between the Medicine vs. no medicine
group.
Fourth, something to remember about regressions is that you can use the regression outputs to
predict the DV for a new person.
In this regression, the estimates were:
Intercept: 16.94
HrsTherapy1: 1.55
Medicine1: -5.88
HrsTherapy1*Medicine1: 6.04
So the regression equation is:
Mood1 = 16.94 + 1.55 (Number hours of therapy per month) + 5.88 (1 if they got the
medicine, 0 if not) + 6.04 (Number hours of therapy per month)(1 if they got the medicine, 0
if not)
So, if someone did 5 hours of therapy per month and didn’t get the medicine, we would
predict that their mood would be:
16.94 + 1.55(5) - 5.88(0) + 6.04(5)(0) =
24.69
See how this falls right on the red line, cool!
And, if someone did 4 hours of therapy per month and did get the medicine, we would
predict that their mood would be:
16.94 + 1.55(5) - 5.88(1) + 6.04(5)(1) =
49.01
See how this falls right on the teal line. Cool! Always good to verify that things are working
multiple ways!
So far in class we have mainly talked about interactions between two IVs in which one is
continuous and another is
binary
. This case is easy to understand because you can plot it as two
lines, one for each level. What happens if both the IVs are continuous?
6
I made a second set of data called Mood2, HrsTherapy2, and Medicine 2. In this dataset, now
instead of receiving medicine or not, it is the amount of medicine with four levels: none (0), a
little (1), medium (2), or a lot (3).
Make a Flexplot putting Mood2 as the Outcome Variable and HrsTherapy2 and Medicine2 as the
Predictor Variables. Describe what you see and explain what it means.
There are four slopes. The slope is flat for the no-medicine group, and the slopes get
progressively stronger with more medicine. This can be described like a fan or like a hand with
spread-out fingers. This means that there is a synergistic effect between therapy and medicine –
with more medicine, the influence of therapy on mood has a bigger influence. Or, it could also
be stated in another way – with higher levels of therapy, the benefits of medicine becomes
bigger!
Now run a regression with HrsTherapy2, Medicine2, and their interaction as predictors of
Mood2.
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Is the HrsTherapy2 regression term significantly positive or negative? Note, this row tests
whether HrsTherapy2 is significant for the no medicine (Medicine2 = 0) group.
Positive influence of HrsTherapy1 on Mood1 within the no medicine (0) group
No influence of HrsTherapy1 on Mood1 within the no medicine (0) group
**Estimate =
0.07, p-value non-significant. You can see that the slope is flat for the purple (medicine
0) group.
Negative influence of HrsTherapy1 on Mood1 within the no medicine (0) group
Is there a significant interaction? Note, if this is positive, it means that the slope of HrsTherapy1
is more positive for increasing levels of medicine. So it is more positive for group 3 than 2 than 1
than 0.
Positive interaction
**Estimate is 2.05, p<.001. This tests whether for more medicine,
the slope for therapy increases. Or likewise, for higher amounts of therapy, the benefit
of medicine increases. This is the fanning-out pattern in the graph.
No difference
Negative interaction
Is the Medicine2 regression term significant? This tests whether more medicine is associated
with better mood
when HrsTherapy2 is zero.
Stated another way, when someone does not
receive any therapy, does the medicine makes a difference?
Medicine group has more positive mood when HrsTherapy1 = 0
*See estimate 4.76,
p<.001. In the graph below, in the circled red part, when HrsTherapy2 is 0, the purple
line does look somewhat lower than the blue, green, and yellow lines. Note, only the
yellow line goes all the way to zero – this is because the lowest numbers of therapy for
observations in the other groups is around 1. But what this term in the regression tests
for is, if we were to extend these lines to 0, whether there is a general increase in where
these lines hit HrsTherapy=0.
No difference
Medicine group has more negative mood when HrsTherapy1 = 0
8
Suppose we want to predict someone’s Mood who goes to 6 hours of therapy per month, and is
on the medium dose (2) of the medicine. What would their mood be?
The estimates we got are below:
So the regression equation is:
Mood = 8.8 + .07(HrsTherapy) + 4.7(Medicine) + 2.1(HrsTherapy)(Medicine)
8.8 + .07(6) + 4.7(2) + 2.1(6)(2) =
43.8
Notice how 43.8 falls on the green line when HrsTherapy=6!
9
What do you understand about interactions now that you didn’t understand before about
interactions?
Answers will vary for different students
What do you still not understand about interactions?
Answers will vary for different students
If you feel like you still don’t understand something important, how will you get this
information?
NA – I think I understand the most important things
Re-watch lecture videos
Ask my group members
Go to office hours
Good job learning about interactions!
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