# FactorAssumptions

Set of Assumptions for Factor and Principal Component Analysis. Tests for Kaiser-Meyer-Olkin (KMO) and Communalities in a dataset. It provides a final sample by removing variables in a iterable manner while keeping account of the variables that were removed in each step.

## Installation

- You can install from CRAN
- You can install the released version of FactorAssumptions from Github

```
install.packages("FactorAssumptions")
## install devtools if not already
if (!requireNamespace("devtools", quietly = TRUE)) {
install.packages("devtools")
}
## install FactorAssumptions from Github
devtools::install_github("storopoli/FactorAssumptions")
```

## What is KMO and Communalities?

*Factor Analysis* and *Principal Components Analysis* (PCA) have some precautions and assumptions to be observed (Hair et al. (2018)).

The first one is the KMO (Kaiser-Meyer-Olkin) measure, which measures the proportion of variance among the variables that can be derived from the common variance, also called systematic variance. KMO is computed between 0 and 1. Low values (close to 0) indicate that there are large partial correlations in comparison to the sum of the correlations, that is, there is a predominance of correlations of the variables that are problematic for the factorial/principal component analysis. Hair et al. (2018) suggest that individual KMOs smaller than 0.5 be removed from the factorial/principal component analysis. Consequently, this removal causes the overall KMO of the remaining variables of the factor/principal component analysis to be greater than 0.5.

The second assumption of a valid factor or PCA analysis is the communality of the rotated variables. The commonalities indicate the common variance shared by factors/components with certain variables. Greater communality indicated that a greater amount of variance in the variable was extracted by the factorial/principal component solution. For a better measurement of factorial/principal component analysis, communalities should be 0.5 or greater (Hair et al. (2018)).

## Vignette

I encourage you to check the vignette on how to use the package.

# References

Hair, Joseph F., William C. Black, Barry J. Babin, and Rolph E. Anderson. 2018. *Multivariate Data Analysis*. 8th ed. Cengage Learning.