A) Source of data

Participants were sampled from a two-wave survey of the Pigg Party, a popular Japanese avatar community application, which has avatars, pseudonym names, and private rooms [Reference Takano and Tsunoda21] (Fig. 1). The first-wave survey was conducted from April 26 to May 2, 2020, and the second-wave survey was conducted from June 1 to 7, 2020. Similarly as in a previous study [Reference Yokotani and Takano22, Reference Yokotani and Takano23], we analyzed 3504 participants in the first wave, who agreed to the study and completed our questionnaire survey without any missing data. Participants with missing data were excluded [Reference Yokotani and Takano22, Reference Yokotani and Takano23]. Similarly, we analyzed 658 participants in the second wave who completed the first and second wave surveys without any missing data. Each participant received 100 Japanese yen of virtual currency as a reward for their cooperation. Their ages were in the range of 23–25 years on average (Table 1) and most participants were cisgender females, who were born and identified themselves as females and were in relationships with male partners (50.9 and 77.2% in the first and second waves, respectively).

Fig. 1. Example of online chatting with friends in a Pigg Party room.

Note: Each room has one owner. Room owners can freely change their room decorations. Each avatar corresponds to an individual user who can freely change his/her appearance. Furthermore, the user's pseudonym name is denoted at the foot of the avatar.

Table 1. Basic statistics of participants

Notes: GHQ: General Health Questionnaire. GHQ0 indicates no psychiatric symptoms, whereas GHQ12 indicates 12 psychiatric symptoms. PES: perceived emotional support. PES1 indicates low emotional support level, whereas PES4 indicates high emotional support level in Pigg party.

B) Outcomes

To evaluate psychiatric symptoms, we used the General Health Questionnaire-12 (GHQ) [Reference Goldberg24], Japanese version [Reference Doi and Minowa25]. This questionnaire comprises 12 questions that elicit information on psychiatric symptoms such as concentration and anxiety. The items on the questionnaire are rated on a four-point scale. The rating method of this questionnaire is 0-0-1-1 [Reference Doi and Minowa25]. Participants were categorized into GHQ0, GHQ1, …, GHQ12 based on their scores. Higher scores indicated more psychiatric symptoms. Approximately 20% of participants did not exhibit any psychiatric symptoms [GHQ0] (Table 1).

To evaluate perceived social support (PES) in Pigg Party, we used the PES scale [Reference Fukuoka and Hashimoto26] with minor revisions for the Pigg Party users [Reference Yokotani and Takano23]. The scale involved six emotional support items such as “Cheer up when I am depressed.” The responses to these items were scored using a five-point scale ranging from (1) “the friend in the Pigg Party would never do it” to (5) “the friend in the Pigg Party would likely do it.” Specifically, participants with scores between 1 and 1.99, 2 and 2.99, 3 and 3.99, and 4.00 and 5.00 were categorized into PES1, PES2, PES3, and PES4, respectively. Higher scores indicate higher social support. Approximately 70% of participants received emotional support from the Pigg Party (Table 1).

C) Predictors

To evaluate the communication frequency of the participants in the Pigg Party, we sampled the time stamps of their chats using the administrator role. The Pigg Party has two types of personal chat channels: private and group. In the private channel, the communication is limited to two users, and the contents of the chat are only disclosed to the two users (Fig. 2). The group channel is similar to the private channel, but it can involve three or more users, and the contents of the chat are disclosed to the users of the group (Fig. 2). Time stamps of private and group chats from April 1 to 30 and from May 1 to 31 were collected for the first- and second-wave participants, respectively.

Fig. 2. Examples of private and group chat channels in the Pigg Party.

Private and group chat frequencies corresponded to the number of direct communication paths between two users in a 1-h slot (Fig. 3(a)). For example, user A privately chats with user B from 14:20 to 14:50 and privately chats with user C from 14:55 to 15:10. Hence, user A has two direct communication paths in the 14:00 time slot, whereas users B and C have one direct path. Furthermore, users A and C have one direct path in the 15:00 time slot, whereas user B does not have any in this time slot. Hence, the frequencies of private communication of users A, B, and C in the 14:00 time slot are 2, 1, and 1, respectively (Fig. 3(b)). Similarly, the frequencies of private communication of users A, B, and C in the 15:00 time slot are 1, 0, and 1, respectively (Fig. 3(b)). We used the same method to estimate the frequency of group communication.

Fig. 3. Example of the estimation of private chat frequencies.

The frequency of group communication was transformed into 168 time frames over 24 h/week and displayed as a probability distribution in these time frames (hereafter referred to as communication time distribution) (Fig. 4). Similarly, the frequency of private communication was transformed and displayed as a communication time distribution. The frequencies of group and private chats were approximately 9 and 3 times per day on average, respectively (Table 1).

Fig. 4. Group communication time distributions among users with psychiatric symptoms.

Notes: There are 13 classes of GHQ, from 0 to 12, but only the top two and bottom two are shown in the figure.

D) Statistics

To estimate the social rhythm, the peak value of the autocorrelation function was used. The peak value of the autocorrelation function is frequently used in speech studies to estimate the fundamental frequency [Reference Zhao, O'Shaughnessy and Minh-Quang27]. To clarify cyclic errors, window or smoothing functions were not used in the autocorrelation function used in this study:

(1)\begin{equation}R(j )= \frac{1}{N}\mathop \sum \limits_{i= 1}^N v(i )v({i + j} ) \end{equation}

In equation (1), V(i) is a signal at i time point and V(i + j) is a signal at i + j time points. When R(k − 1) is lower than R(k) and R(k) is higher than R(k + 1), R(k) is considered as a peak value.

To estimate the explanation rate of a 24-h cycle, we used time-domain linear regression analysis [Reference Shumway, Stoffer, Shumway and Stoffer28]. In equation (2), S is a 168-dimensional vector of communication frequencies. Average is a function that returns average of a vector. I is a vector with 168 elements, all of which are 1. Hence, S_adj is a 168-dimensional vector of communication frequencies minus its mean. In equation (3), F and F ⁻¹ are discrete Fourier transformation and inverse discrete Fourier transformation, respectively. F_full involves all valid 84 frequencies. Real is a function that only returns real numbers. Hence, S′_full is the signal simply recovered by the Fourier transform and Fourier inverse transform. In equation (4), F ₂₄ involves only a 24-h frequency (frequency is 0.4166) and the other frequencies are 0. Hence, S′ ₂₄ is the signal expressed only in a 24-h cycle. In equation (5), R ² is a function that returns the coefficient of determination. The denominator and numerator show the coefficients of determination for S′_full and S′ ₂₄, respectively. Hence, rate represents the explanation rate of a 24-h cycle ranging between 0 and 1. If the sum of S is 0, we remove these data from the analysis of the explanation rate, because these data always return rate as 1.0 and overestimate the rate:

(2)\begin{align}{S_{adj}}& = S- Average(S )\times I\end{align}

(3)\begin{align}S^{\prime }_{full} & = Real({F^{ - 1}}({F_{full}}({S_{adj}})))\end{align}

(4)\begin{align}S_{24}^{\prime } & = Real({F^{ - 1}}({F_{24}}({S_{adj}})))\end{align}

(5)\begin{align}rate& = \frac{{{R^2}({S_{24}^{\prime },{S_{adj}}} )}}{{{R^2}({S_{full}^{\prime }, {S_{adj}}} )}}\end{align}

For transformation of communication time frequencies, we used five transformations. First, by dividing the individual frequencies by the sum of all frequencies, the individual frequencies were expressed as probabilities (probability, Fig. 4). The number of time points was 168 (7 days × 24 h) and the number of communication channels was two (private and group). Hence, the total number of features of raw data and probability was 336. Second, we used FFT. Given that FFT requires the time points to be as a power of 2, we repeated the first 88 time points, and thus used a total of 256 time points (2⁸). Based on the sampling theorem, FFT extracted 128 features with one intercept for both private and group communication times. Hence, the total number of features of FFT was 258. Third, we used STFT on the aforementioned 256 time points. We used a window size of 24 without overlap because many studies indicated that 24-h cycles were prevalent in social media use [Reference Leypunskiy11, Reference Murnane, Abdullah, Matthews, Choudhury and Gay12]. We obtained 598 magnitude features via STFT. Fourth, we used DWT on the aforementioned 256 time points, and obtained 256 approximation coefficients and 256 detail coefficients. Fifth, we used the FCT. We set the longest duration of Chirplet as 24 and obtained 200 features.

The neural architecture of the psychiatric symptom classifier involved a two-dimensional convolutional neural network [Reference Chen, He, Yang and Zhang29] and bidirectional long short-term memory (LSTM) frame [Reference Graves and Schmidhuber30] (Fig. 5). As the dimensionalities of the input data were different, all the data were expanded to 1000 dimensions and then stored as two-dimensional arrays. The two-dimensional arrays were input into the two-dimensional convolutional layer, which summarizes features in the near region. To summarize features in the remote region, we also used a bidirectional LSTM layer. The results of the bidirectional LSTM were in an array containing a temporal order and were compressed into a one-dimensional array matching the number of prediction outputs. The architecture also involved two drop out layers and L2 regularization to avoid overfitting [Reference Srivastava, Hinton, Krizhevsky, Sutskever and Salakhutdinov31]. Details of the architecture are provided in Table 2.

Fig. 5. Neural architecture of the psychiatric symptom classifier. 2D-CNN, 2-dimensional convolutional neural network; LSTM, long-short term memory.

Table 2. Details of the neural architecture of the GHQ symptom classifier

Note: None in output shape means sample size.

* The number of input dimensions was changed according to the transformation model.

^† The number of output dimensions was changed according to the prediction outcomes. The optimizer was the adaptive moment estimation algorithm (Adam). Learning rate: 0.001, beta_1: 0.9, beta_2: 0.999, epsilon: 1 × 10⁻⁷, and decay: 0.0.

Conv, convolutional; 2D, two-dimensional; LSTM, long short-term memory.

The data from first-wave participants were used as training data, and the data from second-wave participants were used as testing data. Training data were unbalanced by the number of psychiatric symptoms; thus, we used the synthetic minority over-sampling technique [Reference Chawla, Bowyer, Hall and Kegelmeyer32]. Although the early stopping function was involved, the classifier trained up to 20 epochs, which corresponds to the maximum number of epochs for all six types of inputs.

To show statistically significant differences of accuracies between trained model and random classifiers, we used 1000 random classifiers. Random classifiers are models that randomly predict the label of the test data based on the distribution of labels in the training data. Through the 1000 random classifiers, we obtained 1000 accuracies. These 1000 accuracies were considered to be independent of each other and normally distributed [Reference Yokotani and Takano22, Reference Bond33]. Therefore, it was possible to estimate a confidence interval based on the normal distribution for these 1000 accuracies. If the accuracy of the trained model was higher than the upper limits of the confidence interval, then it was significantly higher than the accuracy of the random classifier.