# Robust Compositional Analysis of Physical Activity and Sedentary Behaviour Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design of Study

^{−2}. The data were collected during the 2013–2016 academic years in elementary and secondary schools. SB, LIPA, MPA, and VPA were measured by the ActiGraph GT3X accelerometer (ActiGraph, LLC, Pensacola, FL, USA); sleep was not considered. Participants were asked to wear accelerometers for seven consecutive days, except during water-based activities. The days on which the accelerometer was worn for at least 10 h were considered valid and participants were included if at least three valid weekdays and one valid weekend day of their activity were available. The time sampling interval was set to 60 s, which has been the most frequently used epoch in the literature [24]. Each minute epoch was classified using standard counts per minute thresholds as SB (0–100 counts/min), LIPA (101–2295 counts/min), MPA (≥2296–4011 counts/min) and VPA (≥4012 counts/min), based on Evenson’s cut-points [25]. These cut-points demonstrated significant higher accuracy for SB and different levels of PA intensity than other cut-points in adolescents [26]. For the purpose of the study, averaged results of movement behavior for each participant were taken.

#### 2.2. Compositional Data

#### 2.3. Compositional Regression

^{2}) was computed for all regression models to evaluate the goodness of fit. Since the main purpose of the modelling was to investigate the sign and size of the relationships, we focused on the statistical significance of the model parameters and allowed for small values of R

^{2}as generally accepted in our field [35]. Note that the coefficient of determination is invariant to orthogonal coordinate representation of predictors, so for any pivot coordinates the resulting value is identical.

#### 2.4. Dealing with Outliers

## 3. Results

#### 3.1. Relationship between Various Movement Behaviour Intensities

#### 3.2. Changes in Movement Behaviour with Increasing Age

^{2}values differ due to the different response coordinates.

#### 3.3. The Association between Movement Behaviour and Obesity

^{2}, the predictive power of these graph is rather limited.

^{2}after re-allocating 60 min. For an average girl resp. boy from our sample (15.1 years old with a height of 1.64 m resp. 1.71 m), this would mean a 2.05 kg resp. 1.91 kg reduction in weight. For more details, see Table 9.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Ternary diagrams visualizing how the structure of PA and SB is associated with age. Each plot represents relationship between three of four behaviors; (

**a**) SB, LIPA and MPA, (

**b**) SB, LIPA and VPA, (

**c**) SB, MPA and VPA, (

**d**) LIPA, MPA and VPA. The lighter the point color, the higher the age of an individual. The diagrams indicate that the proportions of time spent in SB and VPA is associated with higher age, whereas the effect is the opposite for LIPA and MPA.

**Figure 2.**Ternary diagrams visualizing how the structure of PA is associated with age using robustly centered data. Each plot represents relationship between three of four behaviors; (

**a**) SB, LIPA and MPA, (

**b**) SB, LIPA and VPA, (

**c**) SB, MPA and VPA, (

**d**) LIPA, MPA and VPA. Plotting of the centered data is recommended when the data are concentrated near the borders of the triangle. Note that tick labels are no longer meaningful after centering.

**Figure 3.**Predicted means of the dominance of the movement composition components with age. Both SB and VPA increase whereas LIPA and MPA decrease.

**Figure 4.**Compositional mean barplot for the underweight/normal and overweight/obese adolescent groups.

**Figure 5.**Robust compositional mean barplot for the underweight/normal and overweight/obese adolescent groups.

**Figure 7.**Predicted zBMI for SB-to-VPA time re-allocations between 0 and 60 min for the mean MB composition (close to 16 h).

MB | SB | LIPA | MPA | VPA |
---|---|---|---|---|

SB | $0$ | $0.1460$ | $0.2544$ | $0.7757$ |

LIPA | $0.1460$ | $0$ | $0.1577$ | $0.8993$ |

MPA | $0.2544$ | $0.1577$ | $0$ | $0.7828$ |

VPA | $0.7757$ | $0.8993$ | $0.7828$ | $0$ |

MB | SB | LIPA | MPA | VPA |
---|---|---|---|---|

SB | $0$ | $0.1669$ | $0.2801$ | $0.6624$ |

LIPA | $0.1669$ | $0$ | $0.1578$ | $0.8351$ |

MPA | $0.2801$ | $0.1578$ | $0$ | $0.6946$ |

VPA | $0.6624$ | $0.8351$ | $0.6946$ | $0$ |

PA | ${\widehat{\beta}}_{2}^{\left(PA\right)}$ | Standard Error | p-Value |
---|---|---|---|

LIPA | $1.4295$ | $0.1597$ | $<0.001$ |

MPA | $-1.3179$ | $0.1816$ | $<0.001$ |

VPA | $-0.1116$ | $0.0397$ | $0.014$ |

^{2}= 0.3005 for all models. LIPA, light-intensity physical activity; MPA, moderate physical activity; VPA, vigorous physical activity.

MB | ${\widehat{\beta}}_{1}^{\left(PA\right)}$ | Standard Error | p-Value | ${R}^{2}$ |
---|---|---|---|---|

SB | $0.0200$ | $0.0087$ | $0.023$ | $0.0119$ |

LIPA | $-0.1040$ | $0.0074$ | $<0.001$ | $0.2969$ |

MPA | $-0.0709$ | $0.0088$ | $<0.001$ | $0.1335$ |

VPA | $0.1464$ | $0.0157$ | $<0.001$ | $0.1674$ |

**Table 5.**Center of movement behavior for the whole data set and for underweight/normal and overweight/obese subgroups.

Group | SB | LIPA | MPA | VPA |
---|---|---|---|---|

All | $0.60749$ | $0.33605$ | $0.03812$ | $0.01833$ |

Underweight/normal | $0.60753$ | $0.33488$ | $0.03829$ | $0.01930$ |

Overweight/obese | $0.60694$ | $0.34121$ | $0.03734$ | $0.01451$ |

**Table 6.**Robust center of movement behavior for the whole data set and for underweight/normal and overweight/obese subgroups.

Group | SB | LIPA | MPA | VPA |
---|---|---|---|---|

All | $0.60517$ | $0.33675$ | $0.03833$ | $0.01975$ |

Underweight/normal | $0.60557$ | $0.33550$ | $0.03840$ | $0.02053$ |

Overweight/obese | $0.60806$ | $0.33885$ | $0.03738$ | $0.01571$ |

MB | ${\widehat{\mathit{\beta}}}_{1}^{\left(\mathit{M}\mathit{B}\right)}$ | Standard Error | p-Value |
---|---|---|---|

SB | $0.3756$ | $0.1897$ | $0.048$ |

LIPA | $-0.3077$ | $0.1964$ | $0.118$ |

MPA | $0.1388$ | $0.1436$ | $0.334$ |

VPA | $-0.2066$ | $0.0813$ | $0.011$ |

^{2}= 0.0258 for all models. MB, movement behavior; SB, sedentary behavior; LIPA, light-intensity physical activity; MPA, moderate physical activity; VPA, vigorous physical activity.

MB | ${\widehat{\mathit{\beta}}}_{1}^{\left(\mathit{M}\mathit{B}\right)}$ | Standard Error | p-Value |
---|---|---|---|

SB | $0.3237$ | $0.1616$ | $0.046$ |

LIPA | $-0.2277$ | $0.1966$ | $0.248$ |

MPA | $0.1388$ | $0.1550$ | $0.439$ |

VPA | $-0.2163$ | $0.0690$ | 0.00$2$ |

Shift from SB to VPA (min) | $15$ | $30$ | $45$ | $60$ |

Predicted zBMI (kg/m^{2}) | $0.12$ | $0.19$ | $0.25$ | $0.3$0 |

Weight reduction for an “average” girl (kg) | 0.83 | 1.35 | 1.73 | 2.05 |

Weight reduction for an “average” boy (kg) | $0.78$ | $1.26$ | $1.62$ | $1.91$ |

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**MDPI and ACS Style**

Štefelová, N.; Dygrýn, J.; Hron, K.; Gába, A.; Rubín, L.; Palarea-Albaladejo, J.
Robust Compositional Analysis of Physical Activity and Sedentary Behaviour Data. *Int. J. Environ. Res. Public Health* **2018**, *15*, 2248.
https://doi.org/10.3390/ijerph15102248

**AMA Style**

Štefelová N, Dygrýn J, Hron K, Gába A, Rubín L, Palarea-Albaladejo J.
Robust Compositional Analysis of Physical Activity and Sedentary Behaviour Data. *International Journal of Environmental Research and Public Health*. 2018; 15(10):2248.
https://doi.org/10.3390/ijerph15102248

**Chicago/Turabian Style**

Štefelová, Nikola, Jan Dygrýn, Karel Hron, Aleš Gába, Lukáš Rubín, and Javier Palarea-Albaladejo.
2018. "Robust Compositional Analysis of Physical Activity and Sedentary Behaviour Data" *International Journal of Environmental Research and Public Health* 15, no. 10: 2248.
https://doi.org/10.3390/ijerph15102248