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The Factor Analysis: Definition and Logic

Factor Analysis

The logic behind the factor analysis is grouping variables into factors, each of which represents several variables that correlate highly with one another (Field, 2013). Factors, therefore, attempt to explain the maximal quantity of common variance between the original variables by using a lower number of dimensions (Field, 2013).

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The purpose of factor analysis is to find “latent variables” (supposedly represented by factors after the analysis is done). It is suggested that factors reflect certain properties of a phenomenon that are not directly measured (Warner, 2013). However, factors remain formal constructs, and they should not be “reified” (Warner, 2013, p. 830). Another important purpose of factor analysis is dimension reduction (Warner, 2013).

Roughly speaking, the steps involved in factor analysis include creating a correlation matrix, identifying clusters of variables that have high correlation scores, and extracting factors on which the original values load highly (Field, 2013).

The matrices produced during factor analysis include the correlation matrix for the original variables, the non-rotated factor loadings matrix, the tables with eigenvalues for factors, etc. If a rotation is ordered, SPSS produces additional matrices (e.g., the transformation matrix and the rotated components matrix) (George & Mallery, 2016).

Rotation can be conducted if the researcher is unsatisfied with factor loadings–e.g., they are difficult to interpret, loadings are too high for one factor and too low for the others, etc. Rotation allows for making interpretation easier (Field, 2013).

An issue that emerges during factor analysis is the number of factors to be retained. Kaiser recommended retaining factors with eigenvalues>1 (as cited in Field, 2013), but for a different number of variables, factors with the eigenvalue=1 explain different amounts of variance (1% for 100 variables, 10% for 10 variables) (Field, 2013).

In the future, the author of this paper might use factor analysis to reduce the dimensions and perhaps find “latent variables” while assessing causes affecting the levels of depression.

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References

Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.

George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 step by step: A simple guide and reference (14th ed.). New York, NY: Routledge.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

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StudyCorgi. (2020, December 18). The Factor Analysis: Definition and Logic. Retrieved from https://studycorgi.com/the-factor-analysis-definition-and-logic/

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"The Factor Analysis: Definition and Logic." StudyCorgi, 18 Dec. 2020, studycorgi.com/the-factor-analysis-definition-and-logic/.

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StudyCorgi. "The Factor Analysis: Definition and Logic." December 18, 2020. https://studycorgi.com/the-factor-analysis-definition-and-logic/.

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StudyCorgi. 2020. "The Factor Analysis: Definition and Logic." December 18, 2020. https://studycorgi.com/the-factor-analysis-definition-and-logic/.

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StudyCorgi. (2020) 'The Factor Analysis: Definition and Logic'. 18 December.

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