TPC Journal-Vol 11-Issue-3 - FULL ISSUE

The Professional Counselor | Volume 11, Issue 3 271 Three preliminary tests are necessary to determine if data are factorable, including (a) an inter-item correlation matrix, (b) the Kaiser–Meyer–Olkin (KMO) test for sampling adequacy, and (c) Bartlett’s test of sphericity (Beavers et al., 2013; Mvududu & Sink, 2013; Watson, 2017). The purpose of computing an inter-item correlation matrix is to identify redundant items (highly correlated) and individual items that do not fit with any of the other items (weakly correlated). An inter-item correlation matrix is factorable if a number of correlation coefficients for each item are between approximately r = .20 and r = .80 or .85 (Mvududu & Sink, 2013; Watson, 2017). Generally, a factor or subscale should be composed of at least three items (Mvududu & Sink, 2013); thus, an item should display intercorrelations between r = .20 and r = .80/.85 with at least three other items. However, inter-item correlations in this range with five to 10+ items are desirable (depending on the total number of items in the inter-item correlation matrix). Bartlett’s test of sphericity is computed to test if the inter-item correlation matrix is an identity matrix, in which the correlations between the items is zero (Mvududu & Sink, 2013). An identity matrix is completely unfactorable (Mvududu & Sink, 2013); thus, desirable findings are a significant p-value, indicating that the correlation matrix is significantly different from an identity matrix. Finally, before proceeding with EFA, researchers should compute the KMO test for sampling adequacy, which is a measure of the shared variance among the items in the correlation matrix (Watson, 2017). Kaiser (1974) suggested the following guidelines for interpreting KMO values: “in the .90s – marvelous, in the .80s – meritorious, in the .70s – middling, in the .60s – mediocre, in the .50s – miserable, below .50 – unacceptable” (p. 35). Factor Extraction Methods Factor extraction produces a factor solution by dividing up shared variance (also known as common variance) between each test item from its unique variance, or variance that is not shared with any other variables, and error variance, or variation in an item that cannot be accounted for by the factor solution (Mvududu & Sink, 2013). Historically, principal component analysis (PCA) was the dominant factor extraction method used in social sciences research. PCA, however, is now considered a method of data reduction rather than an approach to factor analysis because PCA extracts all of the variance (shared, unique, and error) in the model. Thus, although PCA can reduce the number of items in an inter-item correlation matrix, one cannot be sure if the factor solution is held together by shared variance (a potential theoretical model) or just by random error variance. More contemporary factor extraction methods that only extract shared variance—for example, principal axis factoring (PAF) and maximum likelihood (ML) estimation methods—are generally recommended for EFA (Mvududu & Sink, 2013). PAF has utility if the data violate the assumption of normality, as PAF is robust to modest violations of normality (Mvududu & Sink, 2013). If, however, data are largely consistent with a normal distribution (skewness and kurtosis values ≤ ±1), researchers should consider using the ML extraction method. ML is advantageous, as it computes the likelihood that the inter-item correlation matrix was acquired from a population in which the extracted factor solution is a derivative of the scores on the items (Watson, 2017). Factor Retention. Once a factor extraction method is deployed, psychometric researchers are tasked with retaining the most parsimonious (simple) factor solution (Watson, 2017), as the purpose of factor analysis is to account for the maximum proportion of variance (ideally, 50%–75%+) in an inter-item correlation matrix while retaining the fewest possible number of items and factors (Mvududu & Sink, 2013). Four of the most commonly used criteria for determining the appropriate number of factors to retain in social sciences research include the (a) Kaiser criterion, (b) percentage of variance among items explained by each factor, (c) scree plot, and (d) parallel analysis (Mvududu