Use polynomial regression with response surface analysis to test congruence and incongruence of two predictors¶

Strategy · All strategies
Evidence · 6 claims (6 for) · 2 studies (2 associational), q2–q3 · 0 of 2 report an effect size · 6 claims rest on one study

Description¶

The article recommends that researchers test linear and curvilinear (quadratic) relations jointly, rather than assuming linear relations, when examining how two predictors combine to predict an outcome. Centering scores around the scale midpoint (not the mean), comparing first-order, interaction, and full polynomial models via F-change tests, then bootstrapping slopes and curvatures along the lines of congruence and incongruence lets researchers locate "at what levels of autonomous motivation or controlled motivation, a motivational correlate will be even higher (or lower)". The approach also guards against inflated Type I error when testing interactions.

Design Implications¶

Context¶

Requirements¶

• Both predictors measured on comparable scales and centered around their scale midpoints before model fitting; bootstrap resampling to obtain confidence intervals for slopes and curvatures

Constraints¶

• The article notes that different combinations of linear and nonlinear relations can yield similar response-surface patterns, so no accurate prediction of the strength of individual relations is possible from the surface alone; only two of approximately five hundred SDT studies had used this approach

Target Learners¶

• Researchers studying motivation-outcome relations in school populations

Target Learning Goals¶

• Accurate modeling of how autonomous and controlled motivation jointly predict academic achievement

Claims¶

• Higher grades occur when high autonomous motivation coincides with low controlled motivation (incongruence), not congruence [+W]
• In 8 countries, a non-parallel asymmetric congruence/incongruence polynomial explained a modest 4.1% of achievement variance yet a 41% increase over the additive model [+W]
• In 3 countries, a quadratic-effects-of-x-and-y polynomial explained 7.2% of achievement variance (an 11% increase over the linear model) [+W]
• Across 37 countries, polynomial models with nonlinear or interactive effects of autonomous and controlled motivation on mathematics achievement always fit better than linear additive-only models [+W]
• In 12 countries, a level-dependent incongruence polynomial with free cubic effect of control explained 7.8% of achievement variance (a 30.9% increase over the additive model) [+W]
• In 14 countries, a cubic effect of autonomous motivation best fit the motivation-achievement relation, explaining 10.7% of achievement variance (an 8.1% increase over the additive model) [+W]

Related Strategies¶

• Sdt Quality Of Motivation Grades Account

Examples¶

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Key Sources¶

• Mouratidis, A., Michou, A., Sayil, M., & Altan, S. (2021). It is autonomous, not controlled motivation that counts: Linear and curvilinear relations of autonomous and controlled motivation to school grades. Learning and Instruction, 73, 101433. https://doi.org/10.1016/j.learninstruc.2020.101433