Engagement and Secondary English Achievement: A Multi-Method Study of Climate, Family, and Psychological Capital

English-language proficiency gates access to tertiary education, employment, and competitive examinations in India, yet large learning-outcome surveys continue to document wide variation in secondary-stage English achievement. Classroom climate, parental involvement, psychological capital, and student engagement are the constructs most often linked to such achievement, but their joint contribution is usually summarised through a single average-effect model. This study examines how these four constructs relate to English achievement among Indian secondary students, using a variance-decomposition framework that distinguishes unique from shared explanatory variance. Cross-sectional survey data were collected from 1,605 students in classes XI and XII (52.6% female; mean age 16.74 years) drawn from 107 secondary schools in West Bengal, India. Six complementary variance-partitioning analyses were applied to the zero-order correlation matrix: a saturated structural equation model, dominance analysis, commonality analysis, suppression and redundancy diagnostics, mutual-information dependence decomposition, and community-aware bridge centrality. The full model accounted for 31.4% of the variance in English achievement. Engagement showed the strongest direct standardised association (β = .327) and the largest unique variance contribution (43.6% of explained variance). Commonality analysis indicated that only 29.7% of explained variance was uniquely attributable to single predictors, with 70.3% shared among combinations of predictors. Suppression diagnostics revealed no suppression but substantial redundancy for three of four predictors, and engagement showed the highest cross-domain bridge strength (BS = .722). Engagement appears as the most central associational construct in the system, but the four predictors operate substantially as overlapping representations of related learner and contextual processes rather than as independent unique contributors. Convergent associational evidence across multiple methods is stronger than evidence from any single method, but the cross-sectional design precludes causal inference; longitudinal and experimental work is needed before intervention claims can be made.