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Comparison of WABA and DETECT to Hierarchical Linear Modeling (HLM)

Description of the Hierarchical Linear Modeling (HLM) approach

The basic idea of this approach (HLM) is that groups at the lowest level have intercepts (usually group averages) and slopes that represent the correlation among variables within each group. The intercepts (usually group averages) and slopes for each group vary across groups and the idea is to explain this variability. The intercepts and slopes at the lowest level are the "dependent" variables. There must be significant variation between groups on the dependent variable. Once this is established variables at the same level or more importantly variables at the higher level are used to predict the differences at lower levels. In general, the predictor variables at the higher level do not vary within the lower level. For example, a variable such as group size varies only between groups. The most elaborate description of this approach can be found in Byrk and Raudenbush (1992).

Compatibility of Within and Between Analysis (WABA/DETECT) with hierarchical linear modeling

WABA does not require that dependent variables be at only the lowest level of analysis. In this sense, the two approaches are very different. Using WABA, one might find a dependent and independent variables that vary at higher levels. If one finds effects that associate with multiple levels and if one is interested in the effects of higher levels on lower levels, HLM certainly could follow WABA. In this way they can complement each other.

In WABA, the question is whether a particular variable or relationship varies at one or multiple levels. In HLM, levels are assumed to be known, particularly for independent variables. Thus, WABA may test some assumptions made by HLM. In this way the approaches can complement each other.

In WABA variables that do not vary within groups have a given level to which they associate. Such variables are not the focus of WABA. But these variable are the focus of HLM. In this way the approaches may seem to differ. Nevertheless, WABA would ask of such a variable whether it varies at still higher levels.

In general, there are no parts effects in HLM. Only wholes are viewed as valid effects.

HLM is restricted to a 2 or 3 level formulation. WABA and DETECT can handle any number of levels.

There are reports that HLM fails with groups of size 2. In contrast, WABA includes all size groups.

Misconceptions and misunderstandings about WABA/DETECT

Statement #1. "Although the WABA model has recently been expanded to handle interactions at each level, cross level interactions to our knowledge are not possible" (Hoffman, Griffin, & Gavin, 2000, p502)

Response: The type of interaction that can be examined with WABA is one where, in one condition, the variables reflect individual level effects. In a second condition the same variables show group effects. Such analyses provide information about the conditions that seem to foster individual versus group effects. Clearly this is a cross level interaction. This type of interaction is not possible in HLM because the level is assumed as known. It is possible that HLM can handle some interactions across levels. A WABA approach to interactions can be found in Schriesheim, Castro, and Yammarino (2000). Also see the multiple-relationship analysis tutorial.

Statement #2. Since HLM can only handle three levels, we should not consider any more than three.

Response: WABA allows hierarchically nested variables to be consider at any number of levels because what it asks is, which levels may underlie a particular set of variables? WABA allows for situations where a set of variables and relationships may hold at several levels. In this case, HLM might be used to sort out how the network of variables fit together. WABA also allows for variables not to hold at levels above or below some focal level (see the multiple-level tutorial). Thus, because WABA asks a different set of questions than HLM, any number of levels can be considered.

Statement #3 WABA only considers levels at adjacent pairs handling only two levels at a time.

Response. This is partly true in that each level is considered sequentially. But it is also possible to consider an overall analysis that considers the lowest and highest levels.

Statement #4. WABA does not consider the slopes (correlations) within groups

Response: WABA considers pooled within-group correlations and uses them to assess the plausibility of alternative views of the data. WABA does not attempt to predict variability among such slopes, but does attempt to assess such variability (see the material about James' "rwg."). Using multiple-relationship analysis, within and between correlations within conditions are used to assess the plausibility of alternatives within conditions.

References

Byrk, A. & Raudenbush, S. (1992). Hierarchical linear models. Thousand Oaks, CA : Sage:

Hoffman, D., Griffin, M., & Gavin, M. (2000). The application of hierarchical linear modeling to organizational research In K. Klein & S. Kozlowski (Eds.) Multi-level theory, research, and methods in organizations. San Francisco: CA: Jossey-Bass (pp. 467-511).

Schriesheim, C., Castro, S., and Yammarino, F. (2000). Investigating Contingencies: An examination of the impact of span of supervision and upward contollingness on leader-member exchange using traditional and multivariate within- and between-entities analysis. Journal of Applied Psychology, 85, 659-677.

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