# 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

- Janssen, I.; LeBlanc, A.G. Systematic review of the health benefits of physical activity and fitness in school-aged children and youth. Int. J. Behav. Nutr. Phys. Act.
**2010**, 7, 40. [Google Scholar] [CrossRef] [PubMed] [Green Version] - World Health Organization (WHO). Physical Activity and Young People; WHO: Geneva, Switzerland, 2015; Available online: http://www.who.int/dietphysicalactivity/factsheet_young_people/en (accessed on 19 August 2018).
- McMahon, E.M.; Corcoran, P.; O’Regan, G.; Keeley, H.; Cannon, M.; Carli, V.; Wasserman, C.; Hadlaczky, G.; Sarchiapone, M.; Apter, A.; et al. Physical activity in European adolescents and associations with anxiety, depression and well-being. Eur. Child Adolesc. Psychiatry
**2017**, 26, 111–122. [Google Scholar] [CrossRef] [PubMed] - Gába, A.; Dygrýn, J.; Mitáš, J.; Jakubec, L.; Frömel, K. Effect of accelerometer cut-off points on the recommended level of physical activity for obesity prevention in children. PLoS ONE
**2016**, 11, e0164282. [Google Scholar] [CrossRef] [PubMed] - Malina, R.M. Physical activity and fitness: Pathways from childhood to adulthood. Am. J. Hum. Biol.
**2001**, 13, 162–172. [Google Scholar] [CrossRef] [Green Version] - Telama, R.; Yang, X.; Viikari, J.; Välimäki, I.; Wanne, O.; Raitakari, O. Physical activity from childhood to adulthood: A 21-year tracking study. Am. J. Prev. Med.
**2005**, 28, 267–273. [Google Scholar] [CrossRef] [PubMed] - Gába, A.; Mitáš, J.; Jakubec, L. Associations between accelerometer-measured physical activity and body fatness in school-aged children. Environ. Health Prev. Med.
**2017**, 22, 43. [Google Scholar] [CrossRef] [PubMed] - Carson, V.; Ridgers, N.D.; Howard, B.J.; Winkler, E.A.H.; Healy, G.N.; Owen, N.; Dunstan, D.W.; Salmon, J. Light-intensity physical activity and cardiometabolic biomarkers in us adolescents. PLoS ONE
**2013**, 8. [Google Scholar] [CrossRef] [PubMed] - Chaput, J.P.; Saunders, T.J.; Carson, V. Interactions between sleep, movement and other non-movement behaviours in the pathogenesis of childhood obesity. Obes. Rev.
**2017**, 18, 7–14. [Google Scholar] [CrossRef] [PubMed] - Tremblay, M.; LeBlanc, A.; Kho, M.; Saunders, T.; Larouche, R.; Colley, R.; Goldfield, G.; Connor Gorber, S. Systematic review of sedentary behaviour and health indicators in school-aged children and youth. Int. J. Behav. Nutr. Phys. Act.
**2011**, 8, 98–119. [Google Scholar] [CrossRef] [PubMed] - Biddle, S.J.H.; Asare, M. Physical activity and mental health in children and adolescents: A review of reviews. Br. J. Sports Med.
**2011**, 45, 86–95. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chastin, S.F.M.; Palarea-Albaladejo, J.; Dontje, M.L.; Skelton, D.A. Combined effects of time spent in physical activity, sedentary behaviors and sleep on obesity and cardio-metabolic health markers: A novel compositional data analysis approach. PLoS ONE
**2015**, 10. [Google Scholar] [CrossRef] [PubMed] - Aitchison, J. The statistical analysis of compositional data. J. R. Stat. Soc. Ser. B
**1982**, 44, 139–177. [Google Scholar] [CrossRef] - Zhu, W.; Ainsworth, B.; Liu, Y.L. A Comparison of Urban Black and White Women’s Physical Activity Patterns. Res. Q. Exerc. Sport
**2002**, 73, A36. [Google Scholar] - Williams, S.M.; Farmer, V.L.; Taylor, B.J.; Taylor, R.W. Do more active children sleep more? A repeated cross-sectional analysis using accelerometry. PLoS ONE
**2014**. [Google Scholar] [CrossRef] [PubMed] - Carson, V.; Tremblay, M.S.; Chaput, J.-P.; Chastin, S.F.M. Associations between sleep duration, sedentary time, physical activity, and health indicators among Canadian children and youth using compositional analyses. Appl. Physiol. Nutr. Metab.
**2016**, 41, S294–S302. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fairclough, S.J.; Dumuid, D.; Taylor, S.; Curry, W.; McGrane, B.; Stratton, G.; Maher, C.; Olds, T. Fitness, fatness and the reallocation of time between children’s daily movement behaviours: An analysis of compositional data. Int. J. Behav. Nutr. Phys. Act.
**2017**, 14, 64. [Google Scholar] [CrossRef] [PubMed] - Dumuid, D.; Olds, T.; Lewis, L.K.; Martin-Fernández, J.A.; Katzmarzyk, P.T.; Barreira, T.; Broyles, S.T.; Chaput, J.P.; Fogelholm, M.; Hu, G.; et al. Health-related quality of life and lifestyle behavior clusters in school-aged children from 12 countries. J. Pediatr.
**2017**. [Google Scholar] [CrossRef] [PubMed] - Dumuid, D.; Maher, C.; Lewis, L.K.; Stanford, T.E.; Martín Fernández, J.A.; Ratcliffe, J.; Katzmarzyk, P.T.; Barreira, T.V.; Chaput, J.P.; Fogelholm, M.; et al. Human development index, children’s health-related quality of life and movement behaviors: A compositional data analysis. Qual. Life Res.
**2018**, 27, 1473–1482. [Google Scholar] [CrossRef] [PubMed] - Dumuid, D.; Stanford, T.E.; Pedišić, Ž.; Maher, C.; Lewis, L.K.; Martín-Fernández, J.A.; Katzmarzyk, P.T.; Chaput, J.P.; Fogelholm, M.; Standage, M.; et al. Adiposity and the isotemporal substitution of physical activity, sedentary time and sleep among school-aged children: A compositional data analysis approach. BMC Public Health
**2018**, 18, 311. [Google Scholar] [CrossRef] [PubMed] - Fairclough, S.J.; Dumuid, D.; Mackintosh, K.A.; Stone, G.; Dagger, R.; Stratton, G.; Davies, I.; Boddy, L.M. Adiposity, fitness, health-related quality of life and the reallocation of time between children’s school day activity behaviours: A compositional data analysis. Prev. Med. Rep.
**2018**, 11, 254–261. [Google Scholar] [CrossRef] [PubMed] - Pedišić, Ž.; Dumuid, D.; Olds, T.S. Integrating sleep, sedentary behaviour, and physical activity research in the emerging field of time-use epidemiology: Definitions, concepts, statistical methods, theoretical framework, and future directions. Kinesiology
**2017**, 49, 252–269. [Google Scholar] - Mitáš, J.; Dygrýn, J.; Rubín, L.; Křen, F.; Vorlíček, M.; Nykodým, J.; Řepka, E.; Bláha, L.; Suchomel, A.; Feltlová, D.; et al. Multifaktoriální výzkum zastavěného prostředí, aktivního životního stylu a tělesné kondice české mládeže: Design a metodika projektu. Tělesná Kult.
**2018**. [Google Scholar] [CrossRef] - Cain, K.L.; Sallis, J.F.; Conway, T.L.; Van Dyck, D.; Calhoon, L. Using accelerometers in youth physical activity studies: A review of methods. Phys. Act. Heal.
**2013**, 10, 437–450. [Google Scholar] [CrossRef] - Evenson, K.R.; Catellier, D.J.; Gill, K.; Ondrak, K.S.; McMurray, R.G. Calibration of two objective measures of physical activity for children. J. Sports Sci.
**2008**, 26, 1557–1565. [Google Scholar] [CrossRef] [PubMed] - Trost, S.G.; Loprinzi, P.D.; Moore, R.; Pfeiffer, K.A. Comparison of accelerometer cut points for predicting activity intensity in youth. Med. Sci. Sports Exerc.
**2011**. [Google Scholar] [CrossRef] [PubMed] - De Onis, M.; Onyango, A.W.; Borghi, E.; Siyam, A.; Nishida, C.; Siekmann, J. Development of a WHO growth reference for school-aged children and adolescents. Bull. World Heal. Organ.
**2007**, 85, 812–819. [Google Scholar] [CrossRef] - Pawlowsky-Glahn, V.; Egozcue, J.J.; Tolosana-Delgado, R. Modeling and Analysis of Compositional Data; Wiley: Hoboken, NJ, USA, 2015; ISBN 9781119003144|9781118443064. [Google Scholar]
- Fišerová, E.; Hron, K. On the interpretation of orthonormal coordinates for compositional data. Math. Geosci.
**2011**, 43, 455–468. [Google Scholar] [CrossRef] - Hron, K.; Filzmoser, P.; de Caritat, P.; Fišerová, E.; Gardlo, A. Weighted pivot coordinates for compositional data and their application to geochemical mapping. Math. Geosci.
**2017**, 49, 797–814. [Google Scholar] [CrossRef] - Rousseeuw, P.J.; van Zomeren, B.C. Unmasking multivariate outliers and leverage points. J. Am. Stat. Assoc.
**1990**, 85, 633–639. [Google Scholar] [CrossRef] - Buccianti, A.; Grunsky, E. Compositional data analysis in geochemistry: Are we sure to see what really occurs during natural processes? J. Geochem. Explor.
**2014**, 141, 1–5. [Google Scholar] [CrossRef] [Green Version] - Muller, I.; Hron, K.; Fiserova, E.; Smahaj, J.; Cakirpaloglu, P.; Vancakova, J. Interpretation of compositional regression with application to time budget analysis. Austrian J. Stat.
**2018**, 47, 3–19. [Google Scholar] [CrossRef] - Hrůzová, K.; Todorov, V.; Hron, K.; Filzmoser, P. Classical and robust orthogonal regression between parts of compositional data. Statistics (Ber.)
**2016**, 50, 1261–1275. [Google Scholar] [CrossRef] - Abelson, R.P. A variance explanation paradox: When a little is a lot. Psychol. Bull.
**1985**, 97, 129–133. [Google Scholar] [CrossRef] - Maronna, R.A.; Martin, R.D.; Yohai, V.J. Robust Statistics: Theory and Methods; Wiley: Hoboken, NJ, USA, 2006; ISBN 9780470010921. [Google Scholar]
- Yohai, V.J. High breakdown-point and high efficiency robust estimates for regression. Ann. Stat.
**1987**, 15, 642–656. [Google Scholar] [CrossRef] - Hron, K.; Filzmoser, P. Exploring compositional data with the robust compositional biplot. In Advances in Latent Variables: Methods, Models and Applications; Carpita, M., Brentari, E., Qannari, E.M., Eds.; Springer International Publishing: Cham, Switzerland, 2015; pp. 219–226. ISBN 978-3-319-02967-2. [Google Scholar]
- Von Eynatten, H.; Pawlowsky-Glahn, V.; Egozcue, J.J. Understanding perturbation on the simplex: A simple method to better visualize and interpret compositional data in ternary diagrams. Math. Geol.
**2002**, 34, 249–257. [Google Scholar] [CrossRef] - Dumuid, D.; Stanford, T.E.; Martin-Fernández, J.-A.; Pedišić, Ž.; Maher, C.A.; Lewis, L.K.; Hron, K.; Katzmarzyk, P.T.; Chaput, J.-P.; Fogelholm, M.; et al. Compositional data analysis for physical activity, sedentary time and sleep research. Stat. Methods Med. Res.
**2017**. [Google Scholar] [CrossRef] [PubMed] - Pesenson, M.Z.; Suram, S.K.; Gregoire, J.M. Statistical analysis and interpolation of compositional data in materials science. ACS Comb. Sci.
**2015**, 17, 130–136. [Google Scholar] [CrossRef] [PubMed] - Filzmoser, P.; Hron, K.; Reimann, C. Univariate statistical analysis of environmental (compositional) data: Problems and possibilities. Sci. Total Environ.
**2009**, 407, 6100–6108. [Google Scholar] [CrossRef] [PubMed] - Palarea-Albaladejo, J.; Martín-Fernández, J.A.; Olea, R.A. A bootstrap estimation scheme for chemical compositional data with nondetects. J. Chemom.
**2014**, 28, 585–599. [Google Scholar] [CrossRef] - Agerbo, E.; Sterne, J.A.C.; Gunnell, D.J. Combining individual and ecological data to determine compositional and contextual socio-economic risk factors for suicide. Soc. Sci. Med.
**2007**, 64, 451–461. [Google Scholar] [CrossRef] [PubMed] - Campbell, G.P.; Curran, J.M.; Miskelly, G.M.; Coulson, S.; Yaxley, G.M.; Grunsky, E.C.; Cox, S.C. Compositional data analysis for elemental data in forensic science. Forensic Sci. Int.
**2009**, 188, 81–90. [Google Scholar] [CrossRef] [PubMed] - Leite, M.L.C. Applying compositional data methodology to nutritional epidemiology. Stat. Methods Med. Res.
**2016**, 25, 3057–3065. [Google Scholar] [CrossRef] [PubMed] - Mert, M.C.; Filzmoser, P.; Endel, G.; Wilbacher, I. Compositional data analysis in epidemiology. Stat. Methods Med. Res.
**2016**, 1–14. [Google Scholar] [CrossRef] [PubMed] - Filzmoser, P.; Hron, K.; Reimann, C.; Garrett, R. Robust factor analysis for compositional data. Comput. Geosci.
**2009**, 35, 1854–1861. [Google Scholar] [CrossRef] [Green Version] - Filzmoser, P.; Hron, K. Robust statistical analysis of compositional data. In Compositional Data Analysis: Theory and Applications; Pawlowsky-Glahn, V., Buccianti, A., Eds.; John Wiley & Sons, Ltd.: Chichester, UK, 2011; pp. 59–72. ISBN 9781119976462. [Google Scholar]
- Filzmoser, P.; Hron, K. Robust statistical analysis. In Robustness and Complex Data Structures; Becker, C., Fried, R., Kuhnt, S., Eds.; Springer: Heidelberg, Germany, 2013; pp. 117–131. ISBN 9781119976462. [Google Scholar]
- Tanaka, C.; Reilly, J.J.; Huang, W.Y. Longitudinal changes in objectively measured sedentary behaviour and their relationship with adiposity in children and adolescents: Systematic review and evidence appraisal. Obes. Rev.
**2014**, 15, 791–803. [Google Scholar] [CrossRef] [PubMed] - Orme, M.; Wijndaele, K.; Sharp, S.J.; Westgate, K.; Ekelund, U.; Brage, S. Combined influence of epoch length, cut-point and bout duration on accelerometry-derived physical activity. Int. J. Behav. Nutr. Phys. Act.
**2014**, 11, 34. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**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) | $0.78$ | $1.26$ | $1.62$ | $1.91$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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