Sense and nonsense in hierarchical regression analysis: Comment on Smyth.

Abstract

With use of illustrative data, analysis of covariance via hierarchical regression analysis is contrasted with hierarchical analyses used by Smyth (1982). It is shown that Smyth's analyses did not address the hypotheses he wished to test and that the results yielded by these analyses are meaningless. Hierarchical multiple regression analysis is popular among social scientists. Regrettably,, however, one often encounters the use of hierarchical analysis with what appear to be utter disregard of its requirements and lack of understanding of the nature of the answers it provides (for extensive discussions, see Cohen & Cohen, 1975; Pedhazur, 1982). The purpose of this comment is to discuss incorrect applications of hierarchical analyses in an article by Smyth (1982) published in this journal. It should be noted that the comment is addressed exclusively to this aspect of Smyth's article. Specifically, it deals with the first two paragraphs of his Results section and with his Table 1 (Smyth, 1982, pp. 558-559). Smyth (1982) stated that he resorted to hierarchical regression analysis "since conventional analyses of covariance (ANCOVAS) would ignore the possibility of the covariate (neuroticism) interacting with the experimental manipulations" (p. 558).

Perfectionism dimensions, perfectionistic attitudes, dependent attitudes, and depression in psychiatric patients and university students.

“…In each analysis, depression was predicted and the following variables were entered sequentially: (a) personality (e.g., SPP), (b) hassles (e.g., interpersonal hassles) or coping (i.e., perceived coping difficulties), and (c) the Personality × Hassles Product Vector or the Personality × Coping Product Vector. This analytic strategy is consistent with Pedhazur (1984) and allowed us to quantify, for instance, “the proportion of variance incremented by [the personality variable by hassles variable product vector], over and above the proportion of variance accounted for by” (Pedhazur, 1984, p. 480) both the personality variable and the hassles variable when predicting depression. To protect against the potential influence of multicollinearity, we centered predictor variables (Aiken & West, 1991).…”

“…In the second series of hierarchical regression analyses predicting depression, gender was entered in Step 1, perfectionism dimensions were entered in Step 2, and dysfunctional attitudes were entered in Step 3. This analytic strategy enabled us to assess, for example, “the proportion of variance incremented by [perfectionism dimensions], over and above the proportion of variance accounted for by” (Pedhazur, 1984, p. 480) both gender and dysfunctional attitudes when predicting depression. For psychiatric patients, perfectionism dimensions did not predict additional variance in depression beyond the effect of dysfunctional attitudes (see Table 4).…”

Relation of hassles and personality to subjective well-being.

“…As personality was expected to influence the appraisal of stressors (Lazarus & DeLongis, 1983), the personality measures were always entered first into each analysis. The hassles measure was always entered on the second step, and the interaction term, on the last (Pedhazur, 1984).…”

Hysteria scale elevations in low back pain patients: A risk factor for misdiagnosis?

“…The mean age of the male low back pain patients was not significantly different from that of the male control subjects; however, the female low back pain patients were significantly older than the female normal control subjects, t (112) = 4.22, p < .0001 . In order to determine if this age difference was a relevant variable that should be used as a covariate in further analyses, the relative variance contributions of age and diagnostic status were assessed according to the procedure outlined by Pedhazur (1984). Only on the Hy5 subscale was age a significant factor, F (1, 91) = 7.325, p < .01 .…”