Table 3.

Model estimates of polynomial regression analyses and response surface analyses among 373 dyads

Parenting practices	Model	Polynomial regression slope					RSA coefficient								R 2 adj
		b1	b2	b3	b4	b5	a1	a2	a3	a4	a5	C	S	a4’
Disengagement	SRSQD	0.05	-0.16**	0.01	-0.04	0.06	-0.10	0.03	0.21**	0.12	-0.06	1.23*	0.35	0.26	0.04
Expectation	SRRR	-0.05	0.37***	0.09	0.12	0.04	0.31***	0.25	-0.42***	0.221	0.05	-2.16	-1.53	0.15	0.18
Facilitation	SRSQD	0.03	0.30***	0.00	-0.01	-0.02	0.33***	-0.03	-0.27***	-0.02	0.02	6.59	-0.10	-0.09	0.17
Monitoring	SRSQD	0.03	0.15***	0.00	0.02	0.04	0.18***	0.06	-0.12*	0.03	-0.04	-1.70	-0.20	0.18	0.05
Non-directive support	SRSQD	-0.02	0.26***	0.00	-0.00	0.02	0.24***	0.02	-0.28***	0.02	-0.02	-6.13	0.08	0.08	0.10
Autonomy support	SRR	-0.03	0.29***	-0.01	0.02	-0.01	0.31***	0.00	-0.26***	-0.05	0.00	5.81	-	-	0.16

Note: SRR shifted rising ridge model; SRRR rotated and shifted rising ridge model; SRSQD rotated squared difference model. The b₁ to b₅ are the coefficients in the polynomial regression equation of the corresponding model. The a₁ coefficient (b₁ + b₂) represents the slope of the line of congruence (LOC); the a₂ coefficient (b₃ + b₄ + b₅) represents the linear or curvilinear shape of the LOC; the a₃ coefficient (b₁ - b₂) represents the slope of the line of incongruence (LOIC); the a₄ coefficient (b₃ – b₄ + b₅) represents the linear or curvilinear shape of the LOIC; the a₅ coefficient (b₃– b₅) represents whether the first principal axis (FPA) and LOC are equal. In the SRSQD model, the C coefficient (-1/2(b₂/b₅)) is a shifting constant applied to the X predictor. the S coefficient (-b₄/(2b₅)) is scaling factor for X. the a₄’ (b₃/S² − b₄/S + b₅) coefficient is the relevant index that tests for the presence of a misfit effect. Covariates adjusted for parent’s gender and education, adolescents’ gender and single child status. ^*p < 0.05; ^**p < 0.01; ^***p < 0.001