1997 Research Methods Forum
No. 2 (Summer 1997)
Introduction Jeffrey R. Edwards, Jeanne C. King
Regression Models for Discrete and Limited Dependent Variables Michael R. Frone
Hierarchical Linear Models in Organizational Research: Cross-level Interactions Mark A.Griffin, David A. Hofmann
The Qualitative Corner What Are We Doing When We Cite Others Work in the Methodological Accounts We Provide of Our Research Activities?Karen Locke
Current and Future Research Methods in Strategic ManagementMichael A. Hitt
Validity, Variance, and the Interpretation of Power Values Jose M. Cortina
Do Structural Equation Models Correct For Measurement Error?Richard P. DeShon
Hierarchical Linear Models in
Mark A. Griffin, The University of Queensland
David A. Hofmann, Texas A&M University
Organizations are inherently hierarchical structures that encompass a variety of hierarchical relationships. For example, the hierarchical structure that occurs when individuals are nested within work groups and work groups within departments results in three possible levels of analysis. Recently, more and more organizational scientists are recognizing this hierarchical structure by developing and testing theoretical models that span multiple levels of analysis (e.g., House, Rousseau, Thomas-Hunt, 1995).
In cases where variables exist at more than one level of analysis (e.g., a lower level outcome and both lower level and higher level predictors), there are three main options for data analysis. First, one can disaggregate the data such that each lower level unit is assigned a score representing the higher level unit within which it is nested and then use traditional analytical approaches (e.g., OLS regression). For example, all individuals might receive a score representing their work group=s cohesion with the investigation between cohesion and satisfaction carried out at the individual level. The problem with this solution is that OLS regression techniques assume that the random errors are independent, normally distributed, and have constant variance. This assumption, however, will likely be violated because the random error component within nested data will, in addition to a lower level unit component (e.g., individual), include higher level unit (e.g., group) random error which renders observations within units dependent -- since a portion of the random error is unit-level error which is constant across observations within units. In addition, this unit-level random error is also likely to vary across units, thereby violating the constant variance assumption (see Bryk & Raudenbush, 1992). In addition to violating this assumption, the disaggregation approach results in another problem. Statistical tests involving the variable at the higher level unit are based on the total number of lower level units (e.g., the effect of group cohesion is assessed based on the number of individuals, not the number of groups) which can influence estimates of the standard errors and the associated statistical inferences (Bryk & Raudenbush, 1992; Tate & Wongbundhit, 1983).
The second major approach is to aggregate the lower level units and investigate relationships at the aggregate level of analysis. For example, one could investigate the relationship between group characteristics and individual outcomes by aggregating the individual outcomes to the group level. The disadvantage of this approach is that potentially meaningful individual level variance in the outcome measure is ignored. In summary, the traditional choice has been between a disaggregated model that violates statistical assumptions and assesses the impact of higher level units based on the number of lower level units, or an aggregated model that discards potentially meaningful lower level variance.
Hierarchical linear models (HLM; Bryk & Raudenbush, 1992) represent the third major approach to dealing with hierarchically nested data structures. These models are specifically designed to overcome the weakness of the disaggregated and aggregated approaches discussed above. First, these models explicitly recognize that individuals within a particular group may be more similar to one another than individuals in other groups and, therefore, may not provide independent observations. More specifically, these approaches explicitly model both individual and group level residuals, therefore, recognizing the partial interdependence of individuals within the same group (this is in contrast to OLS approaches where individual and group level residuals are not separately estimated). Second, these models allow one to investigate both lower level unit and higher level unit variance in the outcome measure, while maintaining the appropriate level of analysis for the independent variables. Therefore, one can model both individual and group level variance in individual outcomes while utilizing individual predictors at the individual level and group predictors at the group level. Thus, hierarchical linear models overcome the disadvantages of the previous two approaches because one can model explicitly both within and between group variance (i.e., one is not forced to discard potentially meaningful within group variance) as well as investigate the influence of higher level units on lower level outcomes while maintaining the appropriate level of analysis.
Another particular strength of HLM is the way that it addresses cross-level interactions. In these interactions, a variable at a higher level of analysis moderates the relationship between variables at a lower level of analysis. Many management interventions seek to influence processes at the organization level so that relationships within organizations are modified. For example, training programs may increase the relationship between motivation and learning outcomes, selection programs may increase the relationship between applicant ability and later work performance, and employee assistance programs may decrease the relationship between work load and distress. In each example, the higher-level unit provides a context which modifies the relationships between lower-level unit relationships.
An example of the HLM approach to modeling cross-level interactions drawn from the area of personnel selection is presented below. The validity of personality predictors of work performance has attracted substantial research interest. One of the findings of this line of research is that conscientiousness significantly predicts individual job performance in a variety of settings. However, it has been argued that the strength of this relationship may vary across different types of work environments (Barrick & Mount, 1993). For example, conscientiousness may be a stronger predictor of work performance when the work environment is highly structured. In contrast, a less structured work environment may result in conscientiousness having a weaker impact on work performance. These propositions are illustrated in Figure 1 which depicts structure at the organizational level of analysis and depicts conscientiousness and performance at the individual level of analysis.
HLM is a 2-stage procedure for investigating data occurring at two levels of analysis. In the first stage, or Level-1 analysis, relationships among individual-level variables are estimated for each group. Specifically, regression parameters are estimated separately for each group. The parameter estimates from the Level-1 analysis are then used as outcome variables in the Level-2 analysis. The example below provides a brief example of the key steps of the HLM analysis. The subscripts are used to identify both individuals (i) and organizations (j). First, individual performance is predicted by individual conscientiousness.
Level 1: PERFij = ßj0 + ßj1CONCij + eij (1)
Different regression estimates are calculated in each organization for both the intercept (ßj0) and the influence of conscientiousness on performance (ßj1). The regression estimates vary across organizations and the organizational structure variable can be used to predict this variation in both ßj0 and ßj1. When variables are centered around the mean of the organization, the intercept represents the mean level of performance in each organization (see Hofmann & Gavin, in press). Using variation in the intercept as the dependent variable gives the following equation:
Level 2: ßj0 = g00 + g01STRUCTUREj + Uj0 (2)
This equation assesses the impact of organizational structure on mean levels of performance in organizations and is represented by the g01 parameter which is also labeled in Figure 1. Next, variation in the relationship between conscientiousness and performance becomes the dependent variable according to the following equation:
Level 2: ßj1 = g10 + g11STRUCTUREj + Uj1 (3)
This equation assesses the degree to which organizational structure moderates the relationship between conscientiousness and performance. The effect is represented by the g11 parameter in the above equation and is labeled in Figure 1.
The above example provides a brief summary of the basic steps involved in HLM to answer questions about cross-level relationships. With respect to cross-level interactions, the HLM approach has a number of advantages over traditional methods. First, the results from equation 1 can be used to assess the degree to which relationships vary across organizations. For example, if there is no systematic variation in the relationship between conscientiousness and performance (variance of ßj1), then no organizational measures can moderate the relationship between these individual measures. Second, the HLM procedure provides more stable estimates of the regression parameters for each organization when compared to OLS methods. Finally, by extending the number of variables in each equation presented above it is possible to build complex interactional models with variables at multiple levels of analysis.
Bryk, A. S. & Raudenbush, S. W. 1992. Hierarchical linear models. Newbury Park, CA: Sage.
Barrick, M.R. & Mount, M.K. (1993). Autonomy as a moderator of the relationships between the big five personality dimensions and job performance. Journal of Applied Psychology, 78, 111-118.
House, R., Rousseau, D.M., & Thomas-Hunt, M. (1995). The meso paradigm: A framework for the integration of micro and macro organizational behavior. In L.L. Cummings, & B.M. Staw (Eds.), Research in organizational behavior (Vol. 17, pp. 71-114). Greenwich, CT: JAI Press.
Hofmann, D.A., & Gavin, M.B. (in press). Centering decisions in hierarchical linear models: Theoretical and methodological implications for organizational science. Journal of Management.
Tate, R.L., & Wongbundhit, Y. (1983). Random versus nonrandom coefficient models for multilevel analysis. Journal of Educational Statistics, 8, 103-120.