You have identified your process as involving:
Follow-up question:
Is the smooth change lasting or reversible?
smooth lasting change
Transformation occurs gradually over time and is persistent. Hence, if the mean changes, there is either an upward or downward trend. Similarly, when the variance and/or dynamics change, they change in a certain direction, and do not revert back.
smooth reversible change
Transformation occurs gradually over time and is transient. Hence, if the mean changes, any increase or decrease is eventually followed by a change in the opposite direction, resulting in a waxing and waning pattern over time. This pattern can be regular or irregular.
I think my process involves:
Not sure?
When you theorize about the process you are interested in, you may realize that the temporal lens that you adopt in your study plays an important role in whether changes will show up as reversible or not. When the time span of your study is limited, or only little detail is obtained, change may appear lasting; in contrast, when the time span of your study or the resolution of your measurements increases, change may show up as reversible. Hence, to decide whether models for reversible change or models for lasting change are most relevant for the process you want to study, you have to consider the temporal design of your study.
When you look at empirical patterns in your intensive longitudinal measurements and you see a smooth increase followed by a smooth decrease (or vice versa), it is clear that the change in the process is reversible. However, when you see smooth change only in one direction (e.g., an increase in the mean, or a decrease in variability), this does not imply that change will also show up as lasting if you were to adopt a different temporal lens based on a different temporal design. Hence, while for the data at hand, choosing a model that only allows for lasting change may be appropriate, you should not conclude that this implies the process cannot show reversible change.
When you are unsure whether the process is characterized by lasting or reversible change, you are advised to continue with both options to get a better overview of the various modeling possibilities.