Heywood Cases
- Occur in factor analysis when a variable provides only a single observed value (e.g., one individual or the same value for all).
- Cause a singularity in the matrix and can produce incorrect factor loadings.
- Common mitigations are removing the problematic variable (with loss of information) or using a different method such as principal components analysis.
Definition
Section titled “Definition”Heywood cases occur in factor analysis when there is a variable with only one observed value, which causes a singularity in the matrix and can result in incorrect factor loadings.
Explanation
Section titled “Explanation”When a variable contributes only a single observed value to the dataset, the covariance (or correlation) matrix used in factor analysis becomes singular. This singularity disrupts the factor analysis calculations and may lead to invalid or misleading factor loadings. Because the matrix cannot be properly inverted or decomposed in the usual way, the estimated factors and loadings can be incorrect.
Examples
Section titled “Examples”Single observed value for one individual
Section titled “Single observed value for one individual”If a variable is observed for only a single individual in the dataset, it creates a Heywood case. For example, in a dataset of physical measurements including height, weight, and shoe size, if only one individual has a shoe size of 13, then the variable “shoe size” would be a Heywood case.
Identical values across all individuals
Section titled “Identical values across all individuals”A Heywood case also occurs when a variable is observed for all individuals but all values are identical. For example, in the same dataset of physical measurements, if all individuals have the same eye color, the variable “eye color” would be a Heywood case because it has a single observed value for the entire dataset.
Notes or pitfalls
Section titled “Notes or pitfalls”- Heywood cases cause singularity in the analysis matrix and can lead to incorrect factor loadings.
- One approach is to remove the problematic variable from the analysis, which may result in loss of valuable information.
- Another approach is to use a different factor analysis method, such as principal components analysis, which the source indicates can handle Heywood cases more effectively.
Related terms
Section titled “Related terms”- Factor analysis
- Principal components analysis