Analysis of Depression in Social Networks: An application in Biostatistics

Donostia. First Edition. 2020

Introduction

Have you ever wondered if using social media so much could affect your mood? There are those who relate misuse of social networks to psychological problems such as depression, but what is true in this idea? Is there scientific evidence that alerts us to real dangers of social networks, or are these fears unfounded?

During the first edition of the Saturdays AI program in Euskadi, the group facemood We embarked on the challenge of analyzing whether we can predict a series of symptoms related to depression based on our use of social networks. To do this, we use a range of statistical tools and Machine Learning that helped us understand the relationship between these variables.

The depression It constitutes a major public health problem, as it is a major risk factor for suicide, which claims hundreds of thousands of lives each year.

Therefore, we understand that knowing in depth the aspects that could be associated with depression is the only way to help design efficient public policies to improve this problem, and definitely,save lives!

Who are we?

As if it were a futsal match, we present our starting quintet:

• Hello!!! I am Ana Patricia Bautista García, Industrial and Systems Engineer and master in Business Analytics and Big Data. This project motivates me because it combines several disciplines such as Data Science, Statistics and Psychology. Which from the beginning seemed to me to be a very complete and interesting exercise to apply the knowledge acquired in AI Saturdays.
• Hello everyone. My name is Henry Corazza Sef and I am a statistician. I began my professional career working in a university hospital as a biostatistician. Although I have chosen to work on the implementation of the 6 Sigma Methodology In the industrial area, I am still interested in Biostatistics.
• Hello! I am Dani, psychologist and neuroscientist. I have dedicated the last few years to brain research. I am also interested in Open Science, and I try to train myself in open data management and reproducible workflows.
• Hello Internet user! My name is Sergio Navarro, engineer software. I work in a small startup alavesa like full stack developer and I spend my time between lines of code, databases and questions of stackoverflow that can solve that bug that doesn't let me sleep.
• Hello, I am Sergio Hernando, graduated in Computer Engineering and recently started in the world of work as a digital architect training in Cloud Computing. I'm usually in the clouds, but in this case they are AWS and Azure.

As a starting point, we rely on the work carried out by a group of Dutch and American researchers titled: ‘Social Media and Depression Symptoms: A Network Perspective’ (DOI:10.1037/xge0000528; accessible too in open). In this study, the researchers examined whether passive social media use (i.e., doing scrolling in the feed news or photographs of our friends and contacts) causes depressive symptoms, or vice versa.

To obtain the data, each of the participants in the study received a questionnaire on their mobile phone in which they had to answer from 0 to 100 how they felt in reference to each of the possible symptoms of depression: lack of energy (Fatigue), low mood (LowMood), loneliness (Loneliness), concentration problems (Concentration), loss of interest (Loss of Interest), feeling of inferiority (Inferiority), hopelessness (Hopeless), and stress (Stress). They also had to answer from 0 to 100 to three questions related to the use of Social Networks: passive use (PSMU), active (ASMU), and news consultation (News: access information of a political nature or public interest). Participants filled out this questionnaire seven times a day for 14 days.

Below is a brief description of the 11 study variables:

To carry out this project, we have planned an analysis strategy according to the scheme below, in which we have used different methodologies and tools:

1. EDA (Exploratory Data Analysis)

2. Cluster Analysis

3. ANOVA of Repeated Measures

4. Regression Analysis

Figure 1. Analysis Strategy.

1. EDA (Exploratory Data Analysis)

As it is a set of data from a scientific publication and having gone through a prior analysis during said research, we could say that it has greater validity compared to a dataset that we obtain through a platform open source like kaggle. However, this does not mean that we should not carry out data analysis on our part, in order to find patterns and prepare the data for analysis tasks. Machine Learning.

The first phase consisted of identifying those measurements that we consider valid. Logically, many of the participants forgot to carry out some of them (carrying out 7 measurements a day for 14 days is not an easy task. ?), or they didn't know how to respond to some of the symptoms (quantifying your mood from 0 to 100 isn't either...). All these measurements were eliminated.

In a second phase, we looked at whether the remaining measurements were coherent: they do not have the same value in all symptoms, they are not recurrent responses, they were carried out within the defined time period, etc.

In this way, we are ready to take action!

2. Cluster Analysis

The next phase consisted of carrying out a Cluster Analysis, one of the techniques of Machine Learning to identify groups in the dataset. We use the methods Elbow and Silhouette to get the number of clusters optimal and the algorithm K-means, technique unsupervised learning to do clustering.

Identification of the optimal number of clusters

Method Elbow: in this the average distortion of the clusters, that is, the average distance of the centroid to all points on the cluster. This is obtained with the algorithm K-means depending on the number of clusters. To solve this exercise, we have created the function plot_elbow, which receives a data set and a chart title. We set the values of the parameters max_k in 10. What the function does is try each value from 1 to 9 and graph the result.

Figure 2. Graph representing the Elbow method.

The graph shows us that, starting at value 3, the dispersion begins to reduce drastically. Therefore, we can take 3 as the optimal value.

Method Silhouette: The coefficient of Silhouette It is defined as the difference between the average distance to the elements of the cluster nearest (b) and the intra-distancecluster average of the elements of a cluster (to) divided by the maximum of the two, only being able to take values between -1 and 1.

Figure 3. Graphic representing the Silhouette method.

With this method we verify that 3 can be a good value to test our cluster analysis.

Algorithm implementation k-means and visualization of the groups in a 3D graph

The algorithm receives a set of data to train it and a number of clusters to divide it. Through the method predict the class of the trained object is obtained in the dataset, and finally each data is represented with a different color depending on the cluster to which it has been assigned. We can see the result in the Figure 4 and the distribution of participants in the Figure 5.

Figure 4. Visualization of the groups in a 3D graph.

Figure 5. Distribution of participants by cluster.

Finally, to conclude with the Cluster Analysis, We have created a series of graphs (overlapping histograms) to identify at a glance the differences in each variable between the members of each cluster.

Figure 6. RR.SS variables. by cluster.

Figure 7. Variables related to depression, for cluster.

Figure 8. Variables related to depression, for cluster.

It is observed that the 3 clusters are different when it comes to symptoms related to depression, being the Cluster 1 the one that contains the higher average scores in relation to the 8 symptoms of the study, so it could be stated that it is the group with the greatest propensity to present a possible depression.

However, as we can see in the Figure 6 (RR.SS variables. by Cluster), in the case of variables related to RR.SS. We did not find major differences between clusters.

Figure 9. Table of averages by cluster.

3. ANOVA of Repeated Measures

There are two aspects to this dataset that especially caught our attention. On the one hand, the fact of having taken measurements for two weeks offers us the possibility of exploring whether these measurements vary over time. Using a line graph or lineplot We can get an idea of how each of the depression-related symptoms that have been measured has varied, on average.

Figure 10. Means of each variable grouped by day of the week.

Although there appears to be some variation over time in some of the variables, we cannot be sure at a glance whether the data would be expected to vary this way by pure chance or because we have not used a very good measuring instrument.

On the other hand, we know that a large number of measurements were carried out on each participant. As we explained above, 125 subjects were monitored for depression-related symptoms for 14 days. Furthermore, each day the participants were asked to fill out the scale every 2 hours from 10:00 to 22:00. Therefore, with seven daily measurements for two weeks in 125 subjects, we have a total of 12,250 observations in the dataset.

But be careful! These observations are not independent of each other. We cannot use a statistical model that takes each of these observations as if they came from different people, because the variability we obtain by repeatedly measuring the same individual will be different from the variability obtained by measuring different individuals (at least if the measurement is minimally reliable).

There is a statistical model that does allow us to analyze the influence of time on our data, but respecting the fact that not all observations are independent, but rather we have groups of 98 observations over time for 125 subjects. This model is called Analysis of Variance (or ANOVA) of Repeated Measures.

As our sample size is not excessively large (125 participants) and we have 8 variables of symptoms related to depression, we decided not to incorporate all the variables into the statistical model and estimate a simplified model for the 'low mood' variable (LowMood). Therefore, it would be a repeated measures ANOVA with two factors: (i) time, where the average scores for each day on this variable are included; and (ii) cluster, where the belonging of each subject to the clusters calculated previously. The null hypothesis of this model states that all means of the LowMood They are the same throughout the 14 days of surveys.

Figure 11. Average of each questionnaire variable per day and cluster.

As we can see in the Figure 11 (variable LowMood), the variability of the data over time is minimal and, in fact, although the result of the statistical test is statistically significant (f(13,26) = 2.261, p = 0.018), the effect size is practically negligible (η2 = 0.02).

Therefore, the repeated measures ANOVA statistical model has informed us that, despite having a dataset Relatively rich in details in the temporal dimension, depression-related symptoms associated with social media use do not seem to vary much over time.

4. Regression Analysis

The first step we took to fit the linear regressions was to calculate the means of all the measurements by participant and variable. This allowed us to “remove” the temporal “repeated measures” aspect of the study.

Next, we build scatter plots between all the study variables, and we calculate the Pearson linear correlation coefficients (r2) for all combinations of variables, with the objective of identifying the various types of correlation and some possible “multicollinearity” between variables (r2 > 90%).

We observed that some variables were highly linearly correlated, as can be seen in the graph below:

Figure 12. Matrix diagram of the scatter plots of the 11 study variables.

To fit an initial model, we had to define a variable “response” or “and". We choose "LowMood”, because it is in principle one of the most important variables of the study.

In the heat map of Pearson linear correlations, multicollinearity is observed between “Loneliness and Hopeless", and "Lower and Hopeless”, so we decided not to use “Hopeless”.

Figure 13. Pearson correlation coefficients heat map
of the 11 variables of the study.

For adjustment of the Regression Model, we use the method “backward”: from the model saturated with all the available independent variables, the method eliminated, one by one, said variables whose p-value > alpha, being alpha = probability of “type 1 error”.

To do this, we create a recurring function called “calculateRegression”, which uses 80% of the data for adjustments, and reserves 20% of the data for testing.

Additionally, the function calculates the “RootMeanSquareError” (RMSE) and the “Coefficient of Determination” (R2) for all settings.

Figure 14. Output of the methodbackward” variable elimination
with little explanatory capacity.

The Final Model adjusted involves 3 variables, being “News” one of them.

LowMood = -0,85 + 0,78 Loneliness + 0,18 Stress + 0,04 News

It is important to highlight that the coefficient of determination (R2) of the adjusted model is “high” (93.1%).

To definitively validate the model, we performed a “Residue Analysis”, also collected in a function called “residualAnalysis”. This function performs the “normality test” (Kolmogorov-Smirnov) of the standardized residuals and prints 3 graphs: Scatter Plot between “Prediction” and “Standardized Residuals”, Histogram of the Standardized Residuals, and “Normal Q-Q Plot” of the Standardized Residuals.

Since the Residual Analysis was also considered satisfactory, the model is statistically validated.

Figure 15. Output of the function “residualAnalysis”.

It is important to note that the weight of “News” (0.04) is much lower than the weights of “Loneliness” (0.78) and “Stress” (0.18), and that, if we had defined a “alpha"more demanding,"News” would not be maintained in the final model.

On the other hand, given the complexity of diagnosing a person with depression, we built a “depression index", to be used as a response variable of a second model. The idea was to compare the 2 models, in order to corroborate the previous conclusions.

The depression index, from now onDeprRate", was calculated as the simple average between "LowMood”, “LostOfInt” and “Hopeless”, since these variables could contain important indications of possible depression, according to the literature.

We follow the same steps outlined above. The final model now contains 5 variables and does not involve any variable related to the use of Social Networks.

DeprRate = -0,025 + 0,31 Loneliness + 0,25 Lower + 0,19 Concentrate + 0,15 Stress + 0,06 Fatigue

The coefficient of determination (R2) of the adjusted model remained high (90.8%), and since the Residual Analysis was also considered satisfactory, the model was validated from a statistical point of view.

It is interesting to note that “Loneliness” again appears as the variable with the greatest weight for “DeprRate", and that "Stress” continues in this second model, with a similar weight.

Note: The 2 functions discussed above are defined in “regression_functions.pyOther functions used in this analysis can also be found in this file, such as:

• printMatrixDiagram: function that generates scatter plots (2 to 2), involving all the study indicators. Useful to see graphically, at a single glance, the indicators that are most correlated with each other.
• printPearsonCorrelations- Generates a heat map of Pearson correlations between all indicators in the study. Useful to see, at a single glance, the indicators that are most correlated with each other and if there is multicollinearity.
• eliminateOutliers: eliminates the standardized residuals considered “high” (less than -3 and greater than +3), in order to subsequently make new adjustments without this data, which often distorts the results. The function prints the deleted data, allowing control of what is being deleted.
• repeatRegression: refits the final linear regression model fitted in “calculateRegression”, now for the data free of “outliers". Also, recalculate the "RootMeanSquareError” (RMSE) and the “Coefficient of Determination” (R2).

Final Conclusions

In relation to Cluster Analysis, it is observed that the 3 clusters formed are different as far as “depression symptoms” are concerned, the Cluster 1 the one that contains the highest means in relation to the 8 symptoms of the study. However, the same does not happen with the Social Networks variables, since the histograms overlapped by cluster they do not show great differences for the variables PSMU, News and ASMU.

On the other hand, the Repeated Measures ANOVA suggests that there are no significant differences throughout the 14 days of surveys conducted for each individual.

The Regression Models Adjusted results indicate that the use of Social Networks has a much lower weight than the other variables used in the study to explain a possible depression.

The Loneliness, the feeling of inferiority, the loss of Concentration and the stress they have a noticeably higher weight for this data set.

This finding coincides with the results of the Cluster Analysis presented previously.

All conclusions presented here refer solely and exclusively to the data set used in this project. To make more conclusive inferences, the study would have to be expanded using a larger sample, among other things.

Future Steps

The study we have carried out shows us that the profile of social media use does not seem to be a good predictor of symptoms related to depression. However, feelings of loneliness and inferiority, concentration problems, stress and fatigue do predict a possible risk of suffering from depression.

What we have learned with this predictive model would allow us to take a next step: build a natural language processing tool that detects users at risk of suffering from depression based on the identification of emotional content related to the variables detected in our study.

Acknowledgments

We thank the mentors and organizers of Saturdays.AI Donostia, especially to Beñat Galdós and Joxemari Gallastegi, for their professionalism, dedication and enthusiasm.

Project presentation: DemoDay

Open video or resource

Repository

In the following repository you will find the code used to develop this application: https://github.com/SaturdaysAI/Projects/tree/master/Donostia/Donostia2020/AISaturdays-depresion-rrss

More artificial intelligence!

The mission of Saturdays.ai is to make artificial intelligence more accessible (#ai4all) through intensive courses and programs where projects for good are carried out (#ai4good).

Explore our AI master’s programme at https://saturdays.ai/master-ia-online/

If you want to learn more about artificial intelligence join our community at community.saturdays.ai or visit us on our website www.saturdays.ai Join us!