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I have a dataset tracking certain outcomes in school children, with all grades being sampled every year for a number of years. There are a number of study designs possible with such a dataset. As I understand it:

Cross-sectional designs would compare, say, different grade at a fixed point in time. For example, they could compare 2018 grade 7 students, 2018 grade 8 students and 2018 grade 9 students.

Longitudinal designs would compare, a single cohort of students across time. For example, they could compare 2016 grade 6 students, 2017 grade 7 students and 2018 grade 8 students.

Is there an analogous term for a design which compares students in a given grade across calendar years?

For example, comparing 2016 year 7 students, 2017 year 7 students and 2018 year 7 students. It is somewhat longitudinal because there is a temporal comparison happening but it isn't the same as in the longitudinal design described above. Is there common terminology one could use to distinguish between the two?

(In this question 'grade' is used to refer to the year level of the student in school, not to a mark on academic assessment.)

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    $\begingroup$ Don't get too caught up in terminology, you can do that. Is it temporal? Maybe, if you suspect there will be differences in say teaching across the years. You can include teachers or classes as random effects. $\endgroup$ – user2974951 Jul 9 at 6:04
  • $\begingroup$ Thanks for the comment - I ask because my employer offers the above three kinds of studies to schools as standardised reports, and for communication purposes it would be clearer if we didn't have to keep distinguishing between the two kinds of longitudinal studies. $\endgroup$ – Luke Thorburn Jul 9 at 6:20
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It appears that the name you are looking for is "time-lag design". This article, after discussing cross-sectional and longitudinal designs, provides the following summary:

The time-lag design is a third simple developmental design, although it is rarely used. In the time-lag design, measurements are obtained from participants all of whom are the same age, but who are tested at different points in historical time. That is, one could study 10-year-olds in 2010, 2020, and so on. In a time-lag design, cohort and period are perfectly confounded. Further, because age is held constant, the time-lag design is most useful for tracking secular trends. Because developmental psychology has a primary goal of studying age-related trends and because age is held constant in this design, the time-lag design has less direct relevance for the field than do the other two simple designs, but timely applications of the time-lag design should not be overlooked.

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