Although mother–child interactions under circumstances of child abuse can be understood by the models of matching theory, the parameters of the hyperbolic, strict, and generalized equations are sensitive to the changes derived from behavioral interventions that focus on the restructuring of interactive patterns. The objective of this research is to determine the impact, under the formulations of the matching theory, of a parent–child interaction therapy intervention in cases with a history of child abuse. The ages of the children ranged from 4 to 9 years, and the ages of the mothers ranged from 24 to 39 years. All dyads attended the Psychological Services Center of the National Autonomous University of Mexico (UNAM) and presented with a history of abuse. Under a single case ABC research design, dyadic interactions were observed at baseline (phase A) and compared with follow-up observations (phase C). To evaluate the adjustment of social attention to child behavior, three propositions derived from the matching theory were used, namely, hyperbolic, strict, and generalized equations. The results indicate that the majority of the interactions tend toward the undermatching of child behavior with respect to maternal attention and that the parameters of the generalized equation better describe the impact of an intervention focused on the restructuring of social exchanges on dyads with abuse. The findings are discussed within the context of social interactions in which the maternal and child behaviors are adjusted according to the reinforcing proportions of each to account for maternal synchronization and child abuse.

尽管可以通过匹配理论模型来理解在虐待儿童情况下的母子互动，但双曲线，严格和广义方程的参数对行为干预引起的变化敏感，这些行为干预着重于交互模式的重组。这项研究的目的是确定在匹配理论的指导下，在有虐待儿童历史的情况下，亲子互动治疗干预的影响。儿童的年龄为4至9岁，母亲的年龄为24至39岁。所有二人组都参加了墨西哥国立自治大学（UNAM）的心理服务中心，并收到了虐待的历史。在ABC个案研究设计下，在基线（阶段A）观察到二元相互作用，并将其与后续观察结果（阶段C）进行比较。为了评估社会对儿童行为的关注度的调整，使用了来自匹配理论的三个命题，即双曲型，严格型和广义方程。结果表明，大多数互动都倾向于导致儿童行为与孕产妇注意力不匹配，并且广义方程的参数更好地描述了干预措施的影响，该干预措施着重于对有虐待的双性恋者进行社会交流的重组。在社会互动的背景下讨论了这些发现，在这种互动中，母婴行为根据各自的强化比例进行了调整，以解决孕产妇同步化和虐待儿童问题。