Table 1.

Measures of summarizing the different aspects of a trajectory

Class	Measure	Note
1. Elementary measures of change	1. Range	Basic descriptive statistics that ignore the temporal trend
	2. Mean-over-time
	3. Standard deviation (SD)
	4. Coefficient of variation
	5. Change	Last observation - First observation
	6. Mean change per week	Weekly value of change
	7. Change/first score	Rescale change based on the first observation
	8. Change/mean-over-time	Rescale the change based on all of the observations
	9. slop b	Achieve from a linear regression model of observations on times
	10. R2 of the linear model	The proportion of variation of observation that could be explained by the linear trend of the time
2. Measures of nonlinearity and in-constituency of change	11. Max Δ1 (Δ1, i = yi + 1 - yi)	indicates that there is at least one big increase between two consecutive scores
	12. SD Δ1	A high value of measure indicates that the first differences are not constant and that the pattern is therefore not linear
	13. SD Δ1 per week	Adjust for the time elapsed between two consecutive scores
	14. Mean | Δ1|	A high value of measure indicates that there are many abrupt changes during the time
	15. Max | Δ1|	A high value of measure indicates that there is at least one crucial abrupt change regardless of the sign
	16. Ratio, max | Δ1|/mean-over-time	To measure the relative importance of the significant abrupt
	17. ratio, max | Δ1|/b	b is the coefficient of linear regression
	18. Ratio, SD Δ1/b	To assess the relative importance of the variability of the first differences
3. Measures sensitive to nonmonotonicity and abrupt short-term fluctuations	19. Mean Δ2 (Δ2, i = Δ1, i + 1 - Δ1, i)	To detect rather regular but nonlinear patterns
	20. Mean |Δ2|	Useful for further classifying trajectories for that measure 19 is close to 0
	21. Max |Δ2|	Indicates whether there is an essential local peak or valley
	22. Ratio, max |Δ2|/mean-over-time	To assess the relative importance of the local peak
	23. Ratio, max |Δ2|/mean |Δ1|	To assess the relative importance of the local peak
	24. Ratio, mean |Δ2|/mean |Δ1|	To assess the relative importance of the fluctuation around the general rate of change
4. Measures contrasting early vs. later change	25. Ratio, early/later change	More remarkable than 1.0 if the magnitude of early change is more significant than the later change
	26. Ratio, early/total change	Share of early change from the total change
	27. Ratio, late/total change	Share of late change from the total change