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A Method to Estimate Free-Living Active and Sedentary Behavior from an Accelerometer


Author Information
Medicine & Science in Sports & Exercise: February 2014 - Volume 46 - Issue 2 - p 386-397
doi: 10.1249/MSS.0b013e3182a42a2d


There is a clear association between physical activity (PA) and a reduced risk for cardiovascular disease, diabetes, obesity, metabolic syndrome, and some types of cancer (8). Recent research has emerged, indicating that sedentary behavior (SB) may also play a key role in determining an individual’s health (31). However, as outlined in the recent Physical Activity Guidelines Advisory Committee Report, little is known about the exact dose–response relationship between PA and specific health outcomes (8). This knowledge gap can be directly attributed to the lack of a valid method to measure behavior across the spectrum of active and SB.

Wearable accelerometers are ideal for collecting information about free-living behavior. They can be worn for extended periods of time, impose minimal inconvenience to the participant and researcher, are relatively inexpensive, and can produce detailed accounts of PA and SB that are relevant to health (e.g., estimates of energy expenditure [EE], time in moderate-to-vigorous PA [MVPA], and time spent sedentary) (16). However, methods to process accelerometer output have yet to realize their potential to provide accurate estimates of EE in free-living environments (4,16). Early work in the field used simple and multiple regressions to estimate METs (7,11,18,29,38) or kilocalories (18,20) from accelerometer counts per minute. Although these approaches are relatively easy to use and provide reasonable objective estimates of PA, their limitations have been well documented (9,24,35).

Recent improvements in device miniaturization, computational power, and extended memory now allow data to be processed by more sophisticated machine learning algorithms. Several groups have reported success using hidden Markov models, decision trees, cross-sectional time series, multivariate adaptive regression splines, and artificial neural networks (25,33). These methods improve EE estimates and provide more detailed information about active and inactive behaviors compared with those originally possible with traditional regression approaches (5,12,32,34,37,41).

In a laboratory calibration study, our group recently developed an artificial neural network (lab-nnet) to estimate METs from second-by-second ActiGraph™ (ActiGraph LLC, Pensacola, FL) accelerometer output (37). The lab-nnet improved MET estimates compared with simple regressions and has been validated on an independent sample (17). By using a single, hip-mounted accelerometer and the open-source computing language and statistics package R (39), our method preserved the simplicity and ease of use afforded by traditional regression approaches. This is particularly important to applied researchers given that most other advanced techniques use expensive analytical software (5,34) and complex multiple accelerometer systems (3,14,15,34,40), rendering their application to free-living environments and large-scale epidemiologic studies impractical.

Although the lab-nnet performs well in laboratory settings and uses more detailed information from the acceleration signal than traditional regression approaches, it produces minute-by-minute MET estimates. This approach assumes a minute consists of only a single activity. In a laboratory, this is not problematic because participants generally perform activities for a prescribed amount of time and the start and stop of activities are controlled. Prediction algorithms are then applied to bouts of homogenous activity. In free-living environments where behavior is unplanned, activities do not start and stop on the minute and several activities can be performed within the same minute (e.g., sit, stand, and walk). Figure 1 illustrates the challenge of applying an algorithm developed in the laboratory to free-living data. The bottom two panels show 2 min and 30 s of free-living accelerometer output (counts per second). In this example, a researcher was observing the participant behavior, and the recorded activities (top panel) were synchronized with the accelerometer output. When the lab-nnet is applied to these data, the five distinct activities are grouped into minute intervals (bottom panel), and METs are predicted for each minute. Preliminary observations indicate that this method may produce substantial error in free-living people, and it may be necessary to first identify where activities start and stop (middle panel) and then apply the prediction algorithm to identified bouts of activity. Crouter et al. (11) recognized this limitation and refined the 2006 Crouter two-regression model (10) to first identify continuous walking or running bouts before estimating METs. The refined method, however, did little to improve MET estimates, which may be due to the use of static regression.

Measuring free-living PA and SB. Bottom and middle panels show 2 min and 30 s of second-by-second counts from the vertical acceleration signal. Top panel shows observer-identified activities. Using the lab-nnet and simple regression approaches, the five distinct activities are grouped into minute intervals (bottom panel), resulting in inaccurate MET estimates. In free-living environments, it may be more appropriate to identify where bouts of activity start and stop (middle panel) and estimate METs for specific activity bouts.

We have refined our lab-nnet to be better suited for free-living applications. Our new method is called the sojourn method, and it is a hybrid machine learning technique that combines artificial neural networks with decision tree analysis. We call this method the sojourn method because an accelerometer signal from a free-living person consists of alternating periods of mostly zeros (no movement) and mostly nonzeros. The nonzeros represent sojourns of sustained activity.

The primary purpose of this study was to validate two versions of the sojourn method and our original lab-nnet in a free-living environment. The first version of the sojourn method uses second-by-second counts from the vertical axis only (Sojourn-1 Axis [soj-1x]), and the second version uses second-by-second counts from the vertical, anterior–posterior, and medial–lateral axes (Sojourn-3 Axis [soj-3x]). We also compare results from the three machine learning approaches to three commonly used regression models (10,11,18).


Recruitment and eligibility

Thirteen participants (five men and eight women) were recruited from the surrounding community. Eligible participants were 18–60 yr and in good physical health (no diagnosed cardiovascular, pulmonary, metabolic, joint, or chronic diseases). All participants completed a health history questionnaire, and an informed consent document approved by the University of Massachusetts Institutional Review Board.

Using a standard floor stadiometer and physicians’ scale (Detecto; Webb City, MO), participant’s height and weight were measured to the nearest 0.25 cm and 0.1 kg, respectively. Participants also completed a short survey asking about their current PA status. Participants were asked to choose a number which best described their activity in a normal week. Possible responses ranged from 0 to 7, with 0 corresponding to “avoided walking or exertion” (e.g., always used the elevator, drove whenever possible instead of walking) and 7 corresponding to “ran more than 10 miles per week or spent over 3 hours per week in comparable physical activity.”

Experimental procedures

Direct observation (DO) served as the criterion for both the development and validation of the sojourn methods. Participants were directly observed in their free-living environment on three separate days. Each day, the observation period lasted for approximately 10 consecutive hours, resulting in ∼30 h of observation for each participant. During this time, participants wore an ActiGraph™ GT3X accelerometer on their right hip. The GT3X was programmed to collect data in 1-s epochs from the vertical, anterior–posterior, and medial–lateral axes, and the normal filter mode was selected.

Criterion: DO

Observers worked in 2- to 4-h shifts, and a total of three different observers completed all of the observation sessions. Observers completed extensive verbal, written, and video training and testing before observing participants in a free-living environment. A detailed description of the training and testing procedures is provided by Kozey Keadle et al. (23). Briefly, observer training focused on strategies to avoid disrupting participant free-living behavior and methods to accurately estimate activity intensity. Upon completion of training, each observer was tested in the identification of activity type (e.g., sit, stand, walk) and intensity (e.g., 3 METs) using a ∼15-min video of free-living behavior. The video was first coded by a group of experienced observers. Study observer responses (activity type and MET value) were compared with the experienced observers’ responses using a Cohen’s kappa coefficient (κ). To be considered “in agreement,” study observers needed to correctly identify both the type and the intensity of the activity. There was a very high level of agreement between the study observer responses and the experienced observer responses (mean κ = 0.92). Furthermore, our DO method has been validated using indirect calorimetry as the criterion. DO estimates of activity intensity were highly correlated with indirect calorimetry (low intensity: intraclass correlation coefficient [ICC] = 0.99, MVPA: ICC = 0.99) and had a small bias (low intensity: percent bias = 2.1%, MVPA: percent bias = −4.9%).

Participants were met by a trained observer in their natural environment (e.g., home, place of work, and school) and observed for approximately 10 consecutive hours. A hand-held personal digital assistant (PDA) (Noldus Information Technology, Wageningen,the Netherlands) with focal sampling and duration coding was used to record participant behavior (activity type, intensity, and duration). Every time behavior changed (e.g., sitting to standing), the observer recorded the new activity type and intensity in the PDA. Each entry was time stamped, and the length of each behavior bout was automatically recorded in the PDA. During the 10-h observation time, subjects were allowed to have “private time” when needed. Reasons for “private time” included behaviors such as using the restroom and changing clothes. During these activities, the observer coded “private” on the PDA.

A log of the start and stop of each behavior was exported to a text file from the PDA using custom software (Noldus: Observer 9.0). These data were used to determine criterion measures of activity and inactivity variables.

Sojourn Method: soj-1x and soj-3x

ActiGraph™ data were downloaded and exported to text files using ActiLife 5.0 (ActiGraph LLC). These data were synchronized with DO records downloaded from the PDA. For an observation to be included in the analyses, valid DO and ActiGraph™ data were required. In addition, behavior coded as “private” by the observer along with the corresponding ActiGraph™ data was eliminated from analyses. All data cleaning and processing were done using the statistics package and computing language R (39).

Method development

Synchronized data from six randomly selected participants (eighteen 10-h observations) were used to develop two versions of the sojourn method. Both sojourn methods are hybrid machine learning approaches that combine artificial neural networks with hand-built decision trees to estimate METs. The hand-built decision trees allow us to combine a priori knowledge on human behavior with the flexible nonparametric properties of the lab-nnet. This approach is well suited to estimate METs from free-living accelerometer output. The first version uses second-by-second counts from the vertical axis only (soj-1x), and the second version uses second-by-second counts from the vertical, anterior–posterior, and medial–lateral axes (soj-3x).

Sojourn-1 axis

Soj-1x uses counts per second from the vertical acceleration signal of a hip-mounted ActiGraph™ activity monitor. It requires five constants, three percentages (5%, 12%, and 55%), and two time cutoffs (10 and 90 s). The constants were chosen by grid search with the objective of minimizing a split sample cross-validated sum of the mean squared errors of its estimates. The step-by-step method is outlined as follows and illustrated in supplemental digital content (see Figure, Supplemental Digital Content 1,, soj-1x algorithm for estimating METs from free-living accelerometer data).

  1. Identify bout intervals. To estimate bouts of activity and inactivity, the soj-1x first identifies alternating intervals of various lengths where all count values are zeros (no movement of hips) or all count values are positive (movement of hips). Long intervals of zeros (≥90 s) are identified as inactivity type 1 (sitting or lying fairly still). Long intervals of positive counts (≥10 s) are identified as activity. Short intervals of zeros (<90 s) and positive counts (<10 s) are identified as “undetermined.” That temporary designation is used because there can be short intervals of positive counts during inactivity due to fidgeting or small movements and there can be short intervals of zeros during activity due to brief bouts of standing still, these instances are temporarily called “undetermined.” Adjacent undetermined intervals are combined into longer intervals that have both zero and positive count values.
  2. Determine whether undetermined intervals are activity or inactivity. The next step is to identify undetermined intervals as either activity or one of four types of inactivity: 1) sitting or lying still, 2) sitting with minimal movement, 3) standing still, or 4) standing with minimal movement. This is based on the percentage of nonzero counts and the duration of the interval.
    1. Inactivity type 1
      1.    i. Nonzero counts ≤5%
      2.    ii. Duration ≥1 s (all intervals with nonzero counts ≤5% are classified as inactivity type 1 regardless of duration)
    2. Inactivity type 2
      1.    i. Nonzero counts >5% and ≤12%
      2.    ii. Duration >90 s
    3. Inactivity type 3
      1.    i. Nonzero counts >5% and ≤12%
      2.    ii. Duration ≤90 s
    4. Inactivity type 4
      1.    i. Nonzero counts >12% and ≤55%
      2.    ii. Duration ≥1 s (all intervals with nonzero counts >12% and ≤55% are classified as inactivity type 4 regardless of duration)
    5. Activity
      1.    i. Nonzero counts ≥55%
      2.    ii. Duration ≥1 s (all intervals with nonzero counts ≥55% are classified as activity regardless of duration)
  3. Estimate MET values. The last step of soj-1x is to assign a non-PA MET value to inactivity types 1–4 and to estimate MET values for activity bouts. Non-PA MET values are based on the Compendium of Physical Activities (1) and several calibration studies (17,22).
    1. Inactivity type 1 = 1 MET
    2. Inactivity type 2 = 1.2 METs
    3. Inactivity type 3 = 1.5 METs
    4. Inactivity type 4 = 1.7 METs

Activity MET values are estimated by applying the previously calibrated and validated lab-nnet (17,37) to activity bouts. If the activity bout lasts for <120 s, the lab-nnet is applied to the entire bout (e.g., one MET value is estimated for the activity bout). If the bout is longer than 120 s, it is segmented into 40-s intervals, and the lab-nnet estimates one MET value for each interval. Intervals <40 s in length are combined with the previous interval, and the lab-nnet is applied to the combined interval. For example, an activity bout lasting 150 s is first divided into three 40-s intervals (120 s). The remaining 30 s will then be combined with the last 40-s interval, resulting in two 40-s intervals and one 70-s interval. The lab-nnet is then applied to each interval, resulting in three estimated MET values for the entire activity bout.

Sojourn-3 axis

Soj-3x uses counts per second from the vertical, anterior–posterior, and medial–lateral acceleration signals of a hip-mounted ActiGraph™ activity monitor. Soj-3x is different from soj-1x in two primary ways: 1) we identify the start and stop of activity and inactivity bout intervals differently, and 2) we apply a neural network that uses acceleration information from three axes to distinguish inactivity intervals as either sedentary (inactivity types 1 and 2) or light intensity (inactivity types 3 and 4) before we assign specific MET values. This method requires five constants: one acceleration threshold (15 counts per second), one time cutoff (30 s), and three percentages (5%, 12%, and 70%). The constants were chosen by grid search with the objective of minimizing a split sample cross-validated sum of the mean squared errors of its estimates. The step-by-step method is outlined as follows and illustrated in the Figure, Supplemental Digital Content 2,, soj-3x algorithm for estimating METs from free-living accelerometer data.

  1. Identify bout intervals. To identify the start and stop of activity and inactivity intervals, soj-3x identifies instances of rapid acceleration or deceleration. Rapid accelerations or decelerations are defined as instances where the absolute difference between adjacent counts from the second-by-second vertical acceleration signal is greater than the acceleration cutoff (≥15 counts per second). In other applications, similar methods have been used to identify falls (which can be thought of as extreme posture transitions) from body worn accelerometers (33). If these intervals are less than the time cutoff (30 s), they are combined with neighboring intervals until the combined interval is longer than the time cutoff.
  2. Determine whether intervals are activity or inactivity. The next step is to identify intervals as either activity, or one of four types of inactivity (described in soj-1x). First, activity is distinguished from inactivity using the percentage of nonzero counts from the vertical axis. To determine inactivity types 1–4, a neural network is applied to inactivity intervals to first distinguish sitting (inactivity types 1 and 2) and standing (inactivity types 3 and 4). Sitting and standing are then further reduced to either inactivity type 1 or 2 (sitting) and inactivity type 3 or 4 (standing) based on the percentage of nonzero counts in the interval.
    1. Sitting—determined via neural network (described as follows)
      1.    i. Inactivity type 1 = nonzero counts ≤5%
      2.    ii. Inactivity type 2 = nonzero counts >5%
    2. Standing—determined via neural network (described as follows)
      1.    i. Inactivity type 3 = nonzero counts ≤12%
      2.    ii. Inactivity type 4 = nonzero counts >12%
    3. Activity
      • • Vertical axis nonzero counts ≥70%

The neural network used to distinguish sitting from standing is different than the lab-nnet used to estimate METs in soj-1x and step 3 of soj-3x. This nnet uses information about the duration of the interval and six statistical features from the vertical, anterior–posterior, and medial–lateral axes, and the resultant vector magnitude of these axes:

  • a. Distribution of second-by-second counts
    •    i. 10th, 25th, 50th, 75th, and 90th percentiles of an interval’s second-by-second count
  • b. Lag 1 autocorrelation
    •    i. Measure of relationship between adjacent counts within an interval
  • 3. Estimate MET values. This step is identical with the MET estimation process used in soj-1x and described previously. Briefly, non-PA MET values are based on the Compendium of Physical Activities (1) and several calibration studies (17,22), and the lab-nnet is used to estimate METs for activity intervals (see step 3 under soj-1x).

Note that the purpose of soj-3x is to estimate METs. In step 2, we distinguish sitting from standing before assigning specific MET values to types of inactivity. These general intensity categories are determined from a neural network that was trained to distinguish sitting from standing activities. All sitting intervals are identified as sedentary, and standing/nonsitting intervals are identified as light. Similarly, inactivity types 1–4 are assigned non-PA MET values based on the Compendium of Physical Activities (1) and several calibration studies (17,22). These methods use activity-type classification to improve MET estimates, an approach that is gaining popularity (6) and recently shown to improve EE estimates (2,13).

In summary, both methods perform the following three main steps: 1) identify when bouts of activity and inactivity start and stop, 2) determine whether bout intervals are activity or inactivity and 3) assign non-PA MET values to inactivity bouts and estimate MET values for activity bouts using the lab-nnet.

Method validation

Data from the seven remaining participants (twenty-one 10-h observations) were used to validate lab-nnet, soj-1x, and soj-3x. We also compared these results with three commonly used regression models—Freedson 1998 (18), Crouter 2006 (10), and Crouter 2010 (11). All ActiGraph™ data were processed in R, and several accelerometer output variables were calculated: MET-hours, time in activity intensity categories (sedentary, <1.5 METs; light, 1.5–2.99 METs; and MVPA, ≥3 METs), minutes in bouts of activity that qualify toward meeting the PA guidelines (guideline minutes), the number of bouts of activity that qualify toward meeting the PA guidelines (guideline bouts), breaks from sitting, and break rate were calculated. MET-hours describe intensity and duration as one metric (e.g., a 5-MET activity performed for 2 h equals 10 MET-hours [5 METs × 2 h = 10 MET-h]) (1), and “guideline” minutes and bouts are defined as moderate-to vigorous-intensity activity that last at least 10 consecutive minutes (8). Because the Freedson regression does not define a sedentary cut point, sedentary time and breaks from sedentary time were calculated using a threshold of ≤100 counts per minute.

Repeated-measures linear mixed models were used to compare estimates with DO. Performance was evaluated using three statistical tools: percent bias, ICC, and root-mean-square error (RMSE). Percent bias (mean difference between the estimate and criterion expressed as a percent of the criterion) provides information about the accuracy of the estimate. If the upper and lower 95% confidence intervals of the bias span 0, then we cannot detect a statistically significant difference between the estimate and the criterion at α = 0.05. In this study, a negative bias indicates underestimation by the prediction method, and a positive bias indicates overestimation by the prediction method. We used a two-way, mixed-model ICC to test the absolute agreement of estimates and DO (ICC function from R package irr) (39). An ICC closer to one indicates high agreement, and an ICC closer to zero indicates low agreement. The RMSE is the square root of the mean squared error, and it provides information about the magnitude of the errors as a result of both bias and variability. It does not indicate the direction of the error (i.e., over- or underestimation).


Participant characteristics (mean ± SD) are reported in Table 1. There were no differences between the development and the validation groups. Results were similar for both groups, but we present results for the validation group only to show how the methods will perform on an independent sample.

Participant characteristics.

During three DO sessions, the ActiGraph™ monitors did not record data and were therefore eliminated from analyses. This resulted in a total of eighteen 10-h validation observations from seven validation participants. After “private time” was eliminated, mean ± SD time per observation was 9.46 ± 0.42 h.

Table 2 shows the mean (95% confidence interval [CI]) estimates of MET-hours and time in activity intensity categories for DO and all prediction algorithms. According to DO, participants spent on average 346.1 min (304.9–387.3) in sedentary, 161.0 min (123.4–198.6) in light, and 60.4 min (46.8–73.9) in MVPA per observation. In general, soj-1x and soj-3x estimated MET-hours and moderate-to vigorous-intensity activity with considerably less bias (except compared with refined Crouter MET-hours (% bias = 0.7) and produced much smaller RMSE compared with the lab-nnet and regression models (Table 2). In addition, soj-3x also improved estimates of sedentary and light-intensity activity. Soj-3x had an approximately 50% smaller RMSE for time in sedentary (25.5 min, 95% CI = 15.4–35.6) and light-intensity (28.8, 95% CI = 19.5–38.2) activity compared with the lab-nnet (sedentary: 53.7 min, 95% CI = 31.4–76.0; light: 55.0 min, 95% CI = 34.2–75.8), soj-1x (sedentary: 50.1 min, 95% CI = 31.7–68.5; light: 49.7 min, 95% CI = 31.5–68.0), Freedson 1998 (sedentary: 55.7, 95% CI = 34.3–77.1; light: 47.1, 95% CI = 28.7–65.5), Crouter 2006 (sedentary: 48.3, 95% CI = 31.1–65.6; light: 59.2, 95% CI = 34.3–84.1), and Crouter 2010 (sedentary: 54.6, 95% CI = 35.1–74.1; light: 58.0, 95% CI = 34.8–81.3). We note that because positive (overestimation) and negative (underestimation) errors cancel each other when they are averaged, an unbiased estimate does not always indicate how the model will perform for an individual.

Lab-nnet, soj-1x, soj-3x, and three traditional regression models compared with DO.

All soj-1x and soj-3x estimates exhibited a significant level of agreement with DO (ICC range = 0.51–0.99) (Table 2). In general, soj-1x and soj-3x estimates more strongly agreed with DO than the lab-nnet (ICC range = 0.28–0.64) and regression models (ICC range = 0.33–0.98) (Table 2). This is illustrated in Figure 2, which plots algorithm estimates against DO for each observation (N = 18). Lab-nnet estimates (top panel, open squares) are more widely spread from one another than soj-1x and soj-3x, indicating the lab-nnet is less precise. Figure 2 also illustrates the higher accuracy of soj-1x (open triangles) and soj-3x (filled circles). This is evident because soj-1x and soj-3x estimates consistently fall closer to the line of identity than lab-nnet estimates. Points that fall on the line of identity indicate the estimate is identical with DO.

Lab-Nnet, soj-1x, and soj-3x estimates for each participant. Model estimates for each participant compared with DO. The closer the point falls to the line of identity, the closer the estimate is to DO. Open squares, lab-nnet; open triangles, soj-1x; filled circles, soj-3x.

Because soj-1x and soj-3x identify bouts of activity, they can provide more detailed estimates of active and SB, including 1) minutes that qualify toward meeting the PA guidelines (guideline minutes), 2) number of activity bouts that qualify toward meeting the PA guidelines (guideline bouts), 3) breaks from sedentary time and 4) break rate. Both methods performed well in estimating these metrics. Table 2 and Figure 2 suggest these estimates have small biases (range = −5.0% to 32.9%), have small RMSE, and are strongly correlated with DO (range = 0.51–0.99). The lab-nnet does not estimate activity bout duration and therefore cannot estimate this level of detail about behavior. In general, the Freedson (18) and the refined Crouter (11) models performed well for estimating guideline minutes (% bias = −5.0 and 11.0, respectively), but all regression models considerably overestimated breaks from sedentary time (bias range = 78.8%–106.6%) (Table 2 and Fig. 3).

Freedson 1998, Crouter 2006, and Crouter 2010 estimates for each participant. Model estimates for each participant compared with DO. The closer the point falls to the line of identity, the closer the estimate is to DO. Open squares, Freedson 1998; open triangles, Crouter 2006; filled circles, Crouter 2010.


In this study, we presented and validated two novel methods specifically designed to estimate free-living PA and SB from a single, hip-mounted accelerometer. By identifying where bouts of activity and inactivity start and stop and by predicting METs for specific bouts, soj-1x and soj-3x greatly improved the performance of the lab-nnet with DO as the criterion measure. Soj-1x and soj-3x also provided accurate estimates of more detailed features of behavior, including breaks from sedentary time and minutes that qualify toward meeting the PA guidelines (guideline minutes).

Free-living versus laboratory methods

The first step in processing sensor signals with any machine learning technique typically involves dividing the signal into small time segments called windows (33). The central difference between soj-1x, soj-3x, and previous approaches is in how the signal is segmented. Laboratory methods most often use a sliding window method where the signal is divided into windows of fixed length. The lab-nnet and the simple regression approaches divide the vertical acceleration signal into minute intervals, and METs are estimated on a minute-by-minute basis (Fig. 1). Other laboratory studies using raw acceleration have defined windows from 0.4 to 12.8 s (5). When sliding window methods are applied to free-living data where activities are unplanned and performed in bouts of many different durations, model performance declines considerably. This has been demonstrated previously (11) and was evident in the current study when the lab-nnet performance significantly declined compared with two previous laboratory validations (17,37). Studies using raw acceleration and much smaller windows have reported similar observations (3,13–15,19,27). Using accelerometers positioned on the sternum, wrist, thigh, and lower leg, Foerester and Fahrenberg (15) reported an overall 95.8% classification accuracy in the laboratory. Performance was reduced to 66.7% when the same analytic methods were applied to free-living data.

Soj-1x and soj-3x use nonfixed, activity-defined windows to segment the acceleration signal. In short, soj-1x and soj-3x use the relationship between adjacent counts from the vertical axis to identify where changes in activity may occur (see Figure Supplemental Digital Content 1,, and Figure Supplemental Digital Content 2 Once the signal is segmented, the hybrid model (artificial neural network decision tree) is applied to each window. Several methods have been proposed to identify changes in walking and gait patterns (e.g., transitioning from walking to ascending stairs, identifying heel-strike) (30,36), but we are not aware of this approach being used to identify when bouts of activity and inactivity start and stop or in the context of free-living PA measurement.

Soj-1x versus soj-3x

In both models, information from the vertical acceleration signal is used to distinguish activity from inactivity (see Figure Supplemental Digital Content 1,, and Figure Supplemental Digital Content 2 The lab-nnet is then applied to bouts of activity to estimate METs. In the current study, this approach to dealing with active bouts significantly improved estimates of time in MVPA (≥3 METs) (Table 2 and Fig. 2). Both soj-1x and soj-3x produced accurate and precise estimates, whereas the lab-nnet significantly overestimated time spent in MVPA. Soj-1x and soj-3x also had much smaller RMSE (4.0 min, 95% CI = 2.1–5.9, and 7.8 min, 95% CI = 4.1–11.8, respectively) compared with the lab-nnet (45.5 min, 95% CI = 32.2–58.8). Small RMSE suggest the model will work well for an individual—this is supported in Figure 2 where we plot individual estimates of MVPA against DO. Soj-1x (open diamonds) and soj-3x (filled circles) estimates consistently fall much closer to the line of identity than the lab-nnet (open squares).

Because SB (e.g., lying, sitting, and standing still) were not included in the initial calibration of the lab-nnet and given the well-documented challenges of estimating METs for these behaviors (9,24,35), soj-1x and soj-3x do not use the lab-nnet to estimate METs for SB. Instead, soj-1x and soj-3x assign MET values from Kozey et al. (22) and Ainsworth et al. (1) to SB. To do this, soj-1x uses information from the vertical axis, and soj-3x uses a simple neural network algorithm (1 hidden layer, 25 hidden units) trained on free-living data. Soj-1x did not improve estimates of time in sedentary (<1.5 METs) and light (1.5–2.99 METs) intensities compared with the lab-nnet (Table 2 and Fig. 2). Conversely, soj-3x improved the estimation of sedentary time by approximately 50% compared with the lab-nnet, soj-1x, and regression approaches (Table 2 and Fig. 2).

Given that soj-1x uses parameters from only the vertical acceleration signal to assign MET values to SB (see Figure, Supplemental Digital Content 1, these results were not surprising. It is well established that the acceleration signal from the vertical axis looks very similar for sitting and standing (with minimal movement) activities (10,23,24). This is true for both integrated (e.g., counts per second) and raw acceleration signals and in both laboratory and free-living settings (12,14,27,28). Recent studies often group sedentary and light-intensity behaviors into a single low-intensity category or estimate intensity for dynamic behaviors only (e.g., walking, running) (5,12,19,40,41). Similarly, studies aimed at identifying posture often group sitting and standing into a general “upright” category (14,27). When this approach is not taken, the largest classification error is reported for these behaviors (5,12). For example, during “controlled free-living” sitting and standing activities, De Vries et al. (12) reported nearly identical counts per second from the vertical axes of a hip-mounted accelerometer, resulting in standing activities being classified as sitting 78.9% of the time. More work is needed to further improve estimates of sedentary and light activities from a single hip-mounted accelerometer. The use of raw acceleration signals may provide the important detail necessary to improve these estimates even further.

Similar to the current study, Midorikawa et al. (28) reported that acceleration data from three axes (vertical, anterior–posterior, and medial–lateral) improved the classification of low-intensity activities compared with vertical accelerations alone. These findings and findings from other laboratory studies (5,27) suggest information from more axes may be necessary for accurate assessment of low-intensity activities. To illustrate this, Figure 4 shows approximately 20 min of free-living data collected from one participant in the current study. According to DO, the participant is sedentary for the first third of the time, and standing in light intensity for the remaining time. Using information from the vertical signal only, soj-1x confuses light intensity with sedentary approximately half of the time. Soj-3x uses the additional information from the anterior–posterior and medial–lateral axes to correctly distinguish sedentary from light intensity. We note that if there is “not enough” or “too much” movement in the anterior–posterior or medial–lateral planes, soj-3x will continue to confuse sedentary and light-intensity activities. However, the smaller bias and RMSE for soj-3x estimates (Table 2) indicate that these errors are much smaller compared with when only the vertical acceleration signal is used (soj-1x).

Second-by-second counts from vertical, anterior–posterior, and medial–later axes (top). Corresponding soj-1x and soj-3x estimates compared with DO (bottom). These data illustrate an example of when the additional information from the anterior–posterior and medial–lateral axes help soj-3x correctly identify light-intensity activity where soj-1x inaccurately estimates this activity as sedentary using information from the vertical axes alone.

There is currently a growing interest among PA epidemiologists and exercise scientists to understand the health consequences of too much sedentary time. Measurement tools and analytic approaches must continue to explore ways to accurately and precisely measure detailed SB characteristics (i.e., total sedentary time and breaks in sedentary time). Soj-3x uses a neural network to first differentiate sitting from standing before assigning specific MET values, and in the current study, this approach led to a large improvement in SB assessment compared with other methods. Using activity-type classification to improve MET estimates is an approach that has been used (6) and recently shown to improve EE estimates (2,13)

Moving beyond traditional regression

Simple linear regression was initially used to model the relationship between accelerometer counts and EE (18,29,38). This approach was well received by the scientific community and produces relatively accurate estimates of EE when applied to locomotion activities in a laboratory setting (10,24,35). The current study demonstrated the limitations of traditional regression approaches when applied in free-living settings where a range of activity types and intensities are performed. Overall performance of the Freedson regression (18) and Crouter two-regression models (10,11) were comparable with the lab-nnet. It is possible that if the acceleration signal was segmented in a similar manner to soj-1x and soj-3x, and the simple regression models were then applied to specific bouts of activity/inactivity, performance would improve. It is also important to note that although we divided our sample into a training data set and a testing data set (such that the algorithms were not trained and tested on the same observations and/or participant), soj-1x and soj-3x should be validated on an independent sample to verify robustness of the method and to compare performance with traditional regression methods. Nonetheless, the adaptive nature of machine learning appears to be better suited for free-living applications where a range of activity types and intensities are performed.

An important step to moving beyond traditional regression approaches is to make sophisticated data processing methods more accessible to applied researchers. The lab-nnet, soj-1x, and soj-3x were developed in R, which is a free and open source software environment for statistical computing. R can be downloaded at, and R programs that can be used to process second-by-second ActiGraph™ output with soj-1x and soj-3x are on the Web site∼jstauden/ The ActiGraph™ output must be a .csv file and a wear-time log can be used to eliminate nonwear time. The programs can be used to estimate MET-hours, time in activity intensity categories (in minutes and as a percent of wear time), guideline minutes, guideline bouts, breaks from sedentary time, and break rate. There is a README file in the .zip file that explains its contents. Programming in R requires some level of expertise, but applying R functions is less of a burden to applied researchers.

Strengths and limitations

This study has several important strengths. First, methods were validated under free-living conditions. It is well accepted that performance in the laboratory does not translate to free-living people, and best practice recommendations consistently highlight the need for free-living validations (4,16,19,21). Several studies have tested methods in “simulated free-living” environments where participants perform a small subset of basic ambulatory movements and postures (15,27), but to our knowledge, this is the first study to observe participants in their own natural environment and to allow participants to perform an unlimited range of activity types and intensities.

Second, participant behavior was directly observed and recorded by trained researchers for approximately 10 consecutive hours. Other studies have used protocols that require participants to annotate their own behaviors (3,25). It is unknown how accurate and reliable participant annotated data are, but intuitively, this approach seems to have inherent limitations: relying on untrained participants to collect data, high degree of participant burden, inability to capture transitions between activities, and inability to capture short bouts of activities. In addition, it is unrealistic for participants to annotate their own behavior for long periods of time; thus, the amount and range of data collected are limited. In this study, we observed each participant, on three separate occasions, for approximately 10 consecutive hours (mean hours ± SD per observation = 9.46 ± 0.42 h). To our knowledge, only one other free-living validation (19) and very few laboratory validations have compared more data to a criterion.

The third and perhaps the most important strength of this study is that the proposed methods use a single, hip-mounted accelerometer (ActiGraph™ GT3X) and an open source computing package that is on the Web site∼jstauden/ The application of previous methods has been limited by complex multiaccelerometer systems and expensive analytical software (25,26,33). The proposed methods were successful using a relatively low sampling rate (1 Hz), information from the vertical acceleration signal only (soj-1x) and information from the vertical, anterior–posterior, and medial–lateral acceleration signals (soj-3x). We anticipate that future work using much higher sampling rates (e.g., 30–100 Hz) will improve these models, but until recently, monitors were not capable of collecting and storing this type of data for prolonged periods of time. Similarly, although performance improved when more information was used, the success of soj-1x is important given that earlier models of the ActiGraph™ (e.g., 7164, GT1M) record motion in the vertical plane only and thus data collected with these monitors require vertical plane only processing techniques.

The main limitation of this study was our homogenous sample. Participants were relatively young (mean ± SD; age = 25.0 yrs. ± 4.9), lean (BMI = 24.0 ± 2.4), and active (PA status = 6.4 ± 0.5). It is possible the constants and thresholds used in the algorithms will need to be adjusted for use in different populations (e.g., obese, elderly). However, we anticipate future validation will demonstrate the robustness of the principles fundamental to the sojourn algorithms. Although, in this study algorithms were validated on seven participants, we do not consider sample size a limitation. Each participant was observed on three separate occasions, for approximately 10 consecutive hours (mean hours ± SD per observation = 9.46 ± 0.42 h). This resulted in approximately 12,600 min of DO synchronized with monitor output, much more data than used in other validation studies. Nonetheless, the proposed methods would benefit from future validation on larger, more diverse samples.

Finally, DO is a relatively novel criterion in the field of PA measurement device validation, and like all measurement methods, it has strengths and limitations. In DO, participants are observed outside the lab for long periods of time. A strength of this approach is that we acquire specific details about behavior that cannot be captured by most other measurement methods (e.g., time in activity intensity categories and time in different postures). DO also allows for an unlimited range of activity types and intensities to be performed in natural settings, which is critical for understanding how the sojourn method will perform in free-living people. However, because DO is used to assess features of behavior, it does not account for the individual variation in EE for a given activity. Nonetheless, as noted earlier, observations from our laboratory indicate that DO is an appropriate criterion for free-living validation studies.

Summary and conclusion

Measuring and classifying human movement from accelerometer (and other) sensors is an active field that has benefited from rapid technological advancements and collaborations from experts in many fields. We are not the first to demonstrate success in using machine learning to process information from body-worn sensors (e.g., accelerometers, gyroscopes, heart rate monitors, ambient sensors, and ventilation sensors) (25,33,35). Very high levels of performance are generally reported, but performance consistently declines when fewer sensors are used and when methods are applied in free-living conditions (13,19). Soj-1x and soj-3x significantly advance the field of PA measurement. Using a single commercially available accelerometer, open source statistical software, novel machine-learning approaches, and supervised training data collected under free-living conditions, soj-1x and soj-3x provide easy to use, and accurate approaches to estimating PA and SB in free-living individuals. This study also demonstrated the effectiveness of using information from the anterior–posterior and medial–lateral axes to more accurately distinguish sedentary and light-intensity activity. Future validation will evaluate the sensitivity of soj-1x and soj-3x to detect change in habitual activity and future refinement will adapt these methods to also identify activity type.

This study was funded by NIH RC1HL099557 and RO1 CA 121005.

The authors thank Natalia Petruski and Amanda Libertine for their assistance with data collection and the subjects for their participation.

Patty Freedson is a member of the Scientific Advisory Board for ActiGraph, Inc.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

Present address for S. Kozey Keadle: Cancer Prevention Fellowship Program, National Cancer Institute, Bethesda, MD.


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© 2014 American College of Sports Medicine