Cramer's V with missing values gives different results - r

Question

My questions concern the calculation of the Cramers V to detect correlation between categorial variables. I 've got a dataset with missing values, but I created a fake dataset for illustration with two variables a and b, one of them containing to NA's.
a <- factor(c("M","","F","F","","M","F","F"))
a2 <- factor(a, levels = c('M','F'),labels =c('Male','Female'))
b <- factor(c("y","y","","y","n","n","n","y"))
b2 <- factor(b, levels=c("y","n"),labels=c("yes","no"))
df<-cbind(a2,b2)
The assocstats function gives me the result for the cramers V:
require(vcd)
> tab <-table(a,b)
> assocstats(tab)
X^2 df P(> X^2)
Likelihood Ratio 1.7261 4 0.78597
Pearson 1.3333 4 0.85570
Phi-Coefficient : 0.408
Contingency Coeff.: 0.378
Cramer's V : 0.289
Now I want to drop the NA's from the levels
a[a==""]<-NA
a3 <- droplevels(a)
levels(a3)
tab <-table(a,b)
assocstats(tab)
But everytime I remove NA's the result looks like this:
X^2 df P(> X^2)
Likelihood Ratio 0.13844 2 0.93312
Pearson NaN 2 NaN
Phi-Coefficient : NaN
Contingency Coeff.: NaN
Cramer's V : NaN
Also, because I have a large dataset I would like to calculate a matrix of the Cramer V results. I found this code here on stack overflow and it seems to work...
get.V<-function(y){
col.y<-ncol(y)
V<-matrix(ncol=col.y,nrow=col.y)
for(i in 1:col.y){
for(j in 1:col.y){
V[i,j]<-assocstats(table(y[,i],y[,j]))$cramer
}
}
return(V)
}
get.V(tab)
Only that the result is different than that with assocstats function:
[,1] [,2] [,3]
[1,] 1.0 0.5 1
[2,] 0.5 1.0 1
[3,] 1.0 1.0 1
This can not be right, because I get this result every time, even when changing the number of observations... what is wrong with this code?
Conclusion:I don't know which one of the result is right. I have a large dataset with a lot of NA's in it. The first asocstat result and the code give different results, altough there is no big difference,because the code only creates a matrix. The second asocstat function gives only NaN.I cant detect any errors... Can somebody help me?

Answer 1

You don't have to replace the "" with NA if you are using factors--any unique value that you don't define in levels will be converted to NA by factor
a <- factor(c("M","","F","F","","M","F","F"))
a2 <- factor(a, levels = c('M','F'),labels =c('Male','Female'))
a
# [1] M F F M F F
# Levels: F M
a2
# [1] Male <NA> Female Female <NA> Male Female Female
# Levels: Male Female
b <- factor(c("y","y","","y","n","n","n","y"))
b2 <- factor(b, levels=c("y","n"),labels=c("yes","no"))
(df <- cbind(a2,b2))
# a2 b2
# [1,] 1 1
# [2,] NA 1
# [3,] 2 NA
# [4,] 2 1
# [5,] NA 2
# [6,] 1 2
# [7,] 2 2
# [8,] 2 1
Above, you're creating a matrix which loses all the labels that you created with factor. I think you want a data frame:
(df <- data.frame(a2,b2))
# a2 b2
# 1 Male yes
# 2 <NA> yes
# 3 Female <NA>
# 4 Female yes
# 5 <NA> no
# 6 Male no
# 7 Female no
# 8 Female yes
require('vcd')
(tab <- table(a2,b2, useNA = 'ifany'))
# b2
# a2 yes no <NA>
# Male 1 1 0
# Female 2 1 1
# <NA> 1 1 0
(tab <- table(a2,b2))
# b2
# a2 yes no
# Male 1 1
# Female 2 1
You need to explicitly tell table if you want to see NA values in the table. Otherwise, it will drop them by default so that you are already "excluding" them when you use assocstats:
assocstats(tab)
# X^2 df P(> X^2)
# Likelihood Ratio 0.13844 1 0.70983
# Pearson 0.13889 1 0.70939
#
# Phi-Coefficient : 0.167
# Contingency Coeff.: 0.164
# Cramer's V : 0.167
For get.V just pass the data frame or matrix, not the table:
get.V <- function(y) {
col.y <- ncol(y)
V <- matrix(ncol=col.y,nrow=col.y)
for(i in 1:col.y){
for(j in 1:col.y){
V[i,j] <- assocstats(table(y[,i],y[,j]))$cramer
}
}
return(V)
}
get.V(df)
# [,1] [,2]
# [1,] 1.0000000 0.1666667
# [2,] 0.1666667 1.0000000