Social jetlag computation

The two intervals problem

According to Roenneberg, Allebrandt, Merrow, & Vetter (2012) supplemental materials, 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 may seem trivial until you take into account that you’re are dealing with two time values detached from a timeline. In other words, \(MSW\) and \(MSF\) represent two moments in two different contexts (one on workdays and the other on work-free days).

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

1. To represent the distance between \(MSW\) and \(MSF\) (i.e., the discrepancy).
2. 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, Pilz, Zerbini, & Winnebeck (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.

             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.

             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.

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

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.