Functional relations among constructs in the same content domain

Journal of Applied Psychology 1998, Vol. 83, No. 2, 234-246 Copyright 1998 by the American Psychological Association, Inc. 0021-9010/98/S3.00 Functional Relations Among Constructs in the Same Content Domain at Different Levels of Analysis: A Typology of Composition Models David Chan Michigan State University and National University of Singapore Composition models specify the functional relationships among phenomena or constructs at different levels of analysis (e.g., individual level, team level, organizational level) that reference essentially the same content but that are qualitatively different at different levels (M. T. Hannan, 1971; K. H. Roberts, C. L. Hulin, & D. M. Rousseau, 1978; D. M. Rousseau, 1985). Specifying adequate composition models is a critical component of good multilevel research. A typology of composition models is proposed to provide a framework for organizing, evaluating, and developing constructs and theories in multilevel research. Five basic forms of composition are described and illustrated. Implications of the typology are discussed. Organizational phenomena have the properties of dy- namic systems, with critical antecedents, processes, and outcomes conceptualized and measured at multiple levels of organizational analysis (e.g., individual, group, organi- zation). Because more researchers are beginning to real- ize that the organizational phenomenon under investiga- tion often is inherently multilevel as opposed to occurring at a single level or in a level vacuum, organizational stud- ies increasingly are adopting a multilevel approach. Sev- eral influential theoretical frameworks for multilevel re- search have been proposed (e.g., House, Rousseau, & Thomas-Hunt, 1995; Klein, Dansereau, & Hall, 1994; Rousseau, 1985). Excellent discussions on important mathematical issues related to the analysis of multilevel data (e.g., Bliese & Halverson, in press; Ostroff, 1993a) and analytical models for structuring multilevel data (e.g., Bryk & Raudenbush, 1987; McArdle & Epstein, 1987; Meredith & Tisak, 1990; Muthen, 1994; Willett & Sayer, 1994) also are available. However, despite the existence of broad theoretical David Chan, Department of Psychology, Michigan State Uni- versity, and Department of Social Work and Psychology, Na- tional University of Singapore. I thank Neal Schmitt, Daniel Ilgen, and Richard DeShon for their helpful comments on the article, and i am grateful to Steve Kozlowski for introducing me to multilevel research. An earlier version of this article was presented at the 1997 Annual Meeting of the Academy of Management in Boston, Massachusetts, August 1997. Correspondence concerning this article should be addressed to David Chan, Department of Psychology, 129 Psychology Re- search Building, Michigan State University, East Lansing, Mich- igan 48824-1117. Electronic mail may be sent to dchan@ pilot.msu.edu. frameworks and methodological advances, the fundamen- tal substantive issue of construct validation in multilevel research has not been addressed adequately. Accompa- nying the increased interest in multilevel research is an increased proliferation of new constructs at multiple lev- els. Unless we have explicit composition models to guide the development and validation of newly proposed con- structs in multilevel research, there is a danger of violating the scientific principle of parsimony. Organizational re- searchers could easily end up with a multitude of labels, all of which purportedly refer to scientific constructs but in reality have no incremental explanatory value. Compo- sition models specify the functional relationships among phenomena or constructs at different levels of analysis (e.g., individual level, team level, organizational level) that reference essentially the same content but that are qualitatively different at different levels (Hannan, 1971; Roberts, Hulin, & Rousseau, 1978; Rousseau, 1985). Specifying functional relationships between constructs at different levels provides a systematic framework for map- ping the transformation across levels. The explicit trans- formation relationships provide conceptual precision in the target construct, which in turn aids in the derivation of test implications for hypothesis testing. Unfortunately, the specification of functional relationships between con- structs has not always been adequate or even explicit in multilevel research. This is partly because no systematic frameworks for specifying functional relationships exist. An adequate typology of composition models addresses the above problems and contributes to multilevel research in at least two important ways. First, it provides an or- ganizing framework for existing focal constructs facilitat- ing scientific communication in multilevel research. Re- searchers can be more confident that they are referring to 234 COMPOSITION MODELS 235 the same construct when it is explicated according to the same form of composition. Meaningful replications and extensions of current findings then are possible. Apparent contradictory findings may be reconciled, and debates may be clarified. For example, many so-called inconsis- tent findings simply could be a result of confusion of terminology (i.e., comparing apples and oranges), and the confusion may become apparent when each study lo- cates its construct in the typology corresponding to the composition model. Organizing existing constructs also aids cumulation of research findings by providing a frame- work for performing meaningful meta-analytic studies in multilevel research. Second, a typology provides a conceptual framework for developing and validating new focal constructs and multilevel theories. As described later in this article, the typology of models could help compose new explanatory constructs from established ones. In addition, being cogni- zant of different models allows the researcher to consider alternative designs, measurements, and data analyses for testing competing hypotheses, modifying existing theories or developing new ones, or performing a more rigorous test of the original hypothesis. The purpose of this article is to propose a typology of composition models. A Typology of Composition Models The proposed typology is concerned with elemental composition; that is, situations in which data from a lower level are used to establish the higher level construct. In other words, the higher level construct is of a collective or aggregate nature and is construed as some form of combination of the lower level units. All lower level units play some substantive role in composing the lower level construct to the higher level construct, and the value of the higher level construct is not solely determined by any single lower level unit (i.e., each unit is used in some way or another, such as for computing the mean level). Note that the use of data from the lower level to establish the higher level construct does not imply that it is neces- sary to begin conceptualization at a level lower than the level of the target or composed construct. The starting level of conceptualization is dependent on the research question. For example, a researcher may start at the group level' with the established construct of group norms and then move down to the individual level to collect percep- tual data for subsequent aggregation to the group level to establish the construct of group norms. The focus on elemental composition is consistent with the actual con- straints and practice in empirical multilevel research. As noted by several researchers (e.g., Ostroff, 1993a; Roberts et al., 1978), we often do not have global indices of the higher level (organizational or group) variables of interest and hence have to rely on aggregated data from the lower level (individuals) to represent the higher level variable. Because the focus is on elemental composition, this article does not address the traditional issues of disaggregation and ecological fallacies (Cronbach, 1976; Hannan, 1971; Langbein & Lichtman, 1978). Table 1 presents the typology of composition models. The typology describes the basic forms composition mod- els can take. The forms described are ideal types. The five basic forms of composition models are: (a) additive, (b) direct consensus, (c) referent-shift consensus, (d) dispersion, and (e) process composition. A theory of the focal construct in a multilevel study may contain one or more of the five composition forms. The five forms of composition models in Table 1 are not presented in any specific order. The reader is cautioned against ordering the five forms in terms of the similarity of functional relationships between constructs. The simplistic notion of similarity of functional relationships is not an adequate way of representing the complexity in or guiding the de- velopment of composition forms because there is an infi- nite number of answers (i.e., dimensions) to the question, "Similar with respect to what?" As shown in Table 1, each composition model is defined by a particular form of functional relationship specified between constructs at different levels. Corresponding to each form of functional relationship is a typical opera- tional process by which the lower level construct is com- bined to form a higher level construct. Note that the opera- tional combination process is the typical form as opposed to a necessary consequence of the functional relationship specified. The column in Table 1 labeled empirical sup- port suggests what constitutes the forms of evidence needed to support the relevant functional relationships and to establish that appropriate combination rules are applied. To illustrate the forms of composition, examples from climate research are consistently used throughout 1 In describing the typology and throughout this article, the terms group and team are used interchangeably to refer to the level of the collection of individuals immediately higher than the individual level. Several researchers have distinguished groups and teams as the polar ends on a continuum of task interdependence (e.g., Salas, Dickinson, Converse, & Tannen- bauem, 1992). In addition, groups are often characterized by low role differentiation and low task differentiation, whereas teams are characterized by high role differentiation, high task differentiation, distributed expertise, and high levels of task in- terdependence (Sundstrom et al., 1990). The present typology is concerned with work groups or work teams in organizations. The terms groups and teams are used to refer to multiple individ- uals formed to perform some organizationally relevant task- functions. These individuals interact, exhibit task interdepen- dence, possess one or more shared goals, and are embedded in a larger organizational setting (Kozlowski et al., 1994, 1996; Salas etal., 1992). 236 CHAN Table 1 A Typology of Composition Models Functional relationships Typical operational combination Empirical support Example from climate research Additive model Higher level unit is a summation of the lower level units regardless of the variance among these units Summing or averaging lower level scores Validity of additive index (e.g., mean of lower level units) From psychological climate to organizational climate (Click's T1985] conceptualization) Direct consensus model Meaning of higher level construct is in the consensus among lower level units Within-group agreement to index consensus and justify aggregation Value of within-group agreement index (e.g., >•„,); validity of aggregated scores From psychological climate to organizational climate (Jarnes et al.'s [1984] conceptualization) Referent-shift consensus model Lower level units being composed by consensus are conceptually distinct though derived from the original individual-level units Within-group agreement of new referent lower level units to index consensus and justify aggregation Value of within-group agreement index (e.g., r^); validity of aggregated scores From psychological climate to organizational collective climate Dispersion model Meaning of higher level construct is in the dispersion or variance among lower level units Within-group variance (or its derivative) as operationalization of the higher level construct Absence of multimodality in within-group distributions of lower level scores; validity of dispersion index From psychological climate to climate strength Process model Process parameters at higher level are analogues of process parameters at lower level No simple algorithm; ensure analogues exist for all critical parameters Nomological validity for source and target constructs at their respective levels to distinguish shared core content from level-specific aspects From psychological climate development to organizational climate emergence the typology. I assume that a researcher collects climate data (i.e., individual perceptual responses on climate questionnaires) from hundreds of individuals across many organizations (or groups). For each composition model, I present examples of hypotheses and explanations of how the model can be applied to the data. Where appropriate, examples other than climate also are presented to clarify the composition form. The first two forms of composition are familiar to most researchers, and I will only describe them briefly. The remaining three forms are less familiar even though they characterize many focal constructs ex- amined in multilevel studies. As mentioned earlier, com- position models are seldom made explicit in existing mul- tilevel research. The following sections describe each of the five composition models in the typology. Additive Models Additive composition models specify a straightforward functional relationship between constructs at different lev- els. In such models, the meaning of the higher level con- struct is a summation of the lower level units regardless of the variance among these units. In additive composition models, the variance of the lower level units is of no theoretical or operational concern for composing the lower level construct to the higher level construct. The typical operational combination process is a simple sum or aver- age of the lower level scores on the lower level variable to represent the value on the higher level variable. The validity of the additive index (e.g., the mean) constitutes empirical support for the composition. In the climate example, the researcher may be interested in relating organizational climate to organizational perfor- mance. The researcher has an established measure of orga- nizational performance but he or she has to develop some conceptualization and measure of the construct of organi- zational climate. Adopting Click's (1985) conceptualiza- tion, the researcher stipulates that all organizations have an organizational climate that can be described as high or low on various dimensions regardless of the level of COMPOSITION MODELS 237 within-organization individual-level agreement. Within- organization agreement, according to this view, is an issue of measurement accuracy reflecting individual-level ran- dom error and sources of bias (see Glick, 1985, pp. 604— 605). Hence, using an additive composition model, the researcher averages the climate perceptions of individuals within each organization, regardless of the within-organi- zation variance, to represent the organizational climate variable. The organizational mean climate scores and the organizational performance variable then are correlated, and the validity coefficient (i.e., validity of the additive index; in this case, the mean) provides empirical support for the additive composition model. Clearly, whether the relationship between organiza- tional climate and psychological climate (i.e., individual- level climate perceptions) is additive or some other com- position form depends on how the construct of organiza- tional climate is conceptualized. For example, if the level of individual perceptual agreement within an organization is central in the substantive definition of organizational climate, then an additive composition model would be inappropriate because within-group (i.e., organization) variance among lower level units (i.e., individual percep- tions) becomes relevant in composing the lower level con- struct (i.e., psychological climate) to the higher level con- struct (i.e., organizational climate). In this case, a direct consensus composition model, described in the next sec- tion, is appropriate. Direct Consensus Models Direct consensus composition is probably the most fa- miliar and popular form of composition among multilevel researchers. This model uses within-group consensus of the lower level units as the functional relationship to spec- ify how the construct conceptualized and operationalized at the lower level is functionally isomorphic to another form of the construct at the higher level. The typical opera- tional combination process is using within-group agree- ment of scores to index consensus at the lower level and to justify aggregation of lower level scores to represent scores at the higher level (e.g., James, Demaree, & Wolf, 1984; Kozlowski & Hattrup, 1992; Ostroff, 1993b; Os- troff & Rothausen, 1997). This operational combination process has two components. The first component in- cludes an operationalization (i.e., a measure) of the con- ceptual definition for each of the two constructs (i.e., one at each level). For example, individual-level perceptual responses on a climate measure are used to operationalize psychological climate, whereas the mean of those individ- ual responses within an organization is used to operation- alize organizational climate. The second component spec- ifies the manner of and precondition(s) for combining the individual lower level measurements to represent the higher level measurement. For example, within-group agreement indexes such as the rwg index (James et al., 1984) may be calculated and some cutoff level of agree- ment is used to justify aggregation of individual re- sponses. In this example, the aggregation procedure and preconditions, together with the conceptual definition of the higher level construct, determine the meaningfulness and validity of the operationalization of the higher level construct. In the climate example, the researcher may follow James (1982) to construe psychological climate as an individual's perception or cognitive representation of the work environment in terms of the psychological meaning and significance to the individual. Organizational climate simply refers to the shared assignment of meanings among individuals within the organization. In this conceptualiza- tion, within-group agreement among individual climate perceptions indicates shared assignment of psychological meaning. It is this sharedness that constitutes functional equivalence between the climate constructs at the two levels. Hence, the definition of organizational climate is essentially the same as psychological climate, except that the former refers to the shared perceptions among the individuals. The conceptual relationship between the two forms of the construct at different levels then drives the manner in which the lower level construct composes to the higher level construct. So the researcher would proceed to check within-group agreement (group here refers to the organization) of individual climate responses using some agreement index (e.g., rn,s). High within-group agreement indicates consensus and justifies aggregation of individual climate responses to represent scores on the organiza- tional climate variable. In direct consensus composition, the lower level attri- butes need not be restricted to individual perceptions. Consensus, as indexed by within-group agreement, can apply to individual-level attributes such as cognitive abil- ity and styles, personality, mental representation, and be- havioral v