Table 3.

Linear and non-linear relationship of parenting style in 2012 with children’s mathematics test scores in 2014, 2018 and children’s number series test scores in 2012, 2016.

Items	2012		2014		2016		2018
	β [95% CI]	p value	β [95% CI]	p value	β [95% CI]	p value	β [95% CI]	p value
Linear regression model	0.05 [0.01, 0.08]	0.012	0.09 [0.04, 0.15]	0.002	0.08 [0.03, 0.13]	0.002	0.10 [0.01, 0.18]	0.032
Non-linear model, regression coefficients (β)
Break point of parenting style (K)	42		46		55		46
< K	0.10 [0.02, 0.17]	0.015	0.20 [0.10, 0.29]	< 0.001	0.07 [0.01, 0.12]	0.013	0.17 [0.03, 0.31]	0.015
≥K	0.01 [-0.05, 0.07]	0.770	-0.07 [-0.20, 0.06]	0.269	0.29 [-0.09, 0.66]	0.134	-0.03 [-0.22, 0.16]	0.771
Difference of β-value between strata	-0.09 [-0.21, 0.03]	0.152	-0.27 [-0.46, -0.08]	0.006	0.22 [-0.17, 0.61]	0.271	-0.20 [-0.48, 0.08]	0.164
Predicted value of children’s mathematical performance at break point	9.66 [9.21, 10.12]		15.14 [14.42, 15.86]		11.51 [10.82, 12.20]		17.67 [16.62, 18.71]
P value for likelihood ratio test	0.147		0.005		0.261		0.153

Adjusted for children’s characteristics (age, sex), parents’ characteristics (mother’s age, father’s age, whether the children’s lived together with the mother ≥ 8 months in the past 12 months, whether the children’s lived together with the father ≥ 8 months in the past 12 months, father’s employment status, mother’s employment status, whether the mother had symptoms of depression, whether the father had symptoms of depression), and household characteristics (urban or rural location, household size).