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. Author manuscript; available in PMC: 2024 Apr 1.
Published in final edited form as: Psychol Methods. 2021 Sep 27;28(2):401–421. doi: 10.1037/met0000407

Table 4.

Double-quadratic multiphase model estimates for Fox and Geese data

Parameter Notation Est. SE p
Growth Trajectory Fixed Effects
Minimum γ 10 4.50 0.21 <.01
Change Onset γ 20 8.66 2.26 <.01
Maximum γ 30 11.30 0.39 <.01
Change Offset γ 40 24.02 1.51 <.01
Random Effects
Change Onset Variance τ 22 45.50 17.86 <.01
Maximum Variance τ 33 19.94 2.32 <.01
Change Offset Variance τ 44 9.09 6.59 .01
Max., Onset Correlation Corr(u2i, u3i) 0.42 0.18 .03
Onset, Offset Correlation Corr(u2i, u4i) −0.14 0.16 .41
Max., Offset Correlation Corr(u3i, u4i) −0.89 <0.01 <.01
Within-Person Residual Variance
Residual Variance σ 2 10.79 0.86 <.01

Note: p-values are obtained from a t-distribution with the default degrees of freedom computed as number of upper-level units (17 children) minus the number of estimated random effects (3), which is 14.