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

272 The Professional Counselor | Volume 11, Issue 3 & Sink, 2013; Watson, 2017). Kaiser’s criterion is a standard for retaining factors with Eigenvalues (EV) ≥ 1. An EV represents the proportion of variance that is explained by each factor in relation to the total amount of variance in the factor matrix. The Kaiser criterion tends to overestimate the number of retainable factors; however, this criterion can be used to extract an initial factor solution (i.e., when computing the EFA for the first time). Interpreting the percentage of variance among items explained by each factor is another factor retention criterion based on the notion that a factor must account for a large enough percentage of variance to be considered meaningful (Mvududu & Sink, 2013). Typically, a factor should account for at least 5% of the variance in the total model. A scree plot is a graphical representation or a line graph that depicts the number of factors on the X-axis and the corresponding EVs on the Y-axis (see Figure 6 in Mvududu & Sink, 2013, p. 87, for a sample scree plot). The cutoff for the number of factors to retain is portrayed by a clear bend in the line graph, indicating the point at which additional factors fail to contribute a substantive amount of variance to the total model. Finally, in a parallel analysis, EVs are generated from a random data set based on the number of items and the sample size of the real (sample) data. The factors from the sample data with EVs larger than the EVs from the randomly generated data are retained based on the notion that these factors explain more variance than would be expected by random chance. In some instances, these four criteria will reveal different factor solutions. In such cases, researchers should retain the simplest factor solution that makes both statistical and substantive sense. Factor Rotation. After determining the number of factors to retain, researchers seek to uncover the association between the items and the factors or subscales (i.e., determining which items load on which factors) and strive to find simple structure or items with high factor loadings (close to ±1) on one factor and low factor loadings (near zero) on the other factors (Watson, 2017). The factors are rotated on vectors to enhance the readability or detection of simple structure (Mvududu & Sink, 2013). Orthogonal rotation methods (e.g., varimax, equamax, and quartimax) are appropriate when a researcher is measuring distinct or uncorrelated constructs of measurement. However, orthogonal rotation methods are rarely appropriate for use in counseling research, as counselors almost exclusively appraise variables that display some degree of inter-correlation (Mvududu & Sink, 2013). Oblique rotation methods (e.g., direct oblimin and promax) are generally more appropriate in counseling research, as they allow factors to inter-correlate by rotating the data on vectors at angles less than 90○. The nature of oblique rotations allows the total variance accounted for by each factor to overlap; thus, the total variance explained in a post–oblique rotated factor solution can be misleading (Bandalos & Finney, 2019). For example, the total variance accounted for in a post–oblique rotated factor solution might add up to more than 100%. To this end, counselors should report the total variance explained by the factor solution before rotation as well as the sum of each factor’s squared structure coefficient following an oblique factor rotation. Following factor rotation, researchers examine a number of factor retention criteria to determine the items that load on each factor (Watson, 2017). Commonality values (h2) represent the proportion of variance that the extracted factor solution explains for each item. Items with h2 values that range between .30 and .99 should be retained, as they share an adequate amount of shared variance with the other items and factors (Watson, 2017). Items with small h2 values (< .30) should be considered for removal. However, commonality values should not be too high (≥ 1), as this suggests one’s sample size was insufficient or too many factors were extracted (Watson, 2017). Items with problematic h2 values should be removed one at a time, and the EFA should be re-computed after each removal because these values will fluctuate