Instabilities in the Solution

    Simulations have revealed that the surmising-from-mood model is unstable in that it sometimes yields profiles that are beyond the empirical range of identity profiles. The source of the instability can be discovered by developing a somewhat simplified version of the solution.

   Assume that we have observed an actor engaging in a disconfirming behavior with fundamental profile

(100_1)

toward an object person with transient profile

(100_2)

while displaying a mood with fundamental profile:

(100_3)

We now seek to assign the actor a new identity with fundamental profile

(100_4)

such that the amalgamation of the observed mood with the unknown actor identity

(100_5)

or - employing (61) with the special symbols in use here -

(100_6)

equals the transient produced by an actor with the unknown identity engaging in the given behavior toward the given object.

(100_7)

This equality can be viewed as a difference

(100_8)

This can be interpreted as meaning that we want to select the new actor identify so as to minimize the difference in (82) while also minimizing the deflections for behavior and object as usual.

The right term in (100_7) is defined by the portion of (15) that relates to actor impressions

(100)

so the overall difference in (100_8) is

(101)

    The unknown profile for the actor identity can be drawn from the final term in the equation above by modifying matrices used in event construction as follows. From (40)

(102)

From (43)

(103)

From (44)

(104)

Now we can write

(105)

so (101) becomes

(106)

Rearranging terms gives

(107)

and then

(108)

    The inverse matrix in (108) is of immediate interest since instability in the solution suggests that the matrix being inverted sometimes is singular. To explore this further we have to expand the parameter matrices with estimated coefficients, setting statistically-non-significant values to zero in order to aid simplification.

(109)

This reduces to

(110)

    The solution in (108) will be undefined if the determinant is zero, and the determinant will be zero if any row or column consists entirely of zeros. This is actually a potential danger in the case of the first row. A zero determinant would result if

(111)

The first equation indicates that reidentifications of an emoting actor can be chaotic or impossible when the actor is directing very lively action to a very quiet person (e.g., grandparents, geezer, old maid, scrooge) or very quiet action (e.g., lull, soothe, contemplate) to a very lively person.

    Interpretation of the second equation in (111) can be focused by recognizing that emotions tend to be either hedonically good or bad - we might say roughly either +2 or -2. Moreover, practically no behaviors are rated as powerless - the range for B_pis roughly 0 to +3. Now it is possible to compute various configurations that are risky for the solution, as shown in Table 1 at the end of this section.

    These results can be summarized as follows

(112)

    There might be additional conditions in which the determinant of (110)

(113)

is zero and the solution of (108) therefore is undefined, but the determinant is too complex for fruitful mathematical analysis. I did calculate its value for 2,187 instances - all combinations of -2.0, 0.0, and +2.0 assigned to the six behavior and object EPA variables that appear in (113), and then I regressed the absolute value of the determinant on the variables and all of their second-order interactions for positive and negative emotions separately, with the following results. When the displayed emotion is hedonically bad:

(114)

This result suggests that reidentifications of an emoting actor will be chaotic or impossible when the displayed emotion is bad (like anger, fear, shame, depression) and the event involves a bad, strong, lively act (e.g., attack) directed at a strong, quiet person (e.g., grandfather or disciplinarian) - a deduction that already has been obtained in (112). When the emotion is hedonically good:

(115)

This suggests problems would arise in reidentifying an emoting actor who directs good, weak, quiet acts at bad, strong persons, but no such acts are defined in our culture.

    Thus (112) probably specifies the main configurations that cause problems.

    Simulations indicate that some of the problem areas identified in (112) lead to reasonable solutions when the analysis seeks an actor identity that confirms behavior and object as well as actor. Probably, though, it is best to treat the configurations specified in (112) as leading to ill-defined results theoretically.

Table 1