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Factor analysis (FA) allows us to simplify a set of complex variables or items using statistical procedures to explore the underlying dimensions that explain the relationships between the multiple variables/items. For example, to explore inter-item relationships for a 20-item instrument, a basic analysis would produce 400 correlations; it is not an easy task to keep these matrices in our heads. FA simplifies a matrix of correlations so a researcher can more easily understand the relationship between items in a scale and the underlying factors that the items may have in common. FA is a commonly applied and widely promoted procedure for developing and refining clinical assessment instruments to produce evidence for the construct validity of the measure.

In the literature, the strong association between construct validity and FA is well documented, as the method provides evidence based on test content and evidence based on internal structure, key components of construct validity.^{1}^{2}

The applications of FA depend on the purpose of the research. Generally speaking, there are two most important types of FA: Explorator Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA).

Exploratory Factor Analysis (EFA) is widely used in medical education research in the early phases of instrument development, specifically for measures of latent variables that cannot be assessed directly. Typically, in EFA, the researcher, through a review of the literature and engagement with content experts, selects as many instrument items as necessary to fully represent the latent construct (e.g., professionalism). Then, using EFA, the researcher explores the results of factor loadings, along with other criteria (e.g., previous theory, Minimum average partial,^{3}^{4}^{5}

It is important to note that, often, Principal Component Analysis (PCA) is applied and described, in error, as exploratory factor analysis.^{2}^{,}^{6}^{7}^{7}

When prior EFA studies are available for your intended instrument, Confirmatory Factor Analysis extends on those findings, allowing you to confirm or disconfirm the underlying factor structures, or dimensions, extracted in prior research. CFA is a theory or model-driven approach that tests how well the data “fit” to the proposed model or theory. CFA thus departs from EFA in that researchers must first identify a factor model before analysing the data. More fundamentally, CFA is a means for statistically testing the internal structure of instruments and relies on the maximum likelihood estimation (MLE) and a different set of standards for assessing the suitability of the construct of interest.^{7}^{,}^{8}

Factor analysts usually use the path diagram to show the theoretical and hypothesized relationships between items and the factors to create a hypothetical model to test using the ML method. In the path diagram, circles or ovals represent factors. A rectangle represents the instrument items. Lines (→ or ↔) represent relationships between items. No line, no relationship. A single-headed arrow shows the causal relationship (the variable that the arrowhead refers to is the dependent variable), and a double-headed shows a covariance between variables or factors.

If CFA indicates the primary factors, or first-order factors, produced by the prior PAF are correlated, then the second-order factors need to be modelled and estimated to get a greater understanding of the data. It should be noted if the prior EFA applied an orthogonal rotation to the factor solution, the factors produced would be uncorrelated. Hence, the analysis of the second-order factors is not possible. Generally, in social science research, most constructs assume inter-related factors, and therefore should apply an oblique rotation. The justification for analyzing the second-order factors is that when the correlations between the primary factors exist, CFA can then statistically model a broad picture of factors not captured by the primary factors (i.e., the first-order factors).^{9}^{10}

Factor analysis methods can be incredibly useful tools for researchers attempting to establish high quality measures of those constructs not directly observed and captured by observation. Specifically, the factor solution derived from an Exploratory Factor Analysis provides a snapshot of the statistical relationships of the key behaviors, attitudes, and dispositions of the construct of interest. This snapshot provides critical evidence for the validity of the measure based on the fit of the test content to the theoretical framework that underlies the construct. Further, the relationships between factors, which can be explored with EFA and confirmed with CFA, help researchers interpret the theoretical connections between underlying dimensions of a construct and even extending to relationships across constructs in a broader theoretical model. However, studies that do not apply recommended extraction, rotation, and interpretation in FA risk drawing faulty conclusions about the validity of a measure. As measures are picked up by other researchers and applied in experimental designs, or by practitioners as assessments in practice, application of measures with subpar evidence for validity produces a ripple effect across the field. It is incumbent on researchers to ensure best practices are applied or engage with methodologists to support and consult where there are gaps in knowledge of methods. Further, it remains important to also critically evaluate measures selected for research and practice, focusing on those that demonstrate alignment with best practice for FA and instrument development.^{7}^{, }^{11}

The authors declare that they have no conflicts of interest.