Compute the self excluded sample mean by group
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egen(stata cmd) compute a summary statistics by groups and store it in to a new variable. For example, the data has three variables, id, time and y, we want to compute the mean of y by for each id and then store it as a new variable mean_y.
In stata, the command would be
egen mean_y = mean(y), by(id)
In R, this task can be completed by ave
Generate dataset:
id <- rep(1:3,each=3) t<-rep(1:3,3) y<-sample(1:5,9,replace=T) my_data<-data.frame(id=id,time=t,y=y)
Orignal data:
> my_data
id time y
1 1 1 4
2 1 2 1
3 1 3 4
4 2 1 2
5 2 2 3
6 2 3 3
7 3 1 4
8 3 2 4
9 3 3 3
> within(my_data, {mean_y = ave(y,id)} )
id time y mean_y
1 1 1 4 3.000000
2 1 2 1 3.000000
3 1 3 4 3.000000
4 2 1 2 2.666667
5 2 2 3 2.666667
6 2 3 3 2.666667
7 3 1 4 3.666667
8 3 2 4 3.666667
9 3 3 3 3.666667
The default summary statistics is mean. However, we can assign a particular function to compute the summary statistics. For example, if we want to compute the sd of y by id, then we can have
within(my_data, {sd_y = ave(y,id,FUN=sd)} )
id time y sd_y
1 1 1 4 1.7320508
2 1 2 1 1.7320508
3 1 3 4 1.7320508
4 2 1 2 0.5773503
5 2 2 3 0.5773503
6 2 3 3 0.5773503
7 3 1 4 0.5773503
8 3 2 4 0.5773503
9 3 3 3 0.5773503
Remark: The within evaluate an expression in an environment created from the data.frame. In addition, it will modify the data.frame and return it back(in our case, it create new variables, mean_y or sd_y )
Here is another usage of ave. We would like to create a self excluded sample mean by group.
Suppose the data has three variables, id, time and y, we want to compute the mean of y by for each id but excluding the value of y of current time period.
id <- rep(1:3,each=3) t<-rep(1:3,3) y<-sample(1:5,9,replace=T) my_data<-data.frame(id=id,time=t,y=y)
Orignal data:
> my_data id time y 1 1 1 4 2 1 2 1 3 1 3 4 4 2 1 2 5 2 2 3 6 2 3 3 7 3 1 4 8 3 2 4 9 3 3 3
First, we need a function to compute the self excluded mean. This function takes a vector and a function(default is mean) as argument. It apply the function to the vector where one of the element is removed. The return value is a vector that i-th element is given by FUN(x[-i])
excludeSelfSummary<-function(x,FUN=mean){
sapply(1:length(x), function(i) FUN(x[-i]))
}
> excludeSelfSummary(1:5,mean)
[1] 3.50 3.25 3.00 2.75 2.50
> excludeSelfSummary(1:5,min)
[1] 2 1 1 1 1
> excludeSelfSummary(1:5,max)
[1] 5 5 5 5 4
Then we pass the excludeSelfSummary into ave as argument.
> within(my_data, {sd_y = ave(y,id,FUN=excludeSelfSummary)} )
id time y sd_y
1 1 1 4 2.5
2 1 2 1 4.0
3 1 3 4 2.5
4 2 1 2 3.0
5 2 2 3 2.5
6 2 3 3 2.5
7 3 1 4 3.5
8 3 2 4 3.5
9 3 3 3 4.0
Of course, we could compute the self excluded minimum or maximum.
> within(my_data, {sd_y = ave(y,id,FUN=function(x) excludeSelfSummary(x,min) )})
id time y sd_y
1 1 1 4 1
2 1 2 1 4
3 1 3 4 1
4 2 1 2 3
5 2 2 3 2
6 2 3 3 2
7 3 1 4 3
8 3 2 4 3
9 3 3 3 4
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