The social jetlag computation

This article provides notes on different approaches to computing social jetlag (SJL) for the Munich ChronoType Questionnaire (MCTQ). It also explains how the method argument in the sjl_rel(), sjl(), sjl_sc_rel(), and sjl_sc() functions works.

It’s helpful to have the standard MCTQ questionnaire and the guidelines for standard MCTQ variable computation open while reading this article. This will enhance your understanding of the data objects discussed. You can download the MCTQ full standard version here and the guidelines for standard MCTQ variables here.

The two intervals problem

According to Roenneberg et al. (2012), the relative social jetlag (SJL_rel), i.e., the discrepancy between social and biological time, must be computed as the difference between MSF (local time of mid-sleep on work-free days) and MSW (local time of mid-sleep on workdays).

SJL_rel = MSF − MSW

This simple equation seems trivial until you consider that it deals with two time values detached from a timeline. In other words, MSW and MSF represent two moments in different contexts (workdays and work-free days).

If you dive into the MCTQ articles, you can see that this computation have two objectives:

Represent the distance between MSW and MSF (i.e., the discrepancy).
Establish what value comes before or after the other, representing that with a +/− signal. That is, when MSW comes before MSF, SJL_rel must be positive, and when MSW comes after MSF, SJL_rel must be negative.
To represent the distance between MSW and MSF (i.e., the discrepancy).
To establish what value comes before or after the other, representing that with a +/− signal. That is, when MSW comes before MSF, SJL_rel must be positive, and when MSW comes after MSF, SJL_rel must be negative.

You can find the rationale about the SJL_rel signal in Roenneberg et al. (2019) (see item “3.2 Social Jetlag Computation”).

Most people have some trouble understanding this. To illustrate what we mean, let’s visualize a timeline overlapping an MSW and MSF value:

             day 1                        day 2
    MSF                MSW       MSF                MSW
   05:00              21:00     05:00              21:00
-----|------------------|---------|------------------|----->
              16h           8h             16h
          longer int.  shorter int.    longer int.

Note that, while doing the representation above, we’re dealing with the assumption that MSW and MSF can be represented in a two-day timeline since people don’t usually sleep more than 24 hours (basic assumption).

As you can see, by overlapping two time values in a two-day timeline, we need to make a choice of what interval to use. For most people MSF and MSW are close to each other, so, usually, we are looking for the shorter interval between the two. But, in some extreme cases, usually when dealing with shift workers, MSW and MSF distance can surpass 12 hours, making the longer interval the correct answer.

To obtain the SJL_rel signal we must check the start value of the interval. If the interval between MSW and MSF starts with MSW, that means that MSW comes before MSF, hence, the signal must be positive. Else, if the interval between MSW and MSF starts with MSF, that means that MSW comes after MSF, hence, the signal must be negative.

Example 1: when MSF − MSW makes a positive SJL_rel

             day 1                        day 2
                       MSW       MSF                
                      21:00     05:00
------------------------|---------|------------------------>

Example 2: when MSF − MSW makes a negative SJL_rel

             day 1                        day 2
                       MSF       MSW                
                      21:00     05:00
------------------------|---------|------------------------>

We call this the two intervals problem. It represents an unsolvable mathematical scenario, if you deprive it of the respondent context. That can generate minor errors when computing SJL, especially if you’re dealing with large datasets.

Methods for computing SJL

the sjl_rel(), sjl(), sjl_sc_rel(), and sjl_sc() functions provides an argument called method that allows you to choose three different methods to deal with the two intervals problem. Here’s how they work.

The sjl() function will be used in the examples, but the same logic apply to the other sjl functions.

`method = "difference"`

By using method = "difference", sjl() will do the exact computation proposed by the MCTQ authors, i.e., SJL will be computed as the linear difference between MSF and MSW.

Let’s see some examples using this method.

Example 3: using the "difference" method

MSW = 04:00

MSF = 06:00

Real difference: + 02:00

MSF − MSW = 06:00 − 04:00 = + 02:00 (right)

Example 4: using the "difference" method

MSW = 23:00

MSF = 03:00

Real difference: + 04:00

MSF − MSW = 03:00 − 23:00 = - 20:00 (wrong)

As you can see with the second example, the "difference" method uses a linear time frame approach, creating problems regarding the circularity of time.

`method = "shorter"` (default method)

By using method = "shorter", sjl() uses the shorter interval between MSW and MSF.

This is the most reliable method we found to compute SJL, considering the context of the MCTQ data. However, it comes with a limitation: when MSW and MSF values distance themselves by more than 12 hours, sjl() can return a wrong output. From our experience with MCTQ data, a SJL greater than 12 hours is highly improbable.

Let’s see some examples using this method.

Example 5: using the "shorter" method

MSW = 04:00

MSF = 06:00

Real difference: + 02:00

             day 1                        day 2
    MSF                MSW       MSF                MSW
   06:00              04:00     06:00              04:00
-----|------------------|---------|------------------|----->
             22h            2h             22h
         longer int.   shorter int.    longer int.

By using the shorter interval, MSW comes before MSF, so SJL_rel must be equal to + 02:00 (right).

Example 6: using the "shorter" method

MSW = 23:00

MSF = 03:00

Real difference: + 04:00

             day 1                        day 2
    MSF                MSW       MSF                MSW
   03:00              23:00     03:00              23:00
-----|------------------|---------|------------------|----->
             20h            4h             20h
         longer int.   shorter int.    longer int.

By using the shorter interval, MSW comes before MSF, so SJL_rel must be equal to + 04:00 (right).

Example 7: when the "shorter" method fails

MSW = 12:00

MSF = 23:00

Real difference: - 13:00

             day 1                        day 2
    MSW                     MSF                      MSW
   12:00                   23:00                    12:00
-----|-----------------------|------------------------|----->
               11h                       13h
           shorter int.              longer int.

By using the shorter interval, MSW comes before MSF, so SJL_rel must be equal to + 11:00 (wrong).

You can see example 7 in the shift_mctq dataset provided by the mctq package (ID 39, on and after night shifts). That’s the only MCTQ^Shift case in shift_mctq where we think that the "shorter" method would fail.

`method = "longer"`

By using method = "longer", sjl() uses the longer interval between MSW and MSF. It’s just the opposite of the "shorter" method showed above.

So, what method should I use?

We recommend that you always use the "shorter" method when computing SJL_rel or SJL (the default sjl() method).

In our tests, the "shorter" method demonstrated to be almost fail-safe. You just need to worry about the SJL computation if you are dealing with shift workers.

When dealing with a large MCTQ^Shift dataset, it will be very difficult to identify SJL errors, unless you look case by case and check the results with your respondents. This is usually not a viable option. We recommend that you mention which method you use to compute SJL and add it as a possible limitation of your results.