Authors: Joe Walsh, Ian Timothy Heazlewood, Mark DeBeliso, Mike Climstein

Corresponding Author:Dr. Mike Climstein (FASMF, FACSM, FAAESS)Clinical Exercise PhysiologySouthern Cross UniversitySchool of Health and Human SciencesGold Coast, Queensland, AustraliaMichael.Climstein@scu.edu.au

Dr. Joe Walsh is with Sport Science Institute http://www.sportscienceinstitute.com

Ian Timothy Heazlewood is Associate Professor and Theme Leader Exercise and Sport Science in The School of Psychological and Clinical Sciences, Faculty of Engineering, Health, Science and the Environment, Charles Darwin University, Darwin, Northern Territory, Australia.

Mark DeBeliso is Professor, Department of Physical Education and Human Performance, Southern Utah University, Cedar City, USA

Dr. Mike Climstein (FASMF, FACSM, FAAESS) is with Clinical Exercise Physiology, Southern Cross University, School of Health and Human Sciences, Gold Coast, Queensland, Australia; Physical Activity, Lifestyle, Ageing and Wellbeing Faculty Research Group, University of Sydney, Sydney, NSW, Australia, 2006.

ABSTRACT

An exploration of clustering of general health orientation psychological motivations for participation in sport was conducted using t-distributed Stochastic Neighbor Embedding (t-SNE). The aim of this research was to assess the suitability of applying t-SNE to creating two-dimensional scatter plots to visualise the relationship between different general health orientation motivators. The data source used for this investigation was survey data gathered on World Masters Games competitors using the Motivations of Marathoners Scales (MOMS). Application of t-SNE plots could assist in visually mapping general health orientation psychological constructs and gaining greater understanding of the underlying patterns in the MOMS tool. Some clustering patterns were observed, with some items in the MOMS connected in a logical manner that complied with those originally proposed by the developers of the MOMS. On tuning the t-SNE model hyperparameters, it became apparent that the t-SNE graphs were able to provide an appropriate representation of clustering with learning rates outside the ranges often recommended (at the time of writing). As t-SNE is a relatively modern approach to visualizing high dimensional data, this was a finding worth reporting. Two-dimensional scatter plots produced using t-SNE may assist in creating hypotheses about the relationships present between psychological constructs in such high-dimensional data.

Key words: t-SNE, Sport Psychology, Motivations Of Marathoners Scales (MOMS), scikit-learn library, LimeSurvey

INTRODUCTION

The World Masters Games

This manuscript focuses on exploration of clustering of scores from psychometric data gathered on masters athletes. Masters athletes are defined as those systematically training for and competing in organized sporting events designed specifically for older adults (44). Competing at sport in older ages has been shown to be beneficial for a number of health indices which includes general cardiovascular health (5), blood pressure (8), improved lipids (14), reduced frailty/sarcopenia(20) and muscular strength and function (41) The biggest masters sporting event (by participant number) is the World Masters Games (WMG). Participation at the WMG is open to sports people of all abilities, limited by age. The minimum age criterion ranges between 25 and 35 years depending upon the sport. The data used in this manuscript was data gathered at the Sydney WMG, which attracted 28,089 competitors who represented 95 countries competing in 28 sports (57, 60, 63). Research on the masters athletes competing at the Sydney WMG has included investigation of smoking prevalence (53), body mass index (26, 50, 51, 52, 54, 56, 58, 63, 64), injury incidence (13, 28, 48, 49, 55) and health (9, 10, 11, 12, 14, 15, 17, 18, 19) of competitors. Masters athletes did not show increased incidence of injury in comparison to other active populations (49, 55), a finding which alleviates one potential concern with promoting participation in masters sport.

The Motivations of Marathoners Scales

The Motivations of Marathoners Scales (MOMS) (37) is a psychometric instrument based upon a series of 56 questions and scored on a seven-point Likert scale (35). To complete the MOMS, participants rated the 56 questions from 1-7 in terms of how important it is as a reason for their participation in sport. A score of 1 would indicate that the item is not a reason for participation, whereas a score of 7 indicates that the item is a very important reason for participation and scores in-between these extremes represented relative degrees of each reason. The following are sample questions which sought responses to word stems such as; to control my weight, to compete with others, to earn respect of peers, to improve my sporting performance, to earn respect of people in general, to socialize with other participants, to improve my health, to compete with myself, to become less anxious, to improve my self-esteem and to become less depressed. A full list of the 56 questions in the MOMS scale and summary statistics for the MOMS scale data gathered at the Sydney WMG has been previously published (40, 60).

The MOMS is a valid and reliable, quantitative instrument for gauging the importance of a range of psychological factors in determining motivations for sports participation. Participant motivation evaluates those factors that enhance or inhibit motivation to participate and are represented by factors such as health orientation, weight concern/weight loss and personal goal achievement (39, 40, 65). The questions in the scale are split into general categories and these are further subset into Scales (40). For example, for questions in the category Physical Health Motives, to improve my health, to prolong my life, to become more physically fit, to reduce my chance of having a heart attack, to stay in physical condition and to prevent illness comprise the General Health Orientation subset of Physical Health Motive questions. The other subset of Physical Health Motivation questions, Weight Concern is composed of to look leaner, to help control my weight, to reduce my weight and to stay physically attractive(40).

The MOMS scale has been adopted to investigate athletes competing in other sports (other than marathon), including at both multi-sport events (24, 32) and individual sports tournaments such as rugby (30), or triathlon (6) (with some adaption). Data collected using the MOMS scale has also been used as a convenience sample for demonstrating applications of data mining techniques that can be used in exercise science and exercise psychology (34, 35, 61, 62).

The age ranges in the research used to develop the MOMS survey instrument had significant overlap with age ranges of participants at the WMG. The questions identified in the MOMS have been demonstrated (7, 21, 42, 45) as important motivational constructs and have been used by sport psychology researchers for more than 25 years. A number of studies have been conducted on the MOMS in the context of masters athletes (1, 2, 3, 22, 23, 24, 25, 26, 27, 33, 47, 64). Heazlewood and colleagues (29) re-evaluated the first and second order factor structure of the MOMS instrument with masters athletes, the factor structure identified in the original MOMS instrument was not reproduced with the WMG male and female cohorts.

t-distributed Stochastic Neighbor Embedding

There are a number of established techniques for visualizing high dimensional data. A relatively modern technique that has a number of advantages over many earlier approaches is t-distributed Stochastic Neighbor Embedding (t-SNE) (38). With t-SNE, high dimensional data can be converted into a two dimensional scatter plot via a matrix of pair-wise similarities.

Stochastic Neighbor Embedding (SNE) converts Euclidean distances between data points into conditional probabilities that represent similarities (36). In t-SNE the SNE cost function is replaced with a symmetrized version with simpler gradients (38) and t-SNE uses a Cauchy Distribution (one dimensional Students-t distribution (as opposed to a Gaussian distribution)) to compute the similarity between two points in the lower-dimensional space (38). This distribution allows for more dispersion in the lower-dimensional space. Similar to SNE, the t-SNE algorithm develops a probability distribution between factor pairs in the higher-dimensional space with higher probabilities assigned to pairs with higher similarity. A similar probability distribution is then developed in a lower-dimensional map and the Kullback-Leibler divergence (37) between the two distributions is then minimized with respect to the points in the maps using gradient descent. The aim is developing a lower dimensional mapping (in our case two dimensions) where this mapping retains the similarities that were present in the higher dimensional data. The cost function for t-SNE is not convex, thus initializing scripts with different random seed values will result in differing outcomes.

AIM

Effective visualization of data plays a crucial role in knowledge discovery (16). The MOMS scale contains complex, multi-dimensional relations between 56 different questions, split into a factor structure that has not been replicated in previous research on WMG athletes (29). The aim of this research was to assess the suitability of applying t-SNE to creating two-dimensional scatter plots to visualise the relationship between different psychological motivators. If suitable plots could be constructed these could assist in visually mapping psychological constructs and gaining greater understanding of the underlying patterns in the MOMS scale. Two-dimensional scatter plots produced using t-SNE may assist in creating hypotheses about the relationships present between psychological constructs in such high-dimensional data.

METHODOLOGY

Data was collected on athletes participating in the Sydney WMG, after approval for the project was granted by a university Research Ethics Committee in accordance with the ethical standards of the Helsinki Declaration of 1975 (revised in 2008) and the Sydney World Masters Games Organising Committee. An online survey was created using Limesurvey, an open-source, web-based application to deliver the survey. The survey consisted of several sections. A total of 3,928 masters athletes completed all 56 questions in the MOMS. This manuscript analyses psychological participation factors contained within the survey. Further details about the survey methodology and an overview of findings from the survey has been previously published (59).

The psychological participation factors included in the survey were 56 questions based on the MOMS (60). These were analysed using the t-SNE package included in the scikit-learn python machine learning library (43). Analysis was conducted using Python 3.6.5 using operating system x86_64-apple-darwin15.6.0 (64-bit). After provisional exploratory analysis of different hyper parameters, it was deemed appropriate to keep the majority of t-SNE hyper parameters fixed at their default settings (the standard settings within the scikit-learn library, with default values and a description of each hyper parameter reported in Table 1) and tune the learning rate hyper parameter. The learning rate was tuned from values of 0.0001 to 1000, which was outside the recommended range in the scikit-learn (43) package recommendations (10-1000) (46). The fixed values for the other main hyper parameters for t-SNE implemented via scikit-learn (46) are listed in Table 1 below.

Table 1. Descriptions and default values for the t-SNE hyper parameters in the scikit-learn package (46)

RESULTS

Figure 1: Learning Rate 100

Figure 2: Learning Rate 10

Figure 3: Learning Rate 0.125

DISCUSSION

The Figures 1-3 are a visual representation of the clustering of the 56 psychological motivations documented in the literature (31, 40, 42, 60). As the dimensional reduction utilized in t-SNE is non-linear the axes in the graphs in Figures 1-3 represent distances in the two-dimensional space, however relating these to equivalent distances in the initial 56 dimensions is a non-linear transformation. Thus, the figures should be used as a visualization tool; however, the interpretability in the units of the initial 56 dimensional data is not apparent or suitable from the figures. In terms of visualization of relationship between the 56 variables, there were clearly patterns of clustering which give insight into relationships within the data. This discussion section focuses upon the general health orientation questions. These questions were utilised as an example of the replication (or disparity) of clustering relationships in the original development of the MOMS instrument (40) when questions are inspected graphically utilising t-SNE.

Inspection of clustering of questions on the t-SNE scatter plots revealed many patterns that were representative of underlying relationships between the different questions. Many of the clustering relationships as proposed in the original scale (40) were evident in this data explored using t-SNE. For example in Figure 1 using a learning rate of 100, for the General Health Orientation items, the questions to stay in physical condition, to become more physically fit, to improve my health are closely clustered closely together in quadrant IV (the lower right) of Figure 1. The questions to reduce my chance of having a heart attack and to prevent illness were also very close in positioning to these other three questions on Figure 1 with no questions from other categories between them.

It was observed that the question to prolong my life, was also to the bottom right of the diagram, but offset far to the right with a significant displacement away from any of the other questions. As the Euclidean distance between points was representative of similarities between the different questions in the MOMS for these masters athletes, this would imply that there was some meaningful difference between the responses to this question and the other 56 questions.

There was some apparent clustering for the other subset of questions within the Physical Health Motives category, namely Weight Concern, comprised of to look leaner, to help control my weight, to reduce my weight and to stay physically attractive. These questions were also closely clustered together with no other questions from other categories in the intervening space. This would imply that the clustering observed for the WMG athletes for these particular questions was compatible with that established in the development of MOMS (40).

Figure 2, produced by reducing the learning rate hyper parameter to 10, displayed a different t-SNE scatter plot, with some alteration in the clustering of questions. In many cases, this figure displayed pairs of similar questions (both in terms of logical underlying meaning in the language usage and in terms of t-SNE dimensionality). Similar to Figure 1, the General Health Orientation questions to stay in physical condition, to become more physically fit, to improve my health were clustered closely together, though for this particular t-SNE scatter-plot, the clustering was in the upper centre part of the figure (Figure 2). This is due to different learning rates and initialisation with a given random seed. The Cartesian coordinates of different questions was not the focus of this manuscript as t-SNE was utilized instead to explore the data in terms of Euclidean distance between the questions (as detailed in the introduction section). Whilst the other three questions within General Health Orientation, namely to reduce my chance of having a heart attack, to prolong my life and to prevent illness are very close in positioning to each other, however situated on the right of Figure 2. They are considerably separated from the first three questions. This would imply two separate subsets of three questions within General Health Orientation. The Weight Concern scale questions in Figure 2 to look leaner, to help control my weight and to reduce my weight are clustered together, not too far from one of the apparent subsets of General Health Orientation questions also on the right hand side of the diagram, with to help control my weight and to reduce my weight more tightly clustered than to look leaner, which is offset slight to the left from the pair. This grouping is logical in terms of the rational interpretation of the language used in the questions, specifically the two more closely grouped questions contain language specific to weight control/reduction, whilst the other question was related to physical appearance.

In Figure 3, the General Health Orientation questions were split into two subgroups with to prolong my life, to reduce my chance of having a heart attack and to prevent illness clustered in the upper centre of Figure 3. The questions to stay in physical condition, to become more physically fit and to improve my health were separated from the other cluster and were located towards the lower left of the graph. There were more than ten questions located between these two clusters across the two t-SNE dimensions. This result implied two different clusterings and was contrary to the grouping of both clusters together under the same category of General Health Orientation.

All of the t-SNE plots in Figures 1-3 have different subgroupings of psychological motivations including those explicitly discussed for motivations within category of General Health Orientation. Although there were differences, the general categorization of questions in the MOMS did also have some shared and clearly visible commonalities with the groupings apparent in t-SNE graphs created across a range of learning rates. Despite differences according to random initialisation parameters and learning rates, the figures demonstrate that t-SNE can be utilised to produce two-dimensional graphs to visualize the relationship between the different psychological motivation questions comprising the MOMS tool. Visual inspection confirms viable patterns of clustering which give insight into relationships within the data, with these patterns being logical in context of the underlying meaning in the language usage and specific groupings of questions. Further review could be conducted on the differences demonstrated between the MOMS general categorization of questions and the t-SNE graphs. An example would be distinct and separate clusters of questions forming two separate clusters for General Health Orientation questions. Based solely on this cursory visual analysis via these scatter plots, it would be advisable to split the General Health Orientation questions into separate groups and similar patterns may be present for other groupings. This splitting is however not advised without further supporting evidence and it should be noted though that devising such alternative groupings is not the aim of this research, which was to assess the suitability of applying t-SNE to creating two dimensional scatter plots to visualise the relationship between different psychological motivators with specific reference to General Health orientation questions. Such graphs were successfully created. These two dimensional scatter plots produced using t-SNE may assist in creating hypotheses about the relationships present between psychological constructs in such high-dimensional data both for the WMG athletes using the MOMS, for others using the MOMS and for applications outside of MOMS using other tools.

It was interesting to note that the hyper parameter tuning was conducted beyond the recommended ranges provided in the scikit-learn package documentation for t-SNE learning rates (10-1000). This extended range was selected based on investigators extensive experience in hyper parameter tuning. The appropriate learning rates for hyper parameter tuning were found to be well below the standard range (e.g. learning rates below 0.1, such as 0.125 in Figure 3). It should be noted that all other values were set as the scikit-learn package defaults (with values used listed in the method section). As t-SNE is a relatively modern technique, findings that could be beneficial in recommendations for implementation such as this should be noted.

CONCLUSION

It was demonstrated that t-SNE could be utilised to produce two-dimensional graphs to visualize the relationship between the different psychological motivation questions comprising the MOMS tool. Visual inspection confirmed the presence of patterns of clustering which gave viable insight into clustering relationships within the data. Patterns were apparent that were logical in terms of the underlying meaning in the language usage and specific groupings of questions

The general categorization of questions in the MOMS had commonalities with the groupings apparent in t-SNE graphs created across a range of learning rates. There were also some differences demonstrated in the t-SNE graphs. An example would be distinct and separate clusters of questions forming two separate clusters for General Health Orientation questions. Based solely on this cursory visual analysis via these scatter plots, it would be advised to split the General Health Orientation questions into separate groups and similar patterns may be present for other groupings. This is however not advised and it should be noted though that devising such alternative groupings is not the aim of this research, which was to assess the suitability of applying t-SNE to creating two dimensional scatter plots to visualise the relationship between different psychological motivators. Such graphs were successfully created. The two-dimensional scatter plots produced using t-SNE may assist in creating hypotheses about the relationships present between psychological constructs in such high-dimensional data.

A secondary finding was apparent based on the learning rates used in hyper parameter tuning. On tuning the t-SNE model hyper parameters, it became apparent that the t-SNE graphs were able to provide an appropriate representation of clustering with learning rates outside the ranges often recommended. As t-SNE is a relatively modern approach to visualizing high dimensional data, this was a notable finding.

APPLICATIONS IN SPORT

The MOMS is a valid and reliable, quantitative instrument for gauging the importance of a range of psychological factors in determining motivations for sports participation. Participant motivation evaluates those factors that enhance or inhibit motivation to participate and are represented by factors such as health orientation, weight concern/weight loss and personal goal achievement. The MOMS has been used by sport psychology researchers for more than 25 years. The MOMS scale has been adopted to investigate athletes competing in marathons, multi-sport events and individual sports tournaments such as rugby or triathlon. Data collected using the MOMS scale has also been used as a convenience sample for demonstrating applications of data mining techniques that can be used in exercise science and exercise psychology. A number of studies have been conducted on the MOMS in the context of masters athletes (1, 2, 3, 22, 23, 24, 25, 26, 27, 33, 47, 64). Heazlewood and colleagues identified the first and second order factor structure of the MOMS instrument in the context of masters athletes (29). It was demonstrated the factor structure identified in the original MOMS instrument was not reproduced within the WMG male and female cohorts (29). The data used in this manuscript was data gathered at the Sydney WMG, the biggest masters sporting event (by participant number), which attracted 28,089 competitors who represented 95 countries competing in 28 sports

Effective visualization of data plays a crucial role in knowledge discovery. The MOMS scale contains complex, multi-dimensional relations between 56 different questions, split into a factor structure that has not been replicated in previous research on masters athletes (29). The aim of this research was to assess the suitability of applying t-SNE to creating two-dimensional scatter plots to more simply visualise the relationship between different psychological motivators specifically those related to general health orientation. Suitable plots were constructed as per the aim of this experiment and these can assist in visually mapping general health orientation psychological constructs and gaining greater understanding of the underlying patterns in the MOMS scale for masters athletes and potentially in the other sports and events where motivation for participation has been examined using the MOMS, such as marathon, triathlon, rugby and other multi-sport events. The two-dimensional scatter plots produced in this paper using t-SNE may assist in creating hypotheses about the relationships present between general health orientation constructs in such high-dimensional data as the 56 questions in the MOMS instrument. This paper demonstrate that t-SNE can be utilised to produce two-dimensional graphs to visualize the relationship between the general health orientation questions comprising the MOMS tool. Some clustering patterns were observed in those motivations classified under general health orientation, with some items in the MOMS connected in a logical manner that complied with those originally proposed by the developers of the MOMS.

Masters athletes are defined as those systematically training for and competing in organized sporting events designed specifically for older adults. Competing at sport in older ages has been shown to be beneficial for a number of health indices which includes general cardiovascular health, blood pressure, improved lipids, reduced frailty/sarcopenia and muscular strength and function. Participation at the WMG is open to sports people of all abilities, limited by age. The minimum age criterion ranges between 25 and 35 years depending upon the sport. Given increased risk of injury from participation in sport at older ages has been shown in prior research to not be present for WMG competitors (49,55), it would make sense to encourage participation in masters sport (conditional on appropriate medical screening) to improve health outcomes. Visualisation of the relationship between many different general health orientation motivations in masters athletes can be accomplished using t-SNE. The clustering patterns observed in the general health orientation motivations, can be visualised in simple two dimensional plots to better understand the relationship between the different general health orientation questions comprising the MOMS tool. As a general finding related to improving understanding of the MOMS, this method may assist in progressing understanding of relationships between different general health orientation psychological constructs in high dimensional data. With better understanding of the relationship between the multi-dimensional factors involved in the motivation behind participation for masters athletes, sports marketing and strategies behind promoting participation in sports and physical exercise across the lifespan can be optimised and tailored to enhance masters sport participation and improve general health outcomes.

ACKNOWLEDGEMENTS

The authors appreciate the time taken by the 3,298 WMG masters athletes in completing the 56 questions in the MOMS survey tool. The authors also appreciate the assistance of Evan Wills in data collection using LimeSurvey and the Sydney World Masters Games Organising Committee in approving the project.

REFERENCES

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General health orientation based psychological motivations for masters athletes, a consideration of clustering utilizing t-distributed Stochastic...