Minimax Decision-Making for Principal Transformational Leadership Strategies: Optimizing Teachers' Work Engagement through Psychological Capital
Keywords:
minimax optimization; minimax regret; psychological capital; teacher work engagement; school leadership; uncertaintyAbstract
School leaders must choose support strategies while the size and stability of their benefits remain uncertain. This study develops a finite-policy minimax framework for a hypothesized psychological-capital pathway and examines its evidential limits using two public Chinese teacher surveys. The surveys were analysed separately: a leadership and engagement dataset provided 1,033 usable records after one invalid leadership response was excluded, while a two-wave psychological-capital dataset contained 431 teachers. Composite-score regressions, 5,000-resample bootstrap indirect-association intervals, longitudinal change tests, predictive validation, and influence checks provided supporting empirical illustrations. Authentic leadership correlated with engagement (r = 0.301), and teacher efficacy correlated with engagement (r = 0.645). Three supplied psychological-capital scores declined after multiplicity correction. Neither survey identified the complete transformational-leadership–psychological-capital–engagement pathway. The decision model therefore used disclosed hypothetical gains, costs, and uncertainty bounds rather than estimated intervention effects. Across 48 parameter settings, minimax loss selected the status quo in 38, illustrating the conservatism that follows when zero benefit remains admissible. Minimax regret could select an active policy under the same uncertainty. Elementary optimality conditions explain these differences and specify when additional evidence can change a decision. The framework supports transparent conditional planning; it does not establish that a principal strategy improves engagement through psychological capital.
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