1 Interactions

  • Interactions have the same meaning they did in ANOVA
  • there is a synergistic effect between two variables
  • However now we can examine interactions between continuous variables
  • Additive Effects: \(Y = B_1X + B_2Z + B_0\)
  • Interactive Effects: \(Y = B_1X + B_2Z + B_3XZ + B_0\)

1.1 Example of Interaction

  • We need to make multivariate set of variables and then force an interaction
  • DV: Reading Speed, IVs: Age + IQ
library(car)
set.seed(42)
# 250 people
n <- 250
# Uniform distrobution of Ages (5 to 15 year olds) 
X <- runif(n, 5, 15)

# normal distrobution of IQ (100 +-15) 
Z <- rnorm(n, 100, 15)

# Our equation to  create Y
Y <- .3*X + .5*Z + .3*X*Z +300 + rnorm(n, sd=10)
#Built our data frame
Reading.Data<-data.frame(ReadingSpeed=Y,Age=X,IQ=Z)

# Plot: Notes: reg.line=FALSE means remove best fit line. 
# smoother=loessLine means add smoothed line called the loess
scatterplot(ReadingSpeed~Age, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

scatterplot(ReadingSpeed~IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

scatterplot(Age~IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

1.2 Lets test an interaction

  1. Center your variables
  2. Model 1: Examine a main-effects model (X + Z) [not necessary but useful]
  3. Model 2: Examine a main-effects + Interaction model (X + Z + X:Z)
  • Note: You can simply code it as X*Z in r, as it will automatically do (X + Z + X:Z)
#Center
Reading.Data$Age.C<-scale(Reading.Data$Age, center = TRUE, scale = FALSE)[,]
Reading.Data$IQ.C<-scale(Reading.Data$IQ, center = TRUE, scale = FALSE)[,]

Centered.Read.1<-lm(ReadingSpeed~Age.C+IQ.C,Reading.Data)
Centered.Read.2<-lm(ReadingSpeed~Age.C*IQ.C,Reading.Data)


library(stargazer)
stargazer(Centered.Read.1,Centered.Read.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
ReadingSpeed
Main Effects Interaction
(1) (2)
Constant 653.207*** 653.632***
(0.980) (0.653)
Age.C 29.778*** 29.851***
(0.337) (0.224)
IQ.C 3.579*** 3.556***
(0.071) (0.047)
Age.C:IQ.C 0.305***
(0.017)
Observations 250 250
R2 0.976 0.989
Adjusted R2 0.976 0.989
Residual Std. Error 15.502 (df = 247) 10.314 (df = 246)
F Statistic 5,028.365*** (df = 2; 247) 7,676.634*** (df = 3; 246)
Note: p<0.1; p<0.05; p<0.01
  • Also change in \(R^2\) is significant, as we might expect
ChangeInR<-anova(Centered.Read.1,Centered.Read.2)
knitr::kable(ChangeInR, digits=4)
Res.Df RSS Df Sum of Sq F Pr(>F)
247 59357.43 NA NA NA NA
246 26169.85 1 33187.58 311.9676 0

1.3 How visualize this?

  • Well, there are some options
  • We can do a fancy-pants surface plot, but that is hard to put into a paper
  • More common this is to examine slope of one factor at different levels of the other (Simple Slopes)
  • What we need to decide is at which levels

1.3.1 Hand picking

  • Manually select the what levels of each you are going to examine
  • For for tracking values of interest
  • here I picked -3 to 3 for age (mix and max) and -15, 0 15 for IQ (theoretical 1 SD and mean)
library(effects)
Inter.1a<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                           xlevels=list(Age.C=seq(-3,3, 1), 
                                        IQ.C=c(-15,0,15)))
knitr::kable(summary(Inter.1a)$effect, digits=4)
-15 0 15
-3 524.445 564.0773 603.7095
-2 549.727 593.9288 638.1305
-1 575.009 623.7803 672.5515
0 600.291 653.6317 706.9725
1 625.573 683.4832 741.3935
2 650.855 713.3347 775.8144
3 676.137 743.1862 810.2354
plot(Inter.1a, multiline = TRUE)

1.3.2 Quantile

  • Examine the levels based on quantiles (bins based on probabiltiy)
  • We will do this into 5 equal bins based on probability cut-offs
  • Does not assume normality for IV
IQ.Quantile<-quantile(Reading.Data$IQ.C,probs=c(0,.25,.50,.75,1))
IQ.Quantile<-round(IQ.Quantile,2)
IQ.Quantile
##     0%    25%    50%    75%   100% 
## -39.89  -9.91  -0.19   9.45  37.50
Inter.1b<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                 xlevels=list(Age.C=seq(-3,3, 1), 
                              IQ.C=IQ.Quantile))
plot(Inter.1b, multiline = TRUE)

1.3.3 Based on the SD

  • We select 3 values: \(M-1SD\), \(M\), \(M+1SD\)
  • Not it does not have to be 1 SD, it can be 1.5,2 or 3
  • Assumes normality for IV
IQ.SD<-c(mean(Reading.Data$IQ.C)-sd(Reading.Data$IQ.C),
         mean(Reading.Data$IQ.C),
         mean(Reading.Data$IQ.C)+sd(Reading.Data$IQ.C))
IQ.SD<-round(IQ.SD,2)
IQ.SD
## [1] -13.89   0.00  13.89
Inter.1c<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                 xlevels=list(Age.C=seq(-3,3, 1), 
                              IQ.C=IQ.SD))
plot(Inter.1c, multiline = TRUE)

1.4 Why center your IVs?

  • The center of each IV represents the mean of that IV
  • Thus when you interact them \(X*Z\), that means \(0*0 = 0\)
  • Also this can reduce multicollineatity issues
  • This is because if \(X*Z\) creates a line, it means you have added a new predictor (XZ) that strongly correlates with X and Z
X<-c(0,2,4,6,8,10)
Z<-c(0,2,4,6,8,10)
XZ<-X*Z
plot(XZ)

c(cor(X,Z), cor(X,XZ), cor(Z,XZ))
## [1] 1.0000000 0.9598833 0.9598833

-But if you center them, now you will make a U-shaped interaction which will be orthogonal to X and Z!

X.C<-scale(X, center = TRUE, scale = FALSE)[,]
Z.C<-scale(Z, center = TRUE, scale = FALSE)[,]
XZ.C<-X.C*Z.C
plot(XZ.C)

c(cor(X.C,Z.C), cor(X.C,XZ.C), cor(Z.C,XZ.C))
## [1] 1 0 0
  • Lets apply this to our class example
  • For example, see below where I manually multiply the values and you can see a very strong positive slope
Reading.Data$Age.X.IQ<-Reading.Data$Age*Reading.Data$IQ
scatterplot(ReadingSpeed~Age.X.IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

  • But when you center them, things change
Reading.Data$Age.X.IQ.C<-Reading.Data$Age.C*Reading.Data$IQ.C
scatterplot(ReadingSpeed~Age.X.IQ.C, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

1.4.1 Lets run an uncentered regression

  • as you can see the the terms have changed from centered models
Uncentered.Read.1<-lm(ReadingSpeed~IQ+Age,Reading.Data)
Uncentered.Read.2<-lm(ReadingSpeed~IQ*Age,Reading.Data)

stargazer(Uncentered.Read.1,Uncentered.Read.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
ReadingSpeed
Main Effects Interaction
(1) (2)
Constant -3.036 304.494***
(7.979) (18.203)
IQ 3.579*** 0.482***
(0.071) (0.182)
Age 29.778*** -0.427
(0.337) (1.725)
IQ:Age 0.305***
(0.017)
Observations 250 250
R2 0.976 0.989
Adjusted R2 0.976 0.989
Residual Std. Error 15.502 (df = 247) 10.314 (df = 246)
F Statistic 5,028.365*** (df = 2; 247) 7,676.634*** (df = 3; 246)
Note: p<0.1; p<0.05; p<0.01
  • lets check the multicollinearity of the uncentered model
vif(Uncentered.Read.2)
##       IQ      Age   IQ:Age 
## 14.89057 59.14549 71.06919
  • We lost our main effect of Age as the variances got all inflated
  • We did not have this problem in the centered model
vif(Centered.Read.2)
##      Age.C       IQ.C Age.C:IQ.C 
##   1.001540   1.001961   1.001144
  • Note: Its more standard to plot the uncentered version, but run the analysis on the centered data

2 Testing Simple Slopes

  • The goal here it figure out when the slope at a given level of another variable is different from zero
  • We chop up the interaction at specific places as we did with the interactions plots (-1 SD, M, +1 SD) on the moderating variable (a third variable that affects the strength of the relationship between a dependent and independent variable)
  • Next we test the slopes on the predictor variable (IV of main interest)
  • Example: Performance on a task, predicted by Level of training, moderated by how hard the challange is
set.seed(42)
# 250 people
n <- 250
#Training (low to high)
X <- runif(n, -10, 10)
# normal distrobution of Challenge Difficulty
Z <- rnorm(n, 0, 15)
# Our equation to  create Y
Y <- 2.2*X + 2.46*Z + .75*X*Z + 16 + rnorm(n, sd=50)
#Built our data frame
Skill.Data<-data.frame(Performance=Y,Training=X,Challenge=Z)
#run our regression
Skill.Model.1<-lm(Performance~Training+Challenge,Skill.Data)
Skill.Model.2<-lm(Performance~Training*Challenge,Skill.Data)
stargazer(Skill.Model.1,Skill.Model.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
Performance
Main Effects Interaction
(1) (2)
Constant 14.238*** 16.173***
(4.909) (3.268)
Training 0.895 1.542***
(0.843) (0.562)
Challenge 2.855*** 2.600***
(0.354) (0.236)
Training:Challenge 0.762***
(0.043)
Observations 250 250
R2 0.210 0.652
Adjusted R2 0.204 0.648
Residual Std. Error 77.510 (df = 247) 51.571 (df = 246)
F Statistic 32.867*** (df = 2; 247) 153.486*** (df = 3; 246)
Note: p<0.1; p<0.05; p<0.01

2.1 Ploting

  • We will use the rockchalk library to visualize our interaction and test our simple slopes
library(rockchalk)
## 
## Attaching package: 'rockchalk'
## The following object is masked from 'package:plyr':
## 
##     summarize
## The following object is masked from 'package:MASS':
## 
##     mvrnorm
m1ps <- plotSlopes(Skill.Model.2, modx = "Challenge", plotx = "Training", n=3, modxVals="std.dev")

m1psts <- testSlopes(m1ps)
## Values of Challenge OUTSIDE this interval:
##         lo         hi 
## -3.5050807 -0.5730182 
## cause the slope of (b1 + b2*Challenge)Training to be statistically significant
round(m1psts$hypotests,4)
##        "Challenge"   slope Std. Error  t value Pr(>|t|)
## (m-sd)      -14.50 -9.5013     0.8131 -11.6848   0.0000
## (m)          -0.61  1.0771     0.5611   1.9196   0.0561
## (m+sd)       13.28 11.6554     0.8282  14.0737   0.0000
  • We see the slope at the mean is not significant,
  • The +1SD and -1SD are significant, this is what is driving the interaction
  • Well trained people at low levels of challenge get worse with more training, while high levels of challenge with more training get better
  • The bonus using rockchalk is that you can change the number of lines (change n=3) you want to see or you can test quantiles as well (change modxVals=“quantile”)
m1pQ <- plotSlopes(Skill.Model.2, modx = "Challenge", plotx = "Training", n=5, modxVals="quantile")

m1pQts <- testSlopes(m1pQ)
## Values of Challenge OUTSIDE this interval:
##         lo         hi 
## -3.5050807 -0.5730182 
## cause the slope of (b1 + b2*Challenge)Training to be statistically significant
round(m1pQts$hypotests,4)
##      "Challenge"    slope Std. Error  t value Pr(>|t|)
## 0%      -40.4989 -29.3016     1.7993 -16.2847   0.0000
## 25%     -10.5190  -6.4694     0.6990  -9.2555   0.0000
## 50%      -0.7985   0.9335     0.5610   1.6640   0.0974
## 75%       8.8382   8.2726     0.6994  11.8278   0.0000
## 100%     36.8939  29.6394     1.7214  17.2183   0.0000

2.1.1 Notes

  • You often don’t need to run the t-tests on the simple slopes, but they can useful to test very specific hypotheses
  • You can run simple slopes analysis on three-way interactions, but lets leave that aside for now as you would have to use a different R-package, again often the plot tells the story

3 Non-Linear interactions

  • You can have non-linear terms interacting with other linear and non-linear terms
  • Example: Quit smoking, X = fear of you health, Z = moderated by Self-Efficacy for quiting
set.seed(42)
# 250 people
n <- 250
#Fear of Health
X <- runif(n, 1, 9)
#Centered Self-Efficacy
Z <- runif(n, 0, 15)
# Our equation to  create Y
Y <- .178*X - .052*X^2 + .164*X*Z + .164*(X^2)*Z+ 3.651 + rnorm(n, sd=50)
#Built our data frame
Smoke.Data<-data.frame(Smoking=Y,Health=X,SelfEfficacy=Z)
#run our regression
Smoke.Model.1<-lm(Smoking~poly(Health,2)+SelfEfficacy,Smoke.Data)
Smoke.Model.2<-lm(Smoking~poly(Health,2)*SelfEfficacy,Smoke.Data)
stargazer(Smoke.Model.1,Smoke.Model.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
Smoking
Main Effects Interaction
(1) (2)
Constant 1.121 0.888
(6.187) (5.857)
poly(Health, 2)1 464.121*** 49.056
(51.816) (90.966)
poly(Health, 2)2 118.649** 50.228
(51.721) (93.073)
SelfEfficacy 5.713*** 5.931***
(0.745) (0.706)
poly(Health, 2)1:SelfEfficacy 60.253***
(11.088)
poly(Health, 2)2:SelfEfficacy 10.879
(11.441)
Observations 250 250
R2 0.353 0.425
Adjusted R2 0.345 0.413
Residual Std. Error 51.685 (df = 246) 48.903 (df = 244)
F Statistic 44.648*** (df = 3; 246) 36.081*** (df = 5; 244)
Note: p<0.1; p<0.05; p<0.01

3.1 Plotting the Simple Slopes when there are Curves

  • These can be done with the ‘effects’ package as I showed you above and last week
  • or we can simply use the plotCurves function from the ‘rockchalk’ package
SmokeInterPlot <- plotCurves(Smoke.Model.2, modx = "SelfEfficacy", plotx = "Health",n=3,modxVals="std.dev")

  • Notice that the second order term was not significant in the main effect model
  • This means you could have missed it. As the model 1 plot would have looked like this:
plotCurves(Smoke.Model.1, plotx = "Health")

  • In other words, you cannot see the higher order effects as they are hidden by the moderating variable
  • How to find these hidden things?
  • You have to test for interactions and changes in \(R^2\)
  • You have try to add higher order terms, but they should be motivated by some theory
  • What if you did not know the second order term was in the model above.
Smoke.Model.1.L<-lm(Smoking~Health+SelfEfficacy,Smoke.Data)
Smoke.Model.2.L<-lm(Smoking~Health*SelfEfficacy,Smoke.Data)
stargazer(Smoke.Model.1.L,Smoke.Model.2.L,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
Smoking
Main Effects Interaction
(1) (2)
Constant -62.385*** -5.746
(9.811) (14.105)
Health 12.606*** 1.370
(1.420) (2.497)
SelfEfficacy 5.649*** -2.384
(0.751) (1.664)
Health:SelfEfficacy 1.627***
(0.304)
Observations 250 250
R2 0.339 0.407
Adjusted R2 0.333 0.400
Residual Std. Error 52.129 (df = 247) 49.444 (df = 246)
F Statistic 63.249*** (df = 2; 247) 56.387*** (df = 3; 246)
Note: p<0.1; p<0.05; p<0.01
ChangeInR.Smoke<-anova(Smoke.Model.1.L,Smoke.Model.2.L)
knitr::kable(ChangeInR.Smoke, digits=4)
Res.Df RSS Df Sum of Sq F Pr(>F)
247 671215.5 NA NA NA NA
246 601410.1 1 69805.32 28.5531 0
  • Reploting as linear by linear interaction
library(rockchalk)
SmokeInterPlot.Linear <- plotSlopes(Smoke.Model.2.L, modx = "SelfEfficacy", plotx = "Health", n=3, modxVals="std.dev")

  • lets check the change in \(R^2\) from Linear interaction model to poly interaction model now
stargazer(Smoke.Model.2.L,Smoke.Model.2,type="html",
          column.labels = c("Linear", "Poly"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)
Dependent variable:
Smoking
Linear Poly
(1) (2)
Constant -5.746 0.888
(14.105) (5.857)
Health 1.370
(2.497)
poly(Health, 2)1 49.056
(90.966)
poly(Health, 2)2 50.228
(93.073)
SelfEfficacy -2.384 5.931***
(1.664) (0.706)
Health:SelfEfficacy 1.627***
(0.304)
poly(Health, 2)1:SelfEfficacy 60.253***
(11.088)
poly(Health, 2)2:SelfEfficacy 10.879
(11.441)
Observations 250 250
R2 0.407 0.425
Adjusted R2 0.400 0.413
Residual Std. Error 49.444 (df = 246) 48.903 (df = 244)
F Statistic 56.387*** (df = 3; 246) 36.081*** (df = 5; 244)
Note: p<0.1; p<0.05; p<0.01
ChangeInR.Smoke.2<-anova(Smoke.Model.2.L,Smoke.Model.2)
knitr::kable(ChangeInR.Smoke.2, digits=4)
Res.Df RSS Df Sum of Sq F Pr(>F)
246 601410.1 NA NA NA NA
244 583529.7 2 17880.49 3.7383 0.0252

3.2 Notes

  • So model with poly is a significantly better fit, but really its not a huge change
  • Would it change the story by much?
  • Most people would ignore the higher order term, but you the choice depends on your theory!
  • Ignoring the higher order term can make it easier to test simple slopes
  • But ignoring the higher order terms can voilate your assumptions, lets compare our linear vs poly models residuals
plot(Smoke.Model.2.L, which=1)

plot(Smoke.Model.2, which=1)

---
title: 'Interactions and Simple Slopes'
output:
  html_document:
    code_download: yes
    fontsize: 8pt
    highlight: textmate
    number_sections: yes
    theme: flatly
    toc: yes
    toc_float:
      collapsed: no
---


```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(fig.width=5)
knitr::opts_chunk$set(fig.height=3.75)
knitr::opts_chunk$set(fig.align='center') 
```

# Interactions

* Interactions have the same meaning they did in ANOVA
  + there is a synergistic effect between two variables
  + However now we can examine interactions between continuous variables
* Additive Effects: $Y = B_1X + B_2Z + B_0$
* Interactive Effects: $Y = B_1X + B_2Z + B_3XZ + B_0$

## Example of Interaction
- We need to make multivariate set of variables and then force an interaction
- DV: Reading Speed, IVs: Age + IQ 

```{r, echo=TRUE, warning=FALSE}
library(car)
set.seed(42)
# 250 people
n <- 250
# Uniform distrobution of Ages (5 to 15 year olds) 
X <- runif(n, 5, 15)

# normal distrobution of IQ (100 +-15) 
Z <- rnorm(n, 100, 15)

# Our equation to  create Y
Y <- .3*X + .5*Z + .3*X*Z +300 + rnorm(n, sd=10)
#Built our data frame
Reading.Data<-data.frame(ReadingSpeed=Y,Age=X,IQ=Z)

# Plot: Notes: reg.line=FALSE means remove best fit line. 
# smoother=loessLine means add smoothed line called the loess
scatterplot(ReadingSpeed~Age, data= Reading.Data, reg.line=FALSE, smoother=loessLine)
scatterplot(ReadingSpeed~IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)
scatterplot(Age~IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)


```

## Lets test an interaction
1. Center your variables
2. Model 1: Examine a main-effects model (X + Z) [not necessary but useful]
3. Model 2: Examine a main-effects + Interaction model (X + Z + X:Z)

- Note: You can simply code it as X*Z in r, as it will automatically do (X + Z + X:Z)

```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}

#Center
Reading.Data$Age.C<-scale(Reading.Data$Age, center = TRUE, scale = FALSE)[,]
Reading.Data$IQ.C<-scale(Reading.Data$IQ, center = TRUE, scale = FALSE)[,]

Centered.Read.1<-lm(ReadingSpeed~Age.C+IQ.C,Reading.Data)
Centered.Read.2<-lm(ReadingSpeed~Age.C*IQ.C,Reading.Data)


library(stargazer)
stargazer(Centered.Read.1,Centered.Read.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```



- Also change in $R^2$ is significant, as we might expect

```{r}
ChangeInR<-anova(Centered.Read.1,Centered.Read.2)
knitr::kable(ChangeInR, digits=4)
```



## How visualize this?
- Well, there are some options
- We can do a fancy-pants surface plot, but that is hard to put into a paper
- More common this is to examine slope of one factor at different levels of the other (Simple Slopes) 
- What we need to decide is at which levels



### Hand picking
- Manually select the what levels of each you are going to examine
- For for tracking values of interest
- here I picked -3 to 3 for age (mix and max) and -15, 0 15 for IQ (theoretical 1 SD and mean)

```{r, echo=TRUE, warning=FALSE, message=FALSE}
library(effects)
Inter.1a<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                           xlevels=list(Age.C=seq(-3,3, 1), 
                                        IQ.C=c(-15,0,15)))

```


```{r}
knitr::kable(summary(Inter.1a)$effect, digits=4)
plot(Inter.1a, multiline = TRUE)
```



### Quantile
- Examine the levels based on quantiles (bins based on probabiltiy)
- We will do this into 5 equal bins based on probability cut-offs 
- Does not assume normality for IV

```{r, echo=TRUE, warning=FALSE}
IQ.Quantile<-quantile(Reading.Data$IQ.C,probs=c(0,.25,.50,.75,1))
IQ.Quantile<-round(IQ.Quantile,2)
IQ.Quantile

Inter.1b<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                 xlevels=list(Age.C=seq(-3,3, 1), 
                              IQ.C=IQ.Quantile))
plot(Inter.1b, multiline = TRUE)
```

### Based on the SD 
- We select 3 values: $M-1SD$, $M$, $M+1SD$
- Not it does not have to be 1 SD, it can be 1.5,2 or 3
- Assumes normality for IV

```{r, echo=TRUE, warning=FALSE}

IQ.SD<-c(mean(Reading.Data$IQ.C)-sd(Reading.Data$IQ.C),
         mean(Reading.Data$IQ.C),
         mean(Reading.Data$IQ.C)+sd(Reading.Data$IQ.C))
IQ.SD<-round(IQ.SD,2)
IQ.SD

Inter.1c<-effect(c("Age.C*IQ.C"), Centered.Read.2,
                 xlevels=list(Age.C=seq(-3,3, 1), 
                              IQ.C=IQ.SD))
plot(Inter.1c, multiline = TRUE)


```


## Why center your IVs?
- The center of each IV represents the mean of that IV
- Thus when you interact them $X*Z$, that means $0*0 = 0$
- Also this can reduce multicollineatity issues
- This is because if $X*Z$ creates a line, it means you have added a new predictor (XZ) that strongly correlates with X and Z

```{r, echo=TRUE, warning=FALSE}
X<-c(0,2,4,6,8,10)
Z<-c(0,2,4,6,8,10)
XZ<-X*Z
plot(XZ)
c(cor(X,Z), cor(X,XZ), cor(Z,XZ))
```

-But if you center them, now you will make a U-shaped interaction which will be orthogonal to X and Z!

```{r, echo=TRUE, warning=FALSE}
X.C<-scale(X, center = TRUE, scale = FALSE)[,]
Z.C<-scale(Z, center = TRUE, scale = FALSE)[,]
XZ.C<-X.C*Z.C
plot(XZ.C)
c(cor(X.C,Z.C), cor(X.C,XZ.C), cor(Z.C,XZ.C))
```

- Lets apply this to our class example
- For example, see below where I manually multiply the values and you can see a very strong positive slope
```{r, echo=TRUE, warning=FALSE}
Reading.Data$Age.X.IQ<-Reading.Data$Age*Reading.Data$IQ
scatterplot(ReadingSpeed~Age.X.IQ, data= Reading.Data, reg.line=FALSE, smoother=loessLine)
```

- But when you center them, things change
```{r, echo=TRUE, warning=FALSE}
Reading.Data$Age.X.IQ.C<-Reading.Data$Age.C*Reading.Data$IQ.C
scatterplot(ReadingSpeed~Age.X.IQ.C, data= Reading.Data, reg.line=FALSE, smoother=loessLine)

```



### Lets run an uncentered regression
- as you can see the the terms have changed from centered models

```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}
Uncentered.Read.1<-lm(ReadingSpeed~IQ+Age,Reading.Data)
Uncentered.Read.2<-lm(ReadingSpeed~IQ*Age,Reading.Data)

stargazer(Uncentered.Read.1,Uncentered.Read.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```



- lets check the multicollinearity of the uncentered model

```{r, echo=TRUE, warning=FALSE}
vif(Uncentered.Read.2)

```

- We lost our main effect of **Age** as the variances got all inflated
- We did not have this problem in the centered model

```{r, echo=TRUE, warning=FALSE}
vif(Centered.Read.2)

```

- Note: Its more standard to plot the uncentered version, but run the analysis on the centered data

# Testing Simple Slopes 
- The goal here it figure out when the slope at a given level of another variable is different from zero
- We chop up the interaction at specific places as we did with the interactions plots (-1 SD, M, +1 SD) on the *moderating* variable (a third variable that affects the strength of the relationship between a dependent and independent variable) 
- Next we test the slopes on the *predictor* variable (IV of main interest)
- Example: Performance on a task, predicted by Level of training, moderated by how hard the challange is
```{r, echo=TRUE, warning=FALSE}
set.seed(42)
# 250 people
n <- 250
#Training (low to high)
X <- runif(n, -10, 10)
# normal distrobution of Challenge Difficulty
Z <- rnorm(n, 0, 15)
# Our equation to  create Y
Y <- 2.2*X + 2.46*Z + .75*X*Z + 16 + rnorm(n, sd=50)
#Built our data frame
Skill.Data<-data.frame(Performance=Y,Training=X,Challenge=Z)
#run our regression
Skill.Model.1<-lm(Performance~Training+Challenge,Skill.Data)
Skill.Model.2<-lm(Performance~Training*Challenge,Skill.Data)

```


```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}

stargazer(Skill.Model.1,Skill.Model.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```



## Ploting 
- We will use the rockchalk library to visualize our interaction and test our simple slopes

```{r, echo=TRUE, warning=FALSE}
library(rockchalk)
m1ps <- plotSlopes(Skill.Model.2, modx = "Challenge", plotx = "Training", n=3, modxVals="std.dev")
m1psts <- testSlopes(m1ps)
round(m1psts$hypotests,4)
```

- We see the slope at the mean is not significant, 
- The +1SD and -1SD are significant, this is what is driving the interaction
- Well trained people at low levels of challenge get worse with more training, while high levels of challenge with more training get better
- The bonus using rockchalk is that you can change the number of lines (change n=3) you want to see or you can test quantiles as well (change modxVals="quantile")


```{r, echo=TRUE, warning=FALSE}
m1pQ <- plotSlopes(Skill.Model.2, modx = "Challenge", plotx = "Training", n=5, modxVals="quantile")
m1pQts <- testSlopes(m1pQ)
round(m1pQts$hypotests,4)
```

### Notes
- You often don't need to run the t-tests on the simple slopes, but they can useful to test very specific hypotheses
- You can run simple slopes analysis on three-way interactions, but lets leave that aside for now as you would have to use a different R-package, again often the plot tells the story

# Non-Linear interactions
- You can have non-linear terms interacting with other linear and non-linear terms
- Example: Quit smoking, X = fear of you health, Z = moderated by Self-Efficacy for quiting
```{r, echo=TRUE, warning=FALSE}
set.seed(42)
# 250 people
n <- 250
#Fear of Health
X <- runif(n, 1, 9)
#Centered Self-Efficacy
Z <- runif(n, 0, 15)
# Our equation to  create Y
Y <- .178*X - .052*X^2 + .164*X*Z + .164*(X^2)*Z+ 3.651 + rnorm(n, sd=50)
#Built our data frame
Smoke.Data<-data.frame(Smoking=Y,Health=X,SelfEfficacy=Z)
#run our regression
Smoke.Model.1<-lm(Smoking~poly(Health,2)+SelfEfficacy,Smoke.Data)
Smoke.Model.2<-lm(Smoking~poly(Health,2)*SelfEfficacy,Smoke.Data)

```


```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}

stargazer(Smoke.Model.1,Smoke.Model.2,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```

## Plotting the Simple Slopes when there are Curves
- These can be done with the 'effects' package as I showed you above and last week
- or we can simply use the plotCurves function from the 'rockchalk' package

```{r, echo=TRUE, warning=FALSE}
SmokeInterPlot <- plotCurves(Smoke.Model.2, modx = "SelfEfficacy", plotx = "Health",n=3,modxVals="std.dev")
```

- Notice that the second order term was not significant in the main effect model
- This means you could have missed it. As the model 1 plot would have looked like this:  

```{r, echo=TRUE, warning=FALSE}
plotCurves(Smoke.Model.1, plotx = "Health")
```

- In other words, you cannot see the higher order effects as they are hidden by the moderating variable
- How to find these hidden things? 
- You have to test for interactions and changes in $R^2$
- You have try to add higher order terms, but they should be motivated by some theory
- What if you did not know the second order term was in the model above. 

```{r, echo=TRUE, warning=FALSE}
Smoke.Model.1.L<-lm(Smoking~Health+SelfEfficacy,Smoke.Data)
Smoke.Model.2.L<-lm(Smoking~Health*SelfEfficacy,Smoke.Data)

```

```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}

stargazer(Smoke.Model.1.L,Smoke.Model.2.L,type="html",
          column.labels = c("Main Effects", "Interaction"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```

```{r}

ChangeInR.Smoke<-anova(Smoke.Model.1.L,Smoke.Model.2.L)
knitr::kable(ChangeInR.Smoke, digits=4)

```

- Reploting as linear by linear interaction

```{r, echo=TRUE, warning=FALSE}
library(rockchalk)
SmokeInterPlot.Linear <- plotSlopes(Smoke.Model.2.L, modx = "SelfEfficacy", plotx = "Health", n=3, modxVals="std.dev")
```


- lets check the change in $R^2$ from Linear interaction model to poly interaction model now

```{r, echo=TRUE, warning=FALSE,message=FALSE,results='asis'}

stargazer(Smoke.Model.2.L,Smoke.Model.2,type="html",
          column.labels = c("Linear", "Poly"),
          intercept.bottom = FALSE,
          single.row=FALSE, 
          notes.append = FALSE,
          header=FALSE)

```

```{r}

ChangeInR.Smoke.2<-anova(Smoke.Model.2.L,Smoke.Model.2)
knitr::kable(ChangeInR.Smoke.2, digits=4)

```

## Notes
- So model with poly is a significantly better fit, but really its not a huge change
- Would it change the story by much?
- Most people would ignore the higher order term, but you the choice depends on your theory!
- Ignoring the higher order term can make it easier to test simple slopes
- But ignoring the higher order terms can voilate your assumptions, lets compare our linear vs poly models residuals

```{r}
plot(Smoke.Model.2.L, which=1)
plot(Smoke.Model.2, which=1)
```


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