Factor Loading

In factor analysis, a value indicating the strength of the relationship between an observed variable and an underlying latent factor.

Source: Spearman 1904

A factor loading shows how strongly a measured variable is related to an underlying latent factor, much like a correlation between the two. A high loading means the variable closely reflects that factor and is a good indicator of it, while a low one means the variable has little to do with it. Examining the loadings shows which items belong to which factor, and so reveals what each factor represents. The strength of the link between item and factor is what it captures. Kline (2015) describes this.

Source: Kline 2015

A factor loading is interpreted by its magnitude and sign: a large absolute value indicates a strong relationship between the variable and the factor, so the variable is a good indicator of it, while a value near zero indicates little relationship. The sign shows the direction. Rough thresholds, such as loadings above a certain value, are used to decide which variables define a factor. So a factor loading is interpreted as showing how strongly and in which direction a variable relates to a factor, with high loadings marking the variables that characterise each factor, which guides the naming and interpretation of the factors in the analysis.

Source: Spearman 1904

Factor loadings relate to communality in that the communality of a variable, the proportion of its variance explained by the common factors, is the sum of its squared loadings across those factors. Each squared loading gives the share of the variable's variance explained by that factor. So factor loadings and communality are linked, with the loadings determining how much of each variable's variance the factors account for, and summing the squared loadings gives the communality, which is why variables with high loadings on the retained factors have high communalities and are well represented by the factor solution.

Source: Spearman 1904

Strong factor loadings are those with large absolute values, indicating that a variable is closely related to a factor and is a good indicator of it, while weak loadings, near zero, indicate little relationship. Conventional guidelines treat loadings above a threshold such as around 0.3 to 0.4 as meaningful, though these are rules of thumb. So strong and weak factor loadings distinguish variables that define a factor from those that do not, with strong loadings identifying a factor's indicators and weak ones suggesting a variable belongs elsewhere or is poorly captured, and these judgements, guided by thresholds and interpretability, shape how the factors are defined.

Source: Spearman 1904

Factor loadings are important because they are the basis for interpreting a factor analysis, showing which variables relate to which factors and thus what each factor represents. They determine how factors are named and understood and which variables best measure each construct. So factor loadings matter for making sense of a factor solution, since the pattern of loadings reveals the structure of the latent factors and identifies the indicators of each, which is central to interpreting the factors, developing measurement scales, and deciding which variables to retain, making the loadings the key output examined when interpreting factor analysis.

Source: Spearman 1904