Selection
As stated in Section 3.2, it is necessary to select an alternative selection criteria to K1 for incorporation into the QIIPMR methodology. A literature review is conducted in Section 2.7 on three suitable alternatives to the K1 criterion; the scree plot, Parallel Analysis (PA) and the Minimum Average Partial (MAP) procedure. In order to carry out the criteria selection, a comparison between the three alternatives is necessary.
In Section 2.7 it was stated that multiple researchers, such as Zwick and Velicer (1982) and Lance and Vandenberg (2009), carried out comparison stud-
ies on selection criteria. Some of their comments were included in Section 2.7 for descriptive purposes. Based on their comparison results and comments on performance, three evaluating factors were selected by this study; evaluating factors against which the alternative selection criteria will be evaluated and compared. These evaluating factors are ease-of-use, subjective employment, and accuracy. Each of the three selection criteria (the scree plot, PA and MAP) are given a rating for each evaluating factor as indicated below.
• Ease-of-use: Poor, Good, or Excellent.
• Subjective employment: Not applicable, Mediocre, or Fully. • Accuracy: Poor, Good, or Excellent.
The rating options listed above are based on this study’s conclusions de- rived from the information gathered through the aforementioned comparison studies in Section 2.7. The rating allocated to each selection criteria, respec- tive of the evaluating factor, is completed with respect to the other selection criteria; the selection criteria are only evaluated against each other. For exam- ple: the selection criteria which is the most easily implemented will be scored Excellent, and the most inaccurate selection criteria will be scored poor.
The scree plot, according to Velicer et al. (2000) and Lance and Vanden- berg (2009), is the most easily implemented selection criteria of the three being assessed. The scree plot also employs subjective analysis to visually determine the number of PCs to retain; an analytical technique not employed by PA and MAP. In addition, the scree plot has adequate performance and accuracy in a study investigated by Lance and Vandenberg (2009), but is less accurate than PA and MAP. Furthermore, Lance and Vandenberg (2009) revealed it has adequate performance and accuracy, but when compared to PA and MAP, is less accurate.
Velicer et al. (2000) state that both PA and MAP boast impressive ac- curacy, but Lance and Vandenberg (2009) found PA to be marginally more accurate than the MAP procedure. Furthermore, the PA and MAP criteria are complicated and calculating-intensive criteria, thus requiring competent personnel to implement them effectively. Although the use of computer pro- grams improved their ease of implementation dramatically, PA is generally more easily implemented than MAP (Hayton et al., 2004). PA and MAP are purely objective, therefore the evaluating factor subjective employment does not apply to their mathematical calculations. The allocated ratings are tabu- lated in Table 3.1.
In order to improve the process of selecting the most appropriate selection criteria to employ in the QIIPMR methodology, the comparison between the
Table 3.1: Comparison ratings of the selection criteria
Selection criterion Ease-of-use Subjective employment
Accuracy
Scree plot Excellent Fully Poor Parallel Analysis (PA) Good Not applicable Excellent Minimum Average
Partial (MAP) procedure
Poor Not applicable Good
selection criteria and the allocated ratings are depicted in Figure 3.6. To simplify the graphical comparison, the rating choices Poor, Good, and Excellent were numerically represented by 1, 2 and 3 respectively. The same applies to the rating choices Not applicable, Mediocre, or Fully.
Figure 3.6: A comparison of three selection criteria
After assessing the information contained in Table 3.1 and depicted by Figure 3.6, it was decided to implement two of the three selection criteria in the QIIPMR methodology. Although the PA and MAP criteria share simi- lar characteristics, PA is chosen as the primary selection criteria because it is more accurate and easily executed than the MAP procedure, according to the sources consulted above. In addition, the PA criterion does not compromise the objectivity of the mathematical techniques employed by QIIPMR.
To support QIIPMR analysts in comprehending and validating the results of the PA criterion, it is beneficial to employ the scree plot as a secondary se- lection criteria. The scree plot will provide an alternative, visual interpretation
of the results; results that are independent of the PA criterion’s calculations. Therefore, the subjective analysis introduced by the scree plot does not influ- ence the mathematical computations of QIIPMR, but assists in the assessment of results. In addition, the scree plot would also indicate if an error has possi- bly been made through the execution of either criteria if agreeing results can not be found. Thus the additional resources required to employ the scree plot is justified by the aforementioned benefits it offers.
In conclusion, the PA criterion will be employed by the QIIPMR as the primary criterion to determine the number of PCs to retain, and the scree plot will fulfil the role of a supporting criterion, improving the comprehension of results obtained and facilitating the detection of possible mathematical errors.