Abstract: Based on the survey data from migrant and urban middle-school students, this study has investigated the linear and nonlinear relationships between different forms of parental involvement and students' learning engagement.We have also tested whether these associations are different for migrant youth and urban youth.The results have showed that:First, the effect of parental school-based involvement on the learning engagement is positive and linear in both migrant and urban middle-school students.Second, increased parental home-based involvement has a diminishing positive effect on migrant middle-school students' learning engagement, whereas the relationship between parental home-based involvement and urban middle-school students' learning engagement is linear.Third, parental academic socialization has a positive linear effect on the learning engagement of migrant middle-school students, but the effect on urban middle-school students is not significant.These results have revealed the differences in the patterns of how different forms of parental involvement are associated with the learning engagement of migrant and urban middle-school students, shedding light on how parents can effectively participate in their children's education.

Key words: parental involvement, learning engagement, migrant middle-school students, nonlinear relationships