Academic journal article The Journal of Parapsychology

Obliquity, Obliqueness, and the Factor Structure of the PBS

Academic journal article The Journal of Parapsychology

Obliquity, Obliqueness, and the Factor Structure of the PBS

Article excerpt

To the Editor:

Lawrence and his collaborators are free to investigate how well the Paranormal Belief Scale (PBS) subscale structure is accounted for by any factor model that they select--including an Orthogonal Seven Factor Model. However, neither Tobacyk, nor his co-authors, in their published research with the PBS ever refer to an Orthogonal Model (seven factor or otherwise) of paranormal belief. The reason for this lack of reference to an Orthogonal Model is straightforward--empirical evidence does not support the notion that the structure of paranormal beliefs (or the structure of the PBS) is mathematically orthogonal. This evidence that the structure of the PBS is not mathematically orthogonal has been clearly presented elsewhere (Tobacyk & Milford, 1983; Tobacyk & Thomas, 1997) and need not be repeated here.

The fact remains that if Lawrence wishes to accurately and fairly test the factor model underlying the construction of the PBS, he must incorporate estimates of the PBS subscale intercorrelations, as reported by Tobacyk and Milford (1983), into his confirmatory factor analysis (CFA). It is not satisfactory to ignore both the data indicating non-orthogonality and Tobacyk's disclaimer of ever advocating an Orthogonal Model--as Lawrence, Roe, and Williams (1997) have done when they force their PBS data to fit a seven factor orthogonal solution and then (mis-) attribute that seven factor orthogonal model to Tobacyk. It appears odd that, given Lawrence's evident preference for oblique (i.e., non-orthogonal) models, he is apparently blind to the evidence for obliqueness clearly provided by Tobacyk and Milford (1983).

Some of the arguments employed by Lawrence, Roe, and Williams (1998) imply confusion between the concepts of mathematical orthogonality and conceptual independence. Two (or more) subscales may be moderately correlated (i.e., not mathematically orthogonal), yet still may be employed as measures of conceptually/functionally independent dimensions--and all of this without implying a split personality" for the researcher using the subscales as measures of "different" dimensions!

For example, on the Graduate Record Exam (GRE) measure of academic potential, the Verbal (V) and Quantitative (Q) subscales are not mathematically orthogonal (i.e., the two subscales are moderately correlated). However, separate GRE-V and GRE-Q scores are customarily computed, reported, interpreted, and employed as functionally independent constructs. This is done because the separate GRE-V and

GRE-Q scores demonstrate discriminant validity and display differential predictive validity. For example, GRE-Q subscale scores may be particularly useful in selecting graduate students in physics or mathematics, while GRE-V scores may be especially suitable in selecting graduate students for history or literature. The routine procedures of computing, using, and interpreting GRE-V and GRE-Q subscale scores as separate constructs does not demonstrate (or imply) that these subscales are mathematically orthogonal (i.e., uncorrelated). Nor does it imply that the constructors of the GRE hold the belief that the two dimensions are mathematically orthogonal. Further, if the "true" factor structure of the GRE were being investigated by CFA, an estimate of the actual correlation between the two subscales would be used in the CPA model. That is, the subscale correlation would not be set to a mathematically orthogonal relationship (i.e., r = 0.0) simply because the GRE-V and GRE-Q are reported, used, and interpreted se parately. In fact, to set the GRE subscale correlation to 0.0, so as to fix orthogonality, would violate the subscale structure and therefore provide an inaccurate and misinformative test of the model!

The same logic applies to the PBS. Although the subscale structure of the PBS is not mathematically orthogonal, it is still reasonable to employ the seven PBS subscales as measures of different dimensions because the factors underlying the subscales are correlated in the low to moderate range. …

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