Application 3: Testing the Factorial Validity of Scores from a Measuring Instrument (Second-Order CF A Model)
Whereas the two previous applications focused on CF A first-order models, the present application examines a CF A model that comprises a second-order factor. As such, we test hypotheses related to the Beck Depression Inventory (Beck, Ward, Mendelson, Mock, & Erbaugh, 1961) as it bears on the nonclinical adolescent population. The example is taken from a study by Byrne, Baron, and Campbell (1993) and represents one of a series of studies that have tested for the validity of second-order BDI factorial structure for high school adolescents in Canada (Byrne & Baron, 1993, 1994; Byrne, Baron, & Campbell, 1993, 1994), Sweden (Byrne, Baron, Larsson, & Melin, 1995, 1996), and Bulgaria (Byrne, Baron, & Balev, 1996, in press). Although the purposes of the Byrne et al. (1993) study were to cross-validate and test for an invariant BDI structure across gender for Canadian high school students, we focus only on factorial validity as it relates to the female calibration sample. (For further details regarding the sample, analyses, and results, readers are referred to the original article.)
As noted in chapter 4, the CF A of a measuring instrument is most appropriately conducted with fully developed assessment measures that have demonstrated satisfactory factorial validity. Justification for CF A procedures in the present instance are based on evidence provided by Tanaka and Huba (1984), and on the aforementioned studies by Byrne and associates that BDI score data are most adequately represented by an hierarchical factorial
structure. That is to say, the first-order factors are explained by some higher order structure which, in the case of the BDI, is a single second-order factor of general depression. Let us turn now, then, to a description of the BDI, and its postulated structure.