Relating constructs with different timescales
This page is about theoretical implications when studying multiple constructs that develop over time at differing timescales.
The timescale at which psychological constructs develop over time give rise to substantive considerations for the measurement frequency of such constructs (see: Time span, process coverage, and granularity). Oftentimes, researchers are interested in studying (the relations between) multiple constructs that are or need to be measured at different timescales in some way or form.
It is important to think about differences in timescales and measurement frequencies between variables because they have implications for the substantive interpretation of the dynamic relations among them.
Below, we discuss various examples of this, including specific common cases in which this occurs: “explicitly versus implicitly lagged relations”, “unconditional versus event-contingent constructs”, and “aggregated versus non-aggregated constructs”. We discuss various things to consider when studying these variables.
1 Key considerations for studying constructs with different timescales
Ideally, we want the frequency of measurements for psychological constructs to match the timescale at which they develop (see: Timescale landing page).
Different constructs may develop over time at a different timescale. For example, there is general consensus that affect develops over time on a moment-to-moment basis (i.e., intervals of about an hour or even shorter), whereas personality traits are assumed to be relatively stable over time (e.g., intervals of a year or longer).
Therefore, when researchers are interested in studying multiple constructs, the frequency of measurement for these constructs may differ.
Batu wants to study how someone’s sleep quality affects their positive affect throughout the day. He decides to measure positive affect three times a day using ESM, and to add the item ‘I slept well last night’ to the first ESM measurement of the day that is prompted in the morning.
It is important to carefully think about how one construct relates to the other, and more specifically when. Does the construct always affect the other, or does it only occur at a specific time?
Batu believes that a person’s sleep quality only affects their positive affect in the morning and at the end of the day. At other moments in the day, sleep quality has no direct effect on positive affect.
The relation between these constructs may not be straightforward. We discuss a few general ways in which constructs may have differing timescales and how this impacts their relation.
1.1 Explicitly and implicitly lagged relations
Repeated measurements refer to a specific time point or interval. It is important to consider to what time point or interval a measurement refers to, in order to concretely hypothesize about the dynamic relations between variables.
Explicitly lagged relations are relations among repeated measures that refer to the specific time point of each measurement occasion (e.g., “I feel satisfied at the moment”). The lag is the interval between the time stamps of the measurements.
Implicitly lagged relations are relations among measures that refer to a different time point or interval. A measurement that refers to a previous time point or interval is known as retrospective assessment [LINK: Ecological momentary vs. retrospective assessments] (“In the past hour, I felt satisfied”). Relations among such variables may be inherently lagged: The time stamp of the measurement occasion is not the time point or interval which the measurement refers to. In contrast to explicitly lagged relations, the lag is not the interval between time stamps of the measurement, but the interval between the time indications of the measurements.
When considering only one variable, the difference in lag interpretation between implicitly and explicitly lagged relations may be trivial. Yet, when considering multiple variables, it is important to think about the lag interpretation between these variables. Both variables could be measured at the same time, but refer to a different time point or interval.
Batu measures sleep quality in the morning at the same time of the first measurement of positive affect. However, the measurement of sleep quality refers to the preceding night, which is an interval of time that happens before the measurement is taken. The items for positive affect refer to how the participant feels at the moment and therefore refer to that specific measurement occasion.
1.2 Unconditional versus event-contingent measurements
Event-contingent measurements are taken only when a specific event takes place, while unconditional measurements are always scheduled. When combining event-contingent and unconditional measurements, it is important to consider that the event-contingent measures are not observed in absence of the event. One must be careful to not draw substantive conclusions for the unobserved relations.
Koen measures smoking multiple times a day (“How many cigarettes have you smoked since the last measurement?”), but only measures positive affect when a participant indicates that they have smoked at least one cigarette. His conclusions about the relation between smoking and positive affect should always include that this relationship is while smoking.
1.3 Time-aggregated vs non-time-aggregated measurements
Aggregation of measurements (e.g., averages) may lead to different theoretical interpretations. It is important to consider the difference between measurements and aggregated measurements with regards to the substantive interpretation of the relations between variables. Furthermore, the substantive interpretation should include the aggregation (e.g., “x relates to the average of y”).
There are multiple ways in which a measurement may be aggregated over time: (1) a summary score of multiple repeated measures such as a mean or sum score or (2) implicitly lagged measurements.
Gulce is interested in a similar relation as Batu between sleep quality and positive affect. However, she believes that sleep quality of the preceding night influences a person’s average positive affect of the following day. She measures sleep quality with one measurement in the morning and positive affect with multiple measurements throughout the day. For the analysis, she computes a daily average of the positive affect measurements. She concludes that there is a relation between sleep quality and daily average positive affect.
An implicitly lagged measurement usually indicates a time-aggregated behavior (e.g., “in the past hour”). Non-time-aggregated items refer to behavior at the time of the measurement occasion (i.e., “at the moment”).
Emilie combines daily measures of smoking and momentary measures of positive affect. The participants receive the momentary measures of positive affect every hour (e.g., “I feel satisfied at the moment”), and they also receive a daily diary at the end of the day about the amount of cigarettes they have smoked that day. With these measures, Emilie may find that participants with overall more positive affect also on average smoke less per day.
[Means and sum scores vs. latent variable models]
[Ecological momentary vs. retrospective assessments]
1.4 Combinations of the above
The different types of multiple measurements explained above generally intertwine. Implicitly lagged measurements are usually also time-aggregated, and for event-contingent measurements the event measurement or the conditional measurement may also be implicitly lagged or time-aggregated.
Koen is also interested in the relation between smoking and positive affect. He measures smoking multiple times a day (“Have you smoked since the last measurement?”), but only measures positive affect when a participant indicates that they have smoked. For the phrasing of the positive affect items, he considers the following three options:
- I feel satisfied at the moment.
- How satisfied were you since the last measurement?
- How satisfied were you since smoking a cigarette?
With the first option, it is clear that the smoking came before the positive affect measurement (an implicit lag), whereas with the second option, the time-aggregated positive affect may also include positive affect from before smoking as we do not know when in this interval the smoking occurred. With the third option, the time-aggregated positive affect only includes the time after the smoking until the measurement occasion, and this interval will differ in lengths. That is, if the person smoked only five minutes before the measurement occasion, the time-aggregation of positive affect is over these five minutes, whereas if the person smoked half an hour before the measurement occasion, this time-aggregation would be over thirty minutes. Koen needs to think about which of these options best aligns with his research question.
2 Conclusion
When studying a relation between two variables that are measured at different frequencies, you need to consider the timing of the measurements, whether the measurements are unconditional or event-contingent, and whether the measurements are aggregated over time.
3 Practical Considerations
The following practical considerations are also important for the decision about the frequency of measurements of multiple constructs, but are not considered further on this website.
Combining measurements of different variables at the same measurement occasion would reduce the burden of participants, but may restrict the researcher the measure a variable at the right timescale.
Measuring multiple constructs with different measurement frequencies will not only lead to differences in the lengths of the intervals, but also to differences in the amount of observations per variable, which most dynamic models are not equipped for.
Citation
@online{berkhout2023,
author = {Berkhout, Sophie W.},
title = {Relating Constructs with Different Timescales},
date = {2023-05-26},
langid = {en}
}