Exploratory Factor Analysis: A Brief Introduction

in this presentation I provide a brief introduction to exploratory factor analysis in Applied Research there are three approaches often described by researchers as factoring analytic techniques principal components analysis exploratory factor analysis and confirmatory factor analysis while EF a and CFA are truly approaches for factor analysis principal component analysis is not pca appears similar to EF a and cfa on the surface but the distinctions are not superficial similarly the distinctions between EF a and cfa are also quite important each of these three methods has a distinct purpose and each is often used in the development of new instruments while pca EFA and cfa are three distinct analytic methods there are also complementary methods that can be used together to strengthen research instruments and outcomes this presentation is an introduction to exploratory factor analysis exploratory factor analysis or EF a for short is an analytic method used for the development of psychometrically sound and measurement instruments suppose you are interested in measuring the extent to which someone might be swayed by social influences unable to find an existing instrument you decide to create your own you create a construct map and write many items that might help you measure social influence the questions you write will correspond to the construct map but their specific content will be based on your theoretical knowledge of the construct that is what you know from previous research when you write a lot of items you end up with a lot of data that can be difficult to interpret this is where EFA comes into play the extent to which responses of items vary together is called covariance we can create a matrix of covariances of items just like we would create a matrix of correlations the goal of EFA is to identify the groups of items that when considered together explain as much of the observed covariance as possible each of these groups of items is called a factor EF a helps us to find meaningful patterns by identifying items which responses seem to clump together or vary in a predictable way it's up to the researcher to think about the content of the items in each group to determine what it is that those items have from a theoretical and conceptual perspective using factors instead of items makes analysis and interpretation simpler because it allows the researcher to work with a simpler more parsimonious presentation of the data in which each aspect of a construct is represented by a single score instead of individual responses to multiple items EFA is an exploratory descriptive approach this means that it can identify many different factor solutions for data set but some of those solutions may not make sense theoretically it also means there is no statistical way to know if the extracted factors are correct or not these decisions are up to the researcher EFA identifies factors but the researcher must decide which ones make sense for the construct of interest one of the guiding tenets of science is parsimony this means that as scientists we should always look for the simplest way to explain and present information within the context of EFA this means we want to identify the fewest number of factors necessary to explain the maximum amount of Co variation among the item responses as possible the EFA process consists of three distinct steps extraction rotation and interpretation when we conduct an EF a the software will extract the same number of factors as there are items included in the analysis the researcher must decide the appropriate number of factors to retain and interpret the most common ways to do this are to review the eigen values associated with each factor and the scree plot for the overall analysis when we conduct an EF a we get values called factor loadings that describe the relationship between each item in each extractive factor factor loadings communicate how much of the variance observed within the variable can be attributed to the factor factor loadings have relative value meaning that higher factor loadings indicate stronger relationships between items and factors when we describe the magnitude of the relationships between items and factors we talk about their loadings to describe the magnitude of a factor we talk about its eigenvalue a factors eigenvalue is the sum of the squared factor loadings for that factor so if five appear to load on a single factor we would square the loading of each factor and then sum the squared values and that will give us the eigenvalue for that factor as a general rule of thumb we begin our initial review of extracted factors by considering only vector to the eigen values greater than or equal to 1.0 this is sort of an arbitrary rule but it gives us a good starting point because our goal is to explain as much of the variation responses as possible with as few factors as possible we're better off with fewer factors that each have larger eigen values keep in mind that ultimately the factor solution we choose should make sense from a theoretical and conceptual standpoint the theoretical and conceptual understanding is more important than the statistical understanding but we can use statistics to verify our understanding of the theory and to approve upon the questions we ask in order to measure concepts related to that theory correctly in addition to or instead of considering eigen values we can begin deciding how many of the extracted factors to retain by inspecting the scree plot when we evaluate eigen values directly we're considering their absolute size and comparing that size to a cut-off values such as 1.0 when we evaluate a scree plot we are actually considering the relative sizes of the eigen values instead of their absolute size and whether they meet that specific criterion to determine the best number of factors to retain using a scree plot we plot two lines one that fits the vertical shape of the plot and one that fits the horizontal shape of the plot the point where these two lines cross is called the elbow of the plot we then begin consideration of the extracted factors by thinking about only those factors that fall to the left of the elbow in this example we would begin our investigation by considering the first six factors that have been extracted EFA offers a feature called rotation to help the researcher to better understand the relationships between items and factors as well as the relationships between factors by changing the perspective from which data are viewed imagine the data points exist in the three-dimensional space all the rotation does is rotate that 3-dimensional space to allow us to take on a new perspective or see things from a different angle this is analogous to putting a globe so that we can see the map of the world from different angles in doing this the factor loadings for each item become larger for the factor that it best measures and smaller for the other factors in the solution we're not changing data values or the relationships between data points we're simply looking at the information from a different angle the decision to rotate or not to rotate a factor solution depends on the number of factors extracted in the extent to which each item loads on just one or more than one different factor if we extract two or more factors and items load on to more than one factor with a loading greater than zero point three we may choose to rotate the solution to change the perspective from which we view the data and the relationships with the factors the type of rotation we use depends on whether the multiple factors are theoretically correlated with each other or not if the multiple factors should correlate with each other we would use an oblique rotation if the multiple factors should not correlate with each other we would use an orthogonal rotation the specific rotation technique we use once we determine whether to use an orthogonal or oblique rotation is often a matter of trial and error it's not unusual to try more than one rotation within a family to see which approach makes the factors most interpretable and consistent with the theoretical construct of interest the final step in the EFA process is that of interpretation this step is exactly what it sounds like it's up to the researcher to determine the aspect of the construct that is being measured by each factor and then to name those factors accordingly EFA is not without its limitations it is most important to remember that EF a is driven by the data and not by the theory underlying the data this means that with the same questions it is feasible that the best solution yielded by an EF a could change for each sample of participants also the guidelines for making decisions throughout the EFA process or rules of thumb not strict rules this is a nice feature because it allows the researcher flexibility to make sure that the final solution makes sense for the theoretical and conceptual perspective but it's also limitation because such a subjective process could result in several different correct solutions it's of utmost importance that the researcher understand construct of interest in the theoretical relationships around that construct to make good decisions throughout the EFA process here are some sources that you might find helpful if you'd like to learn more about the topics introduced in this presentation

Channel: Frances Chumney

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Length: 9min 8sec (548 seconds)

Published: Mon Sep 26 2016