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Piecewise regression with interaction with categorical var - some groups are non-linear after spline

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I have used mkspline to make the variables for a piecewise regression
Code:
mkspline preH 3 postH = time
generate jump = 1
replace  jump = 0 if time < 3
Then fit a piecewise regression with an interaction by a categorical variable with 3 levels:

Code:
mixed hrelsat c.preH#ibn.H_Group i.jump#ibn.H_Group c.postH#ibn.H_Group || CSID: preH jump postH
This works just fine (see attached), but when I plot the raw means by group (see attached) I see that two of the groups appear to have a quadratic trend after the spline while only one is truly linear. Is there a way to incorporate these quadratic trends after the spline for these two groups to at least test if the quadratic is actually significant?


Array Array

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input double CSID byte time double(hrelsat wrelsat H_Group W_Group H5_Exposure W5_Exposure) byte(preH postH) float jump
10056 0                50                46 3 3 1  2 1 0 0
10056 1                50                46 3 3 1  2 2 0 0
10056 2                46                50 3 3 1  2 3 0 1
10056 3                50                43 3 3 1  2 3 2 1
10056 4                48                27 3 3 1  2 3 3 1
10056 5                50                41 3 3 1  2 3 4 1
10060 0                47                46 2 2 4  . 1 0 0
10060 1                35                15 2 2 4  . 2 0 0
10060 2                37                46 2 2 4  . 3 0 1
10060 3                 .                 . 2 2 4  . 3 2 1
10060 4                 .                 . 2 2 4  . 3 3 1
10060 5                 .                 . 2 2 4  . 3 4 1
10073 0                48                44 3 3 5  5 1 0 0
10073 1                50                52 3 3 5  5 2 0 0
10073 2                49                52 3 3 5  5 3 0 1
10073 3                47                52 3 3 5  5 3 2 1
10073 4                51                52 3 3 5  5 3 3 1
10073 5                48                52 3 3 5  5 3 4 1
10080 0                51                52 3 3 7  5 1 0 0
10080 1                51                49 3 3 7  5 2 0 0
10080 2                48                50 3 3 7  5 3 0 1
10080 3                46                46 3 3 7  5 3 2 1
10080 4                45                48 3 3 7  5 3 3 1
10080 5                46                50 3 3 7  5 3 4 1
10081 0                17                20 1 1 .  . 1 0 0
10081 1                 .                 . 1 1 .  . 2 0 0
10081 2                 .                 . 1 1 .  . 3 0 1
10081 3                50                41 1 1 .  . 3 2 1
10081 4                 .                 . 1 1 .  . 3 3 1
10081 5                 .                 . 1 1 .  . 3 4 1
10089 0                45                30 3 2 3  6 1 0 0
10089 1                46                32 3 2 3  6 2 0 0

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