M. J. S T O N E S A N D A L B E R T K O Z M A

A M A G I C A L M O D E L TO P R E D I C T I N D I V I D U A L

D I F F E R E N C E S IN M O O D C H A N G E

(Received 6 June, 1990)

ABSTRACT. We tested a mathematical model of psychological well-being (PWB) with data from a paradigm that included a negative mood induction followed by a positive induction. The propositions from the model encompass the hypothesis that the relative mood prior to either induction has implications for the magnitude of subsequent in- duction effects, such that relative mood is defined by current mood as a ratio of the prevailing mood that is predicted by the model. The findings confirm the hypothesis that the relative mood at baseline predicts mood change in a nonoverlapping time period, even after control for potentially mediating variables.

We described a nonlinear mathematical model of PWB, an impetus for which is Diener's (1984) plea for greater propositional rigour in PWB model building so as to permit falsifiablity, the generation of new and risky hypotheses, and applicability to the single case (Stones and Kozma, 1991; Stones et al., 1990). The scope of this model, that we term coUequially the magical model, includes the aim to reconcile global PWB with its temporally specific attribute of mood. Other models suggest either that PWB comprises short-term and long-term affective states without specification of interdependence (Kozma et al. 1990), or that mood reactivity is indeptendent of global PWB (Larsen and Diener, 1987): the magical model proposes that both mood and global PWB (i.e., the short-term and long-term states) are tuned by a single person parameter (Stones and Kozma, 1991). In this article, we present a secondary analysis of data by Kozma et al. (1990) to illustrate the utility of the model to predict individual differences in the response to a mood induction paradigm.

The model is based on an equation well documented in nonlinear mathematics (May, 1976; Stewart, 1989). The relationship between the scores on a PWB index at times t (/-/) and t + 1 (Hnext) is moderated by a person parameter (M) and an environmental impact term (I). We postulate the latter to comprise two additive components: the prevailing

Social Indicators Research 27: 103-- 111, 1992. �9 1992 KluwerAcademic Publishers. Printed in the Netherlands.

104 M. J. S T O N E S A N D A. K O Z M A

environment to time t (Ip), that affects the score on a global PWB index; the episodic deviation from the prevailing penvironment at time t (dI), that affects a mood index. The model is given as follows:

Hnext = M(1 - H)H + I (1) I -- Hnext - M(1 - H)H (2)

with Hnext and H expressed on a proportionate scale. Stones and Kozma (1991) explain that, because a steady state value to Hnext is asssumed in normally functioning persons, the normal range of M is 1 to 2.9, that give rise to steady states of Hnext between 0.09 to 0.67.

The Stones and Kozma (1991) article provides mathematical and substantive justification for the model, together with a listing of eight fundamental properties, implications for the resolution of known paradoxes in the PWB literature, and the generation of risky predic- tions for future research. Because a detailed rationale for the opera- tionalization of the model is contained in the previous publications, just two points will be made here. First, the //next and H terms are operationalized by transformation of the scores from a PWB index (e.g., a mood or global PWB measure) according to a specified protocol. Second, the person parameter is estimated from the transformed score on a global PWB index, given that this index possesses demonstrated stability over time (Stones and Kozma, 1989). Under conditions of stability, Hnext -- H, and Equation 1 reduces to:

n - - M(1 - H)H, M = 1/(1 - H) (3)

Among the fundamental properties of the model are two with relevance to the relationship between mood and global PWB. First, mood and global PWB indexes are expected to correlate when mea- sured under relatively uniform environment conditions, because the person parameter contributes to both short-term and long-term affec- tive states (property 3 in Stones and Kozma, 1991). In fact, the same steady state of Hnext is predicted for mood and global PWB under conditions of environmental constancy. The findings by Kozma et al. (1990) are consistent with this prediction, with absolute correlations of 0.32 to 0.5 between subcomponents of mood and global PWB. Second, persons either high or low on the person parameter are expected to

A M A G I C A L M O D E L A N D M O O D C H A N G E 105

exhibit greater mood perturbation in response to episodic environmen- tal change than persons midrange on the person parameter (property 4 in Stones and Kozma, 1991). We argued that this property is consistent with Larsen and Diener's (1987) findings that the intensity of short- term affective reactions correlates positively with both positive and negative predictors of global PWB, but not with global PWB itself.

The aim in this article is to test hypotheses that concern individual differences in the response to a mood induction paradigm. Earlier research indicates that half to two-thirds of subjects respond to a standardized mood induction with a substantial change in affect, and the remainder with minimal change (Teasdale and Russell, 1983; Teasdale and Taylor, 1981). An expectation is that the extent of mood change is moderated by the relative mood at baseline, such that relative mood is defined as current mood relative to the usual mood that is predicted by the model, as expressed formally by the ratio of Hnext on a mood index to that on a global PWB index. (We emphasize that relative mood is not the absolute level on a mood index, but its ratio to the steady state predicted by the model). Consequently, we anticipate a negative induction to be relatively ineffective in persons with a relative mood below unity at baseline (i.e., lower than the predicted usual mood) and a positive induction to be ineffective in persons with a relative mood at baseline greater than unity.

Some predictions are illustrated in Figure 1, using representative trends generated from the model. The solid lines indicate trends with a negative followed by a positive induction: the absolute magnitude of both mood changes is greater in the case with the higher relative mood at time 0 (case 1). The dashed lines reveal that, in the absence of a preceding induction, the positive mood change is greater in the case with the lower relative mood prior to the induction (case 4). The general propositions we derive from Figure 1 are that mood change is correlated across sequential inductions, with the magnitude influenced by the relative mood at baseline. Based on the latter, we anticpate a positive induction to provide greater mood change when preceded by a negative induction than when administered without a prior induction. The reason is that the distribution of relative moods immediately prior to the positive induction is expected to be uniformly negative when preceded by a negative induction, but to encompass a negative to

106 M. J. S T O N E S A N D A. K O Z M A

positive range in the absence of an earlier induction. The findings by Kozma et al. (1990, figure 1) confirm this prediction.

In the secondary analyses to follow, we test a risky hypothesis that, with sequential negative (time 0 to 1) then positive (time 1 to 2) inductions, the positive induction effect varies with the relative mood at

1.5

1.0

Relative Mood

Neg. Induction Poe. Induction

0 , 6 .... I

0 1 2

Time

+ Case 1 0 Case 2 ..... Case 8 -~- Case 4

The person parameter value is M=2.2 in all four cases. The mood inductions are o! absolute valueO.07.

Fig. 1. Relative mood in four hypothetical cases with sequential or single mood inductions.

A M A G I C A L M O D E L A N D M O O D C H A N G E 107

time 0. Specifically, the model anticipates the prior induction to pro- duce greater negative mood change in persons higher on relative mood at baseline: greater positive induction effects are also expected in the same persons (i.e. predications illustrated by the solid trend lines in Figure 1). Note the hypothesis that mood change from times 1 to 2 relates positively to the relative mood at time 0 is not open to any contention of spurious correlation, because neither variable is con- tained within the other. The argument about whether or not spurious correlation enters into the relationship between change scores and initial values (cf. Schaie, 1895, pp. 80--82) is circumvented in the present approach.

M E T H O D S

The Kozma et al. (1990) study used two groups of 32 student volunteers, the data from Group 1 being that processed in the second- ary analyses. Group 1 experienced the negative followed by the positive condition of the Velten (1968) mood induction procedure (Group 2 experienced only the positive induction). This procedure involves silent and vocalized readings of a series of mood statements, with each statement followed by an attempt to experience the mood indicated. The scales used by Kozma et al. include the Memorial Unitversity of Newfoundland Scale of Happiness (MUNSH; Kozma and Stones, 1980) to index global PWB and the Memorial University Mood Scale (McNeil, 1986) to index mood. Only the total scores were used as data in the present analyses, with the coefficient alpha reliability shown to exceed 0.8 for both indexes. Not suprisingly, the MUMS proved sensitive to the mood induction, whereas the MUNSH was intransigent. The scores on both indexes were transformed to a proportionate scales following the protocol described in Stones and Kozma (1991), with the person parameter estimated using Equation 3.

R E S U L T S A N D D I S C U S S I O N

The mood scores can be expressed as absolute or relative mood. With the reliabilities of the MUMS and MUNSH given as 0.8, the reliabilities of the change scores for absolute and relative mood between times 1

108 M. J. STONES AND A. KOZMA

and 2 is estimated respectively as 0.79 and 0.77 (cf. Schaie, 1985, p. 81). These reliabilities lie within acceptable limits. The relative mood at the time 0 baseline did not differ significantly from the population value of 1 that is predicted by the model (i.e., a mean of 1.022, standard deviation 0.441, t(31) = 0.28). In the discussion that follows, the findings are presented using the relative mood scores at times 0, 1, and 2 as data. Although analyses with the absolute scores yielded not dissimilar implications, the use of relative scores (1) simplifies the presentation of results, (2) provides uniformity across both sides of the regression equations linking the dependent and independent variables, and (3) takes cognizance of the predicted steady state of mood in the

analyses. The relationship between the relative mood at baseline and the

induced mood change is illustrated in Figure 2 and Table I. Figure 2 showns the relationship between relative mood at times 0, 1, and 2, with the subjects divided between those with a relative mood greater (N -- 14) or less (N -- 18) than unity at baseline. As predicted by the model, the absolute change associated with each induction is greater in persons with the higher baseline mood. The hypothesis that the relative mood at time 0 relates positively to the change in mood from time 1 to time 2 is confirmed statistically by a significant correlation between the

TABLE 1 Regression coefficients in three multiple regression equations

Independent Variables

Dependent Variables1 Positive Positive Relative Mood

Induction Effect Induction Effect (Time 2)

Relative Mood (Time 0) 0.296* 0.298* Relative Mood (Time 1) --0.221 -0.063 0.107 Negative Induction

Effect z -0.294* Person Parameter (M) --0.581"* -0.581"* -0.585"*

Multiple Correlation R = 0.785** R ~ 0.785** R = 0.782**

* p < 0.05 ** p < 0.01 1 The positive induction effect is the change in relative mood from time 1 to time 2. 2 The negative induction effect is the change in relative mood from time 0 to time 1.

1.5 Relative Mood

1.0

0.5

A MAGICAL MODEL AND MOOD CHANGE 109

Neg. Induction Pos. Induction

0.0 I

0 1 2

Time

n High Baseline --e-- Low Baeeline

Negative induction between times 0 to 1: Positive induotion between times I to 2.

Fig. 2. Relative mood at times 0, 1, and 2 in groups above or below unity at the time 0 baseline.

variables (r[30] ---- 0.502, p < 0.01). The relationships are further explored in multiple regressions (Table I) that permit control for such potentially mediating variables as the person parameter and mood at the intermediate time. Column 1 in Table I shows that contributing

110 M. J. STONES AND A. KOZMA

independently to the gain in mood between times 1 and 2 are the relative mood at time 0 and the person parameter, with no significant mediating effect due to the relative mood at time 1. This finding indicates the relationship between baseline mood and the positive induction effect not to be spuriously dependent on either of two potentially mediating variables. Column 2 shows the negative induction effect (i.e., change in relative mood between times 0 and 1) to relate negatively to the positive induction effect, even with control in the predictor array that extends to mood at time 1. This finding indicates a relationship between sequential induction effects that is independent of the mood at intermediate time (i.e., time 1). Column 3 shows the relative mood at time 2 to relate to that at time 0 independent of the effects of the person parameter and mood at the intermediate time.

We conclude from the preceding findings that the relative mood at baseline affects the magnitude of induced mood change (and the level of mood) over a time period that does not include the baseline. The relationships are independent of potential mediating variables that included mood induction effects during an intervening period, the person parameter, and the relative mood immediately prior to the subsequent induction. Consequently, relative mood at any one time is shown to have a nonspurious relationship with mood change and mood level in a nonoverlapping time period. The aim of this article was to demonstrate the utility of the magical model to predict individual differences in the response to a mood induction paradigm. These findings on the relevance of the relative mood at baseline are consistent with this model, and support the proposition from theory that the initial state has implications for future states irrespective of the nature of the intervening events.

R E F E R E N C E S

Diener, E.: 1984, Subjective well-being, Psychological Bulletin 95, pp. 542--75. Kozma, A., Stone, S., Stones, M. J., Hannah, T. E., and McNeil, J. K.: 1990, Long- and

short-term affective states in happiness, Social Indicators Research 22, pp. l 19--38. Kozma, A. and Stones, M. J.: 1980, the measurement of happiness: The development of

the Memorial University of Newfoundland Scale of Happiness (MUNSH), Journal of Gerontology 35, pp. 906--12.

Larsen, R. J. and Diener, E.: 1987, Affect intensity as an individual difference characteristic: a review, Personality and Individual Differences 21, pp. 1--39.

May, R. M.: 1976, Simple mathematical models with very complicated dynamics, Nature 261, pp. 459--67.

A MAGICAL MODEL AND MOOD CHANGE 111

McNeil, J. K.: 1986, Mood: Measurement, Diurnal Variation, and Age Effects. Un- published doctoral thesis (Memorial University of Newfoundland).

Schaie, K. W. and Hertzog, C.: 1985, Measurement in the psychology of adulthood and aging, In J. E. Birren and K. W. Schaie (Eds.), Handbook of the Psychology of Aging (Van Nostrand Reinhold (2nd Ed.), N.Y.).

Stewart, I.: 1989, Does God Play Dice? The Mathematics of Chaos (Basil Blackwell, Oxford).

Stones, M. J. and Kozma, A.: 1989, Happiness and activities in later life: A propensity formulation. Canadian Psychology 30,526--37.

Stones, M. J. and Kozma, A.: 1991, A magical model of happiness. Social Indicators Research 24, 43--62.

Stones, M. J., Rattenbury, C., Taichman, B., Kozma, A., and Stones, L.: 1990, Effective selection of participants for group discussion intervention. Clinical Gerontologist 9, 135--143.

Teasdale, J. D. and Russell, M. L.: 1983, Differentail effects of induced mood on the recall of positive, negative, and neutral words. British Journal of Clinical Psychology 22, pp. 163--71.

Teasdale, J. D. and Taylor, R.: 1981, Induced mood and accessibility of memories: An effect of mood state or of mood industion procedure. British Journal of Clinical Psychology 20, pp. 39--48.

Velten, E.: 1968, A laboratory task for induction of mood states. Behavior Research and Therapy 6, pp. 473--482.

Psychology Department, Memorial University St. John's, New Foundland A1B 3X9, Canada.