EFAkmeans: K-means for EFA
In EFAfactors: Determining the Number of Factors in Exploratory Factor Analysis

EFAkmeans

R Documentation

K-means for EFA

Description

A function performs K-means algorithm on items by calling kmeans.

Usage

EFAkmeans(response, nfact.max = 10, plot = TRUE)

Arguments

`response`	A required `N` × `I` matrix or data.frame consisting of the responses of `N` individuals to `I` items.
`nfact.max`	The maximum number of factors discussed by EFAkmeans approach. (default = 10)
`plot`	A Boolean variable that will print the EFAkmeans plot when set to TRUE, and will not print it when set to FALSE. @seealso `plot.EFAkmeans`. (Default = TRUE)

Details

K-means is a well-established and widely used classical clustering algorithm. It is an unsupervised machine learning algorithm that requires the number of clusters K to be specified in advance. After K-means terminates, the total within-cluster sum of squares (WSS) can be calculated to represent the goodness of fit of the clustering:

WSS = \sum_{\mathbf{C}_k \in \mathbf{C}} \sum_{i \in \mathbf{C}_k} \|i - \mu_k\|^2

where \mathbf{C} is the set of all clusters. \mathbf{C}_k is the k-th cluster. i represents each item in the cluster \mathbf{C}_k. \mu_k is the centroid of cluster \mathbf{C}_k.

Similar to the scree plot where eigenvalues decrease as the number of factors increases, WSS also decreases as K increases. A "significant reduction" in WSS at a particular K may suggest that K is the most appropriate number of clusters, which in exploratory factor analysis implies that the number of factors is K. The "significant reduction" can be identified using the Second-Order Difference (SOD) approach. @seealso EFAkmeans

Value

An object of class EFAkmeans is a list containing the following components:

`wss`	A vector containing all within-cluster sum of squares (WSS).
`nfact.SOD`	The number of factors to be retained by the Second-Order Difference (SOD) approach.

Examples

library(EFAfactors)
set.seed(123)

##Take the data.bfi dataset as an example.
data(data.bfi)

response <- as.matrix(data.bfi[, 1:25]) ## loading data
response <- na.omit(response) ## Remove samples with NA/missing values

## Transform the scores of reverse-scored items to normal scoring
response[, c(1, 9, 10, 11, 12, 22, 25)] <- 6 - response[, c(1, 9, 10, 11, 12, 22, 25)] + 1


## Run EFAkmeans function with default parameters.

 EFAkmeans.obj <- EFAkmeans(response)

 plot(EFAkmeans.obj)

 ## Get the heights.
 wss <- EFAkmeans.obj$wss
 print(wss)

 ## Get the nfact retained by SOD
 nfact.SOD <- EFAkmeans.obj$nfact.SOD
 print(nfact.SOD)

EFAfactors documentation built on Sept. 30, 2024, 1:06 a.m.