Most multi-level models consider just two levels of analysis, in which the two levels have a hierarchical structure – that is, units from one level are nested within the other level (e.g., persons in groups). Another multi-level model allows for an examination of all of the levels – group, individual (perceiver and target), and dyad. Known as the social relations model (SRM;Kenny, 1994; Kenny & La Voie, 1984), it can be used to empirically determine the amount of variance in a particular measure at each level. To do so, there must be a group of persons such that each group member rates every other member in the group on leadership. Such a design is commonly called a round-robin.
Self-ratings may be constructed as well, but they are set aside because they may be qualitatively different from ratings of others. (In a later section of this chapter, we return to the question of what to do with self-ratings.)
The SRM includes five random variables, each of which is a source of variance:
Group: differences among groups in how much leadership is perceived.
Perceiver (individual): differences among individuals in how much leadership they perceive in others, in general.
Target (individual): differences among individuals in how much each is perceived as a leader, in general, by the others.
Relationship (dyad): idiosyncratic perceptions of the extent to which someone is perceived as a leader by a particular other.
Error: measurement noise in the judgment of leadership.
We review each of these components in more detail.
Is there more leadership in some groups than others? Group variance would be indicated by a large amount of variance in the group means of leadership. There are two opposing ways to think about whether leadership would show group effects. The first perspective on leadership is that it is a zero-sum phenomenon; that is, in a group one person becomes the leader and the others become followers, as in a rank ordering. In this case, there would be no expectation that leadership would vary by group, because one member tends to emerge as a leader in each group. The second view is that leadership represents a potential that may or may not be met. For example, if a group fails, the cause for the failure may be that it lacked actual or perceived leadership (Lord et al., 1978). Within this perspective, one would expect group variance, because leadership could be unequally allocated among groups due to different leadership styles, differential participation of the individual group members, unequal power expressed or assigned to each group member, different leadership prototypes (Hogg, 2001), or different group social constructions of leadership responsible for a specific or co-constructed perception of leadership (Meindl et al., 1985).
The perceiver effect represents how much individuals see leadership in others in general: Do some people view others in general as leaders, whereas others do not? For leadership, the perceiver is probably the least theoretically interesting component. However, for measures of socio-emotional leadership (i.e., leadership focusing on member relations, rather than productivity), the perceiver effect might reflect how much the person enjoys being in the group, how much the individual likes the other group members, and how much the person is involved and participates in group activities.
The target effect represents the extent to which a person is seen as a leader in the group; target variance taps into whether people agree as to how much leadership each member exhibits. With social perception, a qualification becomes necessary: A person may be seen one way by members of the group, but the person may not actually be that way. In other words, perception may not necessarily match reality. At the same time, it can be argued that a major part of being a leader is being seen by other group
members as a leader. In this sense, individuals who are perceived as showing more leadership are actually leaders, whereas those perceived as showing less leadership are actually followers. Consensus about the degree to which members are leaders in the group could be based on the amount of influence each person actually has or on shared stereotypes about how leaders are supposed to behave (e.g., leaders are tall, attractive, white males who talk a great deal).
The relationship effect represents the idiosyncratic perception that a perceiver has of a target’s leadership. In the context of leadership ratings, the bulk of relationship variance would represent disagreement between perceivers, but it might also reflect personal preferences or alliances between particular group members. Moreover, leadership, especially socioemotional leadership, might potentially exist at the level of the relationship, as it better reproduces dyadic asymmetries among group members. That is, some members of the group may be more in need of leadership than other members of the group, and those members who are in need of leadership may find it from different members. Yet another view of the relationship effect is that it represents the biases and needs of the perceiver. We return to this notion when we discuss the difference between self-perception and other perception later in this article.
Error represents sources of variance in the judgments that are neither systematic nor replicable. To separate error variance from the relationship variance in the SRM, at least two measures of the construct must be present – either repeated measures in time or different measures of the same construct. For instance, leadership might be measured by five items:
contribution to the task, influence over the group’s solution, leadership exhibited, control of the group’s activities, and preference to have as a leader (Lord, Phillips, & Rush, 1980). As discussed later in this chapter, the SRM makes it possible to conceptualize four different types of error.
The SRM is a random effects model. That is, its components are random variables. Consider the target effect: The interest in a study of leadership is not in knowing which individuals have the highest and lowest target effects, but rather in the amount of variance produced by perceptions of targets in the population. Thus, the major focus in a univariate SRM analysis is the sources of variance in the perception of leadership.
A further complication of the SRM is that it includes two sources of nonindependence that can be interpreted as reciprocity correlations. The first source is a correlation between a person’s perceiver and target effect:
If Jill is seen by others as leader, does she think that others are leaders?
This correlation might well be negative. That is, if Jill is seen as leader,
she may think the others in the group are not leaders. This correlation, which has been called generalized reciprocity, is defined only if there is both perceiver and target variance. The second source involves a correlation between two relationship effects from the same dyad. If Jack especially thinks that Jill is a leader (i.e., more than Jack thinks others are leaders and more than others think Jill is a leader), then does Jill especially think that Jack is a leader (i.e., more than Jill thinks others are leaders and more than others think Jack is a leader)? This correlation, which has been called the dyadic reciprocity correlation, could be negative – for instance, if the group is very hierarchical. Later in this chapter, we discuss the correlations between two variables measured in a round-robin design.
The estimation of the SRM is complicated because it contains five random variables and two covariances. We consider the rather complicated statistical details in the estimation of the SRM variances and covariances in the last section of this chapter.