Daily work and leisure time-use compositions were expressed using pivot isometric log-ratio (ilr) coordinates [34]. The first pivot-coordinate was calculated as the normalised log-ratio of the first compositional part (i.e. behaviour), relative to the geometric mean of the remaining parts within the work and leisure time composition, respectively. The work and leisure time behaviours were sequentially rearranged to place each behaviour in the first position, where after the corresponding ilr-coordinate sets were computed. This way, the relative importance of each behaviour was sequentially represented in the first ilr-coordinate (ilr1) and used in the regression analysis. A detailed description of how the pivot-coordinates were calculated and model development is provided in Additional file 1.

The analysis was performed using two multivariate multilevel models. In both models, the outcome variables were the ilr-coordinates expressing the leisure time-use composition.

In Model 1, we investigated if leisure time physical behaviours differed between each day of the week (e.g. Monday, Tuesday, Wednesday, etc.) and between workday and non-workdays. Thus, day of the week and an interaction between day of the week and type of day (reference = non-workday) were entered as predictors in Model 1. Model 1 was fitted three times. This was done to isolate the association with one of the leisure time behaviours in relation to the others in the first ilr-coordinate (denoted by ilr1).

In Model 2, only workdays were considered as we investigated if work behaviours influenced day-to-day leisure time behaviours. The following predictors were entered in Model 2: the work time-use composition (i.e. work time sent standing, active and sedentary, expressed as ilr-coordinates) and an interaction term between day of the week and the work time-use composition. Model 2 was fitted six times to investigate the association between each part of the leisure time and work compositions, respectively. Of note, only results of the associations between the relative work time spent active and standing (as a proxies of physical work demands) and leisure time physical behaviours are shown. Results on the association between relative work time spent sedentary and day-to-day leisure time physical behaviours are shown in Additional file 2.

Both Model 1 and 2 were adjusted for the following covariates (reference in parenthesis for categorical variables): sex (men), smoking-status (smoker), BMI, and age. Model 2 was further adjusted for work duration. These covariates were chosen as potential confounders based on theoretical assumptions concerning their possible influence on day-to-day pattern of leisure time and work behaviours and work duration [13, 17]. In all models, Monday was selected as the reference category when entering the “type of the day” variable, as this is considered as the first day of the week in Denmark, where the International Standard ISO 8601 is followed.

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