How to use cronbach alpha to check the internal validity of the first dimension?

I have this example dataset that I applied MCA as follows

library("FactoMineR")
library("factoextra")

data(poison)

poison.active <- poison[1:55, 5:15]

res.mca <- MCA(poison.active, graph = FALSE)

The graph

I want to use cronbach alpha to check the internal validity of the first dimension. I know how to do it using PCA but it is not working with MCA as the variables are categorical.

>Solution :

Cronbach’s alpha is a measure of the internal consistency or reliability of a scale. It is typically used for continuous variables, so it may not be appropriate to use it with a categorical MCA solution. You could try using a different measure of internal consistency for categorical data, such as Kuder-Richardson 20 (KR-20) or Coefficient Alpha. These measures are similar to Cronbach’s alpha, but they are specifically designed for categorical data.

To compute KR-20 or Coefficient Alpha, you can use the alpha() function from the psych package in R. Here’s an example of how to compute KR-20 using the alpha() function:

library(psych)

# Compute KR-20 for the first dimension of the MCA solution
alpha(res.mca$ind$coord[,1])

This will compute KR-20 for the first dimension of the MCA solution. You can use the same approach to compute Coefficient Alpha by specifying the alpha argument in the alpha() function.

# Compute Coefficient Alpha for the first dimension of the MCA solution
alpha(res.mca$ind$coord[,1], alpha = "Coefficient Alpha")