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Multiple regression powerful of methods for examining specific scientific hypotheses and relationships among experimental, quasiexperimental, and nonexperimental data. Typically, multiple regression is used as a data-analytic strategy to explain or predict a criterion (dependent) variable with a set of predictor (independent) variables. Wampold and Freund (1987) provided an important and useful overview of the practical uses of multiple regression procedures for counseling research. They also described the distinction between simultaneous, stepwise, and hierarchical regression. In short, simultaneous regression involves cases in which the investigator enters all of the predictors into the analysis at once. Stepwise regression involves choosing which predictors to analyze on the basis of statistics. Hierarchical regression involves theoretically based decisions for how predictors are entered into the analysis. Simultaneous regression and stepwise regression are typically used to explore and maximize p rediction, whereas hierarchical regression is typically used to examine specific theoretically based hypotheses (Aron & Aron, 1999; B. H. Cohen, 2001). For an extensive description of how these methods of multiple regression are computed, please see Pedhazur (1982).
Although Wampold and Freund (1987) noted that use of multiple regression procedures in counseling research was uncommon, it appears that their overall use has become more frequent in recent years. Wampold and Freund reported that only 14% of the research described in articles published in the Journal of Counseling Psychology used multiple regression procedures. During the years 1997-2001, of the quantitative research articles published in the Journal of Counseling Psychology and the Journal of Counseling & Development, 26.82% (70) have used some form of multiple regression (not including structural equation modeling, hierarchical linear modeling, canonical analysis, or any of the various analysis of variance procedures). Thus, the use of multiple regression in explaining relationships among counseling variables of interest has become quite common.
Until the 1990s, stepwise regression was one of the most frequently used statistical methods in psychological research (Thompson, 1989). Like other researchers who have focused efforts on developing appropriate methods of multiple regression (J. Cohen & Cohen, 1983; Pedhazur, 1982), Wampold and Freund (1987) warned against the routine use of stepwise regression. Stepwise, forward, and backward methods of regression have received more criticism than any of the other forms of multiple regression (Aron & Aron, 1999; Chatterjee & Price, 1991; B. H. Cohen, 2001). Often, these methods are criticized because they produce unstable results that are sample specific and do not accurately or consistently reflect the existing relationships within the population. Furthermore, stepwise methods have often led to incorrect computations due to the disregard of appropriate degrees of freedom, as well as inappropriate conclusions regarding the relative importance of predictor variables that are statistically dependent on variabl es already entered into the analysis (Huberty, 1989; Thompson, 1989). Among articles published in the Journal of Counseling & Development and the Journal of Counseling Psychology from 1997-2001, only one has reported using stepwise regression. Perhaps, articles such as "Why Won't Stepwise Methods Die?" (Thompson, 1989), "Stepwise Regression and Stepwise Discriminant Analysis Need Not Apply Here: A Guidelines Editorial" (Thompson, 1995), and "Problems With Step-Wise Regression in Research on Aging and Recommended Alternatives" (Scialfa & Games, 1987) have been effective in getting the message about stepwise regression across to counseling researchers. It is also possible that the nature of counseling research has shifted from an exploratory focus to a clearer focus on theory testing. The latter explanation is, perhaps, a more appropriate reason for not using stepwise regression, because some quantitative methodologists still believe that stepwise regression is appropriate for exploratory purposes (Aron & Aron, 1999; B. H. Cohen, 2001).
Although the routine and inappropriate use of stepwise regression has seemingly been eradicated, new problems surrounding the use of multiple regression procedures in counseling research have emerged from the routine use of another form of regression: hierarchical regression. Almost half of the 70 articles (34, 48.57%) published in the Journal of Counseling Psychology and the Journal of Counseling & Development that have reported use of multiple regression have specifically used hierarchical multiple regression. As Scarr (1985) implied, the prolonged, routine use of any data-analytic strategy often leads to the violation of assumptions inherent in the strategy and neglect of essential guidelines grounded in its appropriate use. Editors and readers alike should beware not only because hierarchical regression has become a routine analytic procedure, but also because several methodological errors may be found surrounding its use in counseling research.
The intent of the current article is to improve subsequent counseling research investigations using hierarchical regression procedures by refreshing basic and necessary guidelines of hierarchical regression procedures that should no longer be ignored. I conducted a content analysis of quantitative research studies published in the Journal of Counseling Psychology and the Journal of Counseling & Development (during the years of 1997-2001) that used hierarchical multiple regression as a primary data analytic procedure by taking a closer look at the logic that researchers have used when using this method. A brief example illustrating the importance of the specific hierarchical order of predictor variable entry in hierarchical regression is provided. Finally, in cases for which appropriate guidelines of hierarchical regression are not feasible, common alternatives are briefly discussed.
HIERARCHICAL REGRESSION
Researchers are often interested in testing theoretical assumptions and examining the influence of several predictor variables in a sequential way, such that the relative importance of a predictor may be judged on the basis of how much it adds to the prediction of a criterion, over and above that which can be accounted for by other important predictors. As B. H. Cohen (2001, pp. 523-524) and Wampold and Freund (1987, p. 377) noted, hierarchical regression has been designed to test such specific, theory-based hypotheses.
In stepwise and simultaneous regression, a common focus is on determining the "optimal" set of predictors by limiting the number of predictors without significantly reducing the [R.sup.2] coefficient. These methods may also be used to examine the degree of standardized unit change in the criterion for every standardized unit change in the predictor variable when holding all other predictor variables in the model constant (at their mean) as indicated by the [beta] coefficient (standardized partial regression coefficient). However, in hierarchical regression, the focus is on the change in predictability associated with predictor variables entered later in the analysis over and above that contributed by predictor variables entered earlier in the analysis. For instance, a researcher may want to know the extent to which measures of positive expectations about counseling and client attendance rate predict therapy outcome over and above preexisting psychopathology variables. In such a case, hierarchical regression a nalysis would be appropriate, provided that preexisting psychopathology variables are entered into the analysis first, followed by positive expectations about counseling and then attendance rate (because preexisting psychopathology and expectancies precede attendance--an important consideration in hierarchical regression discussed later). Substantive theory would also be strongly considered in specifying the order of entry.
Change in [R.sup.2] ([DELTA][R.sup.2]) statistics are computed by entering predictor variables into the analysis at different steps. A predetermined, theoretically based...
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