ARRMA: An Integrative Theoretical and Mathematical Model of Assumed and Actual Dyadic Behavior

Abstract

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In dyadic interaction, do people share a common interpersonal reality? Each assumes the probable response of the other, observes the other’s actual response, and assess the veracity of assumptions. Interpersonal theory stipulates that one’s response invites a similar (e.g., smiling elicits smiling) or a dissimilar (e.g., dominance evokes submission) reciprocal response. Members’ assumptions may be congruent or incongruent with the other’s actual response. A model called ARRMA integrates this dyadic interplay by linking three conceptually and mathematically related phenomena: AssumedReciprocity, Reciprocity, and MetaperceptionAccuracy. Typically studied independently, mathematical derivations reveal the necessity of considering their simultaneity. The theoretical logic of minimal ARRMA models at the individual (i.e., in multiple dyads) and dyadic (i.e., specific dyads) levels are developed, and are then generalized to the full ARRMA at each level. Also specified are statistical methods for estimating ARRMA parameters. ARRMA models shared and idiosyncratic interpersonal realities in dyads.

Keywords

• assumed reciprocity
• reciprocity
• metaperception accuracy
• social relations model
• dyadic behavior