Univariate multilevel modeling.

The univariate multilevel analysis revealed simple correlations between the depressive mood scores and the local statistics (Figure 1). The mean and skewness as well as the detrended skewness showed significant correlations (FDR, q = 0.05). However, such relations depended significantly on the size and location of the time frame, especially for skewness (Figure 1). The mean levels of locomotor activity were negatively associated with depressive mood over a wide range of locations (60 min before to 55 min after) around the EMA recordings, and the associations were not significantly affected by the size of the time frame (data length 120–10 points) [Figure 1(a)]. This indicates that activity levels tend to be low with a higher level of depressive mood, and this relationship is consistent and robust over a long period. On the other hand, skewness (also detrended skewness) exhibited positive correlations in a limited range centered around the EMA recordings (e.g., from location −15 to 55 min with size 60 points for skewness, and −25 to 60 min for detrended skewness) [Figure 1(b) (c)]. This implies that depressive mood is associated with intermittent patterns of locomotor activity even in healthy populations, and this relationship appears instantaneously with the worsening of depressive mood. However, such a relationship disappeared with a small size of the time frame, which is partly attributed to the lack of statistical stability of skewness. Considering these results, we used the time frame centered around the EMA recordings with a size of 60 min while constructing the best-fitting model for depressive mood and examined the effects of the choice of time frame. For the univariate modeling, the coefficient of each predictor was fixed across the subjects because the inclusion of the random effect did not have a large effect on the results.

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Figure 1. Dependency of univariate model coefficients for depressive mood on different time frames.

The estimated values of the univariate model coefficient for depressive mood scores are shown in a colored matrix form consisting of 25 rows (different locations) and 12 columns (different sizes). Each grid cell indicates some specific location and size of a time frame used for calculating the local statistics of locomotor activity. A color in each cell represents the value of the model coefficient (γ₁₀) of the predictors: (a) Mean, (b) Skewness, and (c) Detrended skewness. False discovery rate with a q value of 0.05 was used as the multiple comparison adjustment. Only significant cases are shown by colors. Color bars indicate the value of the model coefficient. Note that the univariate model used for the analysis is as follows; Depressive mood score_ij = γ₀₀ + γ₁₀ (Local statistics of locomotor activity_ij) + ζ_0i + ε_ij (see Results for details).

https://doi.org/10.1371/journal.pone.0074979.g001

Determination of best-fitting model.

Of all multilevel models evaluated, a model consisting of local mean and detrended skewness as the predictors was selected as the best-fitting model to describe the variations of depressive mood scores, where the predictor “mean” and intercept had a random effect. The best-fitting model is as follows: Depressive mood scores_ij = γ₀₀ + γ₁₀ (Mean_ij) + γ₂₀ (Detrended skewness_ij) + ζ_0i + ζ_1i (Mean_ij) + ε_ij, where the Depressive mood scores_ij indicates a score of depressive mood at the jth recording for the ith subject; Mean_ij and Detrended skewness_ij are the local mean and detrended skewness of locomotor activity corresponding to the jth EMA recording (depressive mood score) for the ith subject, respectively; γ₀₀ is the average intercept across all subjects; γ₁₀ and γ₂₀ are the average regression slopes across all subjects for each predictor; the random terms, ζ_0i and ζ_1i, are the between-person residuals; and ε_ij is the within-person residual. As expected from the results of univariate multilevel analysis, the coefficient of both local statistics was significant (Table 3), with a negative value (−0.04 ± 0.01, p < 0.01) for the mean and a positive value (1.40 ± 0.69, p = 0.04) for the detrended skewness.

Although the best-fitting model marked the minimum AIC value, a model incorporating local mean with a random effect (F_1,1386 = 9.80, p < 0.01) and skewness with a fixed effect (F_1,1386 = 3.20, p = 0.07) was equally well-fitted to the data without any significant difference from the best-fitting model (see Table 4 for details). The common feature represented in these models is the intermittency of locomotor activity, characterized by a combination of reduced activity with occasional bursts of locomotor activity.

Dependency on size and location.

We demonstrate the robustness of our model with regard to the choice of the size and location of the time frame by showing the dependency of the model coefficients on this choice (Figure 2). The coefficient of the “mean” was consistently significant with negative values (between −0.06 and −0.04) over a broader range (from location −30 to 20 min with size 60 points) [Figure 2 (a)]. Furthermore, this association was also robust against variation in sizes (120–10 points) [Figure 2 (b)]. In the case of “detrended skewness,” the significant positive coefficients were localized in a limited area around the EMA recordings (from 0 to 30 min with 60 points) [Figure 2 (c)], and this association was confirmed only at a larger size of the frame (data length > 50 points) [Figure 2 (d)].

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Figure 2. Dependency of best-fitting model coefficients for depressive mood on different time frames.

The estimate of the model coefficient of the predictor: (a) Mean (γ₁₀) and (c) Detrended skewness (γ₂₀) of the best-fitting model for depressive mood scores (Depressive mood scores_ij = γ₀₀ + γ₁₀ (Mean_ij) + γ₂₀ (Detrended skewness_ij) + ζ_0i + ζ_1i (Mean_ij) + ε_ij) as a function of the location. In panels (a) and (c), the size of the time frame was fixed at 60 min. The same is shown in panels (b) and (d), except for the dependency on the size of the time frame. For evaluation, the location of the time frame was fixed at 0 min; thus, the frame was centered around the EMA recordings. Error bars indicate standard error of the coefficients. The asterisk and dagger indicate significant cases at the 0.05 and 0.10, respectively.

https://doi.org/10.1371/journal.pone.0074979.g002

Ecological momentary assessment.

In this study, we used the EMA technique to examine momentary symptoms. The approach allows researchers to address subjects’ behavior, psychological states, and physiological reactions at multiple time points as they are experienced in daily life. Collecting data in natural settings can enhance the validity of measurements, thus avoiding the pitfalls of retrospective recall, which highly distort self-report data collection [1]. In the present study, we measured momentary symptoms during the study period using the EMA technique with the following procedures.

A watch-type computer (Ruputer, ECOLOG, 42 g; Seiko Instruments Inc., Tokyo, Japan) [45] was used as the ED to record momentary symptoms. This device has a 20 mm × 30 mm screen and a joystick and buttons as input devices (Figure 3). The subjects were provided all appropriate instructions and also given manuals on how to use the device before the beginning of the study period; in addition, the subjects manipulated the device as a practice exercise until they became accustomed to it.

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Figure 3. Fluctuation of depressive mood and locomotor activity in an office worker.

Filled circles indicate depressive mood scores (y-axis on the left side) recorded by ecological momentary assessment (EMA) over seven consecutive days. The inset in the upper left represents the watch-type activity monitor equipped with EMA software. The locomotor activity measured simultaneously (zero-crossing counts within every 1 min time interval) is also shown (y-axis on the right side). The periods shaded in gray are times during which the subject was sleeping or had taken off the device.

https://doi.org/10.1371/journal.pone.0074979.g003

Adolescents: This group was instructed to complete the EMA questionnaires at randomly selected times within plus or minus 10 min of the predefined times (12:50, 16:30, and 20: 00) over seven consecutive days. The subjects were prompted to complete the questionnaires by a beep signal. If they could not enter the recordings when the device beeped, they were allowed to postpone the recordings twice for 15 min each time. If the recordings were not performed within 30 min, the corresponding EMA questionnaires were canceled.

Undergraduates: The EMA questionnaires were recorded over two consecutive days. The subjects were prompted by a beep signal to complete the EMA questionnaires on average every two hours during their waking period. The signals were programmed to occur randomly within intervals ±12 min of the predefined times (8: 00, 10: 00, 12: 00,…). The subjects were allowed to postpone the recordings twice for 10 min each time. If the recordings were not performed within 20 min, the corresponding questionnaires were canceled. The first experimental day of the week was randomly chosen, regardless of weekdays and weekends, so that the study periods can cover all possible day-conditions.

Office workers: EMA questionnaires were recorded on average every four hours during their waking period, over seven consecutive days. The signals were programmed to occur randomly within intervals ± 24 min of the predefined times (8: 00, 12: 00, 16: 00,…). The subjects were allowed to postpone the recordings twice for 10 min each time. If the recordings were not made within 20 min, they were canceled.

In addition, all subjects were asked to record the EMA questionnaires when they woke up and before they went to bed by choosing “waking up” or “going to bed,” from the menu. The selection of the latter item suspended the prompt for recordings until the former item was selected so that to the subjects’ sleep is not disturbed. Furthermore, they were instructed to remove the device before bathing, showering, or any other activity likely to damage the device. When they removed or wore the device, they were requested to select “taking off” or “putting on,” respectively, from the menu as well as the reason for removing the device. The adolescents were asked to conduct EMA recordings (i.e., event-based EMA [1]) in addition to the scheduled EMA (i.e., time-based EMA [1]) when they felt bad or had physical symptoms, such as severe fatigue, headache, or stomachache. Note that these data were analyzed without distinguishing between the two types of EMA because we obtained the consistent results whether such data points were included or not.

The EMA questionnaires assessed fatigue and mood states. The recording times were automatically registered in the device. Fatigue intensity and mood states were rated using a visual analog scale from 0 to 100, which was displayed on the device screen. The EMA questionnaires of momentary symptoms were randomly ordered, and each of them was displayed one at a time using a visual analog scale; the anchor words “none” and “most intense” were displayed at the respective ends of the scale. The subjects adjusted the length of the scale by manipulating the joystick of the device so that it corresponded to their subjective symptoms. Owing to the limited display resolution, the 0–100 scale for the intensity of subjective symptoms increased at 5-point intervals. Fatigue intensity was assessed by instructing the subjects to score their current fatigue level by presenting a single question with the adjective “fatigued.” Mood states were rated using the Depression and Anxiety Mood Scale (DAMS) [46], which was developed to measure anxious and depressive moods as separately as possible. The DAMS comprises nine adjectives representing different mood states: “vigorous,” “gloomy,” “concerned,” “happy,” “unpleasant,” “anxious,” “cheerful,” “depressed,” and “worried.” From these items, anxious mood (sum of “concerned,” “anxious,” and “worried” scores), positive mood (sum of “vigorous,” “happy,” and “cheerful” scores), and negative mood (sum of “gloomy,” “unpleasant,” and “depressed” scores) were assessed. The depressive mood scores were obtained by combining the last two mood scores [(300 − positive mood) + negative mood]. These mood scores were rescaled in the range 0–100.

Assessment of locomotor activity.

This watch-type device is also equipped with an activity monitor, which is analogous in performance to the commercial actigraph (Ambulatory Monitors Inc., Ardsley, NY, USA), widely used in clinical fields [24,31,32,47]. The sensor for assessing locomotor activity is a uni-axial piezo-electric accelerometer capable of detecting small changes in wrist acceleration (≥0.01 G/rad/s), which makes it possible to register even slight movements. All subjects were instructed to wear this device on the wrist of their respective non-dominant hand throughout the study period, except while bathing or performing rigorous exercises. Zero-crossing counts were accumulated for every 1-min epoch for the undergraduates and office workers. For adolescents, acceleration counts were accumulated for every 10 seconds; these activity data were aggregated to make 1-min values to ensure compatibility with the other groups. Locomotor activity data for periods in which the subjects were not wearing the device or sleeping were excluded from the analysis. An example of locomotor activity data is shown in Figure 3.

Local statistics of locomotor activity.

We calculated the local statistics of locomotor activity data up to the third order moment, but used only the mean and skewness because the first and third order moments are considered to be sufficient to characterize the observed data. While the standard deviation (i.e., the second moment) is a standard measure characterizing variability of given data, it is not appropriate for the case where the data do not obey a normal distribution; the distribution of locomotor activity has nonnegative values, leading to a positively-skewed distribution. Indeed, the standard deviation did not play major roles in predicting depressive mood scores when it was included in the model (results not shown). In contrast, the skewness, as a measure of asymmetry of a distribution, is thought to be more appropriate to characterize the observed asymmetry. Lower or higher mean activity levels could quantify the states related to psychomotor retardation or agitation, respectively [24,26]. Higher skewness could characterize the intermittent bursts of locomotor activity [31,32,48].

In addition, we calculated the skewness from the detrended locomotor activity data, where a trend of activity data is subtracted by fitting the first order polynomial (i.e., linear) function before calculation, This detrending was aimed at eliminating effects of non-stationarity due to, e.g., daily activities; we examined the effects up the third order polynomials without finding systematically different results (results not shown). Thus, we obtained three local statistics of locomotor activity, the mean, skewness, and (linearly) detrended skewness for evaluating the associations with the scores of EMA recordings.

Choice of size and location of time frame.

The local statistics were calculated from the neighboring data of each EMA within a certain time frame with size N and location K. The value of K (min) represents the central position (location) of the time frame against the timing of EMA recordings, and the size N (min) indicates the data points used to calculate the statistics. Thus, the combination of N and K indicates the time frame starting from N/2 − K points (min) prior to each EMA recording and ending at N/2 + K points (min) after the recording. Therefore, the case where N = 60 and K = −30 indicates the time frame staring from 60 min prior to an EMA recording to the timing of the recording.

The choice of the size of the time frame may be important because they could have a significant impact on the robustness of the statistics and their temporal coincidence with the symptoms. Theoretically, the larger the size of the time frame, the greater is the stability and reliability of the estimates. However, the choice of larger time frames with less localized temporal positions may obscure the information on the momentary associations between locomotor activity and self-reported symptoms. In addition, the choice of the location plays an important role to investigate the casual association, whether locomotor activity precedes or follows changes in momentary symptoms. Thus, careful consideration of such a trade-off is required, while the optimal choice of combination of the size and location is in advance unknown. Therefore, we varied the size N and location K of the time frame to examine their effects.

Convergent associations among symptoms.

To evaluate the convergent associations among self-reported moods and fatigue, simultaneously measured by EMA, we calculated correlations among their scores using 2-level mixed MANOVA models with EMA scores as the dependent variables and the type of symptoms (i.e., depressive mood, anxious mood, and fatigue) as the predictor. Various studies demonstrate the co-variation between depressive and anxious moods, suggesting the possibility to categorize them into the same class of a broader negative affect dimension [51,52,53]. Indeed, the validation study of DAMS confirms the significant positive correlation between these two mood scores [46]. Fatigue is known to have an extremely high comorbidity rate with depressive as well as anxious moods. For example, fatigue is a common complaint in depressive patients [54,55,56,57]. In chronic fatigue syndrome, the high rate of its comorbidity with both moods has been reported [58]. Co-variations of fatigue with these moods have also been reported in patients with cancer [59]. Therefore, these three symptoms would be expected to co-vary with each other if the subjects properly performed the EMA recordings; otherwise, such correlations should be absent.

Concurrent associations of symptoms with local statistics of locomotor activity.

To investigate the concurrent associations between self-reported symptoms and simultaneous locomotor activity data, the following multilevel models were estimated. In all models, the scores of EMA recordings were treated as the dependent variables, and the corresponding local statistics of locomotor activity were modeled as the predictors. Firstly, we estimated univariate multilevel models to test the simple correlations between the symptoms and local statistics. In addition, we also examined the effects of the choice of time frame to find an optimal combination of size and location for evaluating the local statistics. With regard to the size of the time frame, we considered 12 different conditions: N = 120, 110, 100, …, 20, 10 min. We also considered 25 different locations: K = −60, −55, −50, …, 55, 60 min. We considered a total of 300 combinations (12 sizes × 25 locations) for each symptom and statistic. The FDR with the q value of 0.05 was used as the multiple comparison adjustment.

Secondly, all possible multivariate multilevel models were evaluated by considering the three predictors and their interaction terms. However, the terms consisting of both skewness and detrended skewness were not considered; the interaction terms we considered were: mean × skewness and mean × detrended skewness. Furthermore, we considered both fixed (i.e., the slope of the predictor does not vary across individuals) and random (i.e., the slope varies across individual) effects for all predictors. In this report, we focus on the results for depressive mood because we could not find a significant association of locomotor activity with fatigue or anxious mood.

We adopted the following procedures to evaluate the goodness-of-fit of the models. If the inclusion of a random effect into a predictor significantly improved the residual variance of the data explained by the model, we considered the random effect for that term [60]. After determining the type of effect of all predictors for all models, we compared the goodness-of-fit by using two types of tests depending on the structure of the models. While comparing the models with nested or inclusive relations, where all predictors used in one model were a subset of the predictors used in another model, we tested the deviance statistic [61]. This approach tests the difference in the −2 log-likelihood on the basis of the chi-square test with degrees of freedom equal to the difference in the number of model parameters to be estimated. If the difference in the −2 log-likelihood was not significant, the model with fewer parameters was selected as the preferable one on the basis of the principle of parsimony. For the non-nested models, we used a statistical test based on the Akaike information criteria (AIC), in which the difference of AIC between models is evaluated using the z-test [62].

To determine the best-fitting model for describing the variations of depressive mood scores, we used a time frame of 60 min centered around the EMA recording (i.e., N = 60, K = 0) on the basis of the investigation of univariate multilevel models (see Results). After determining the best-fitting model, we also considered the effects of size and location by varying them. We considered 12 different sizes (N = 120, 110, 100, …, 20, 10) keeping the location of the frame (K = 0). We also considered 13 different locations (K = −30, −25, −20, …, 25, 30) with the size set at 60 min.

Cross validation for association of depressive mood with local statistics of locomotor activity.

To cross validate the associations of depressive mood scores with local statistics of locomotor activity among the three groups, an ad hoc analysis was performed for the best-fitting model. We added a categorical variable representing the groups (adolescents, undergraduates, and office workers) to the best-fitting model in order to test whether the concurrent associations differed among categories.