Introduction

A Scree plot is a graphical representation of the variance explained by different principal components in an analysis. It is an effective method for visualizing the relative importance of each component in an analysis and for determining the number of components needed to explain a given set of data. The Scree plot is a popular tool used in a variety of fields, such as psychometrics, factor analysis, and data mining. In this article, we will discuss the theory behind Scree plots and how they can be used in data analysis.

Theory

Scree plots are based on the fact that the total variance in a dataset can be decomposed into components such that each component explains a different part of the variance. The components are usually derived from principal component analysis (PCA) or factor analysis. The components are then plotted against their respective eigenvalues (or variances), which represent the amount of variance explained by each component.

When a Scree plot is produced, the eigenvalues are plotted in descending order. If the eigenvalues decrease rapidly after the first few components, then this indicates that the data is well-described by a few components. Conversely, if the eigenvalues continue to decrease slowly, then this indicates that many components are needed to explain the data. The number of components that explain the majority of the variance is determined by “elbowing” the plot, which is when the eigenvalues decrease rapidly after a certain point.

Method

Producing a Scree plot is a straightforward process. The first step is to perform a PCA or factor analysis of the dataset. This will produce the eigenvalues for each component, which will be plotted on the graph. The eigenvalues should then be sorted in descending order and plotted against their respective components.

The next step is to determine the point at which the eigenvalues decrease rapidly. This is done by “elbowing” the plot, which is when the eigenvalues decrease rapidly after a certain point. This point is the number of components that explain the majority of the variance in the data.

Application

Scree plots are widely used in a variety of fields. In psychometrics, they are used to determine the number of factors that explain the variance in a dataset. In factor analysis, they are used to determine the most important components in an analysis. In data mining, they are used to determine the number of clusters needed to describe a dataset.

Conclusion

Scree plots are a useful tool for visualizing the variance explained by different components in an analysis. They are widely used in a variety of fields, such as psychometrics, factor analysis, and data mining. The Scree plot is produced by plotting the eigenvalues for each component in descending order and then determining the point at which the eigenvalues decrease rapidly. This point is the number of components that explain the majority of the variance in the data.

References

Chen, J., Wang, Y., & Wang, Y. (2017). Exploratory factor analysis of data with a scree plot. International Journal of Psychological Studies, 9(2), 1–7. https://doi.org/10.5539/ijps.v9n2p1

Costello, A. B., & Osborne, J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10(7). https://eric.ed.gov/?id=EJ768224

Fay, S. (2016). Scree plot analysis. Retrieved from http://www.statisticshowto.com/scree-plot-analysis/