Labeling Processes

    Instead of seeking an optimal behavior for a given actor and object, events can be constructed (or reconstructed) by seeking an optimal actor for a given behavior on an object or an optimal object for a given actor-behavior performance. Such identifications of people on the basis of incidents are called labelings by sociologists. Consider first the problem of finding an optimal actor. Instead of drawing behavior terms from [f' t'] as in equation (19), we must extract actor terms.

(37)

It is assumed that an identity is recalled from memory with transients equal to fundamentals, so (37) becomes:

(38)

The diagonal matrix, I_a, contains elements of [f' t'] that were not moved to z_a.

(39)

    Assuming that behaviors reappear in interaction fairly infrequently, it is reasonable to treat the behavior transients as equal to fundamentals - that is, each behavior is called fresh from memory as it is recognized.

(40)

Equation (40) lets object transients differ from object fundamentals, and by this rendering of the reidentification problem an object person's circumstantial state as a result of past events affects the calculation of an appropriate actor. However, an alternative construction is that labeling processes ignore all events prior to the last event - the one that is being explained - in which case object transients also would be set equal to fundamentals.

(41)

    In order to partition out an actor profile

(42)

we define a selection matrix

(43)

and a vector registering non-actor terms in [f' t']

(44)

Now with I_a and

(45)

and substituting a for b, equation (34) or equation (36) defines the solution for the optimal actor. For example, the parallel to (36) is

(46)

and the parallel to (34) is

(47)

    The solution for an optimal object identity to fit a given behavior by a given actor is a straightforward variation of the solution for an optimal actor. In particular, corresponding to z_a

(48)

Instead of the diagonal matrix, I_a

(49)

or

(50)

The selection matrix replacing S_a

(51)

The vector registering non-object terms in [f' t'] is

(52)

The solution vector is

(53)

and corresponding to (36) we have

(54)

and the parallel to (34) is

(55)

Incorporating Settings

    Smith-Lovin (1987b) showed that events change impressions of settings and that explicit consideration of the setting for an event changes impression-formation processes for actors, behaviors, and objects. She also showed through Interact simulations that the affect-control model reasonably embraces settings, in the sense that actions get adjusted appropriately when actors try to maintain sentiments about settings as well as about actors, behaviors, and objects of action.

    All of the previous derivations are the same when a setting is included explicitly in analyses, but matrices in Equation (15) change composition, leading to changes in the compositions of other matrices. The left side of (15) - t, defined in (9) - becomes a 12-element vector.

(56)

Additionally, vector t is expanded to include setting terms. Rather than show the expansion of t as given in (16) - the set of prediction terms presented in Smith-Lovin (1987a) and used inInteract-1988 - I will use this opportunity to show the prediction terms used in Interact-1991. For analyses without settings, this is the newer version of (16):

(57)

Analyses of Smith-Lovin's data indicate that we must expand (57) as follows in order to conduct analyses that take account of settings.

(58)

Additionally, coefficients in M are changed to the values that apply when settings are explicit.

    Changes in the order and composition of other matrices in the derivations follow directly from the changes in Equation (15), and the revised derivations need not be presented in detail.