d = data.frame(
Temperature = c(rep("Cool", 6), rep("Warm", 6)),
Bact = c(rep("Bact 1", 2), rep("Bact 2", 2), rep("Bact 3", 2), rep("Bact 1", 2), rep("Bact 2", 2), rep("Bact 3", 2)),
Time = c(15.23,14.32,14.77,15.12,14.05,15.48,14.13,16.13,16.44,14.82,17.96,16.65)
)
I self-created a small data frame for a two-way ANOVA. I want to perform a two-way ANOVA model by
summary(aov(Time~Bact*Temperature, data=d))
Time is the dependent variable while Bact and Temperature are two categorical independent variables.
Instead of doing it in the ANOVA way, I want to learn and prove ANOVA can also be done with a linear regression model. I want to convert my data into dummy variables and perform a linear regression on it. I expect I'll recover the same results. The dummy variables will also include interactions effects between Bact and Temperature.
The problem is that, I don't know how to convert my data frame into dummy variables such that it can be used in the lm() function.
I kind of do the same with you. I want to feel in control so whenever I have time I design the dummies myself with the following:
d = data.frame(
Temperature = c(rep("Cool", 6), rep("Warm", 6)),
Bact = c(rep("Bact 1", 2), rep("Bact 2", 2), rep("Bact 3", 2), rep("Bact 1", 2), rep("Bact 2", 2), rep("Bact 3", 2)),
Time = c(15.23,14.32,14.77,15.12,14.05,15.48,14.13,16.13,16.44,14.82,17.96,16.65)
)
which is:
> d
Temperature Bact Time
1 Cool Bact 1 15.23
2 Cool Bact 1 14.32
3 Cool Bact 2 14.77
4 Cool Bact 2 15.12
5 Cool Bact 3 14.05
6 Cool Bact 3 15.48
7 Warm Bact 1 14.13
8 Warm Bact 1 16.13
9 Warm Bact 2 16.44
10 Warm Bact 2 14.82
11 Warm Bact 3 17.96
12 Warm Bact 3 16.65
So you only need to dummify factors (temperature,bact) so the following process works:
xfactors <- Filter(is.factor,d) #filter only the factors to dummify
b <- data.frame(matrix(NA,nrow=nrow(xfactors),ncol=1)) #make empty data.frame to initiate b
for ( i in 1:ncol(xfactors)) { #start loop
a <- data.frame(model.matrix(~xfactors[,i])) #make dummies here
b <- cbind(b, a[-1]) #remove intercept and combine dummies
}
b <- data.frame(b[-1]) #make a data.frame
#the reference dummy gets excluded automatically by model.matrix
colnames(b) <- c('warm' , 'bact2' , 'bact3') #you will probably want to change the names to sth smaller
> b
warm bact2 bact3
1 0 0 0
2 0 0 0
3 0 1 0
4 0 1 0
5 0 0 1
6 0 0 1
7 1 0 0
8 1 0 0
9 1 1 0
10 1 1 0
11 1 0 1
12 1 0 1
Then to run the model:
new_data <- cbind(b, Time=d$Time) #add time to the data
mymod <- lm(Time ~ warm*bact2+warm*bact3, data=new_data) #compute lm with interactions
#you shouldn't compute the interactions between dummy variables because they come from the same variable
Output:
> summary(mymod)
Call:
lm(formula = Time ~ warm * bact2 + warm * bact3, data = new_data)
Residuals:
Min 1Q Median 3Q Max
-1.00 -0.67 0.00 0.67 1.00
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 14.7750 0.6873 21.498 6.61e-07 ***
warm 0.3550 0.9719 0.365 0.727
bact2 0.1700 0.9719 0.175 0.867
bact3 -0.0100 0.9719 -0.010 0.992
warm:bact2 0.3300 1.3745 0.240 0.818
warm:bact3 2.1850 1.3745 1.590 0.163
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.9719 on 6 degrees of freedom
Multiple R-squared: 0.6264, Adjusted R-squared: 0.3151
F-statistic: 2.012 on 5 and 6 DF, p-value: 0.2097