Table 1 Measures of summarizing the different aspects of a trajectory
From: Clustering of countries according to the COVID-19 incidence and mortality rates
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 |