Behavioral calibration of mobile-phone GPS data for population-representative analyses

• Mobile phone and GPS data provide longitudinal, high-resolution behavioral measurements but rely on non-probability samples and heterogeneous data-generation processes that can distort inference.Potential biases include under-representation of older adults, low-income communities, and some geographic areas.Source: Introduction · pp. 1–2
• Spatial post-stratification can correct geographic count imbalances but may leave demographic and behavioral discrepancies unresolved, especially where geographic units are missing, suppressed, or under-represented.Geographic calibration does not guarantee agreement between GPS-derived behavioral proxies and travel or time-use survey measures.Source: Introduction · p. 2
• BePop jointly calibrates GPS mobility data to socio-demographic population margins and representative behavioral distributions using census data and time-use surveys.It estimates individual-level weights after representing activity sequences in a shared feature space and clustering them into behavioral profiles.Source: Introduction · p. 2
• Across three large U.S. metropolitan areas, BePop improves alignment between GPS-derived behavioral distributions and American Time Use Survey benchmarks.The evaluation also examines downstream mobility indicators and longitudinal analyses during substantial behavioral change, including the COVID-19 pandemic.Source: Introduction · pp. 2–3
• BePop is compatible with weighted estimation and uncertainty quantification, adaptable to application-specific outcomes and reference data, and released as an open-source, data-agnostic Python implementation.The framework is intended to support robust population-representative inference in cross-sectional and longitudinal behavioral studies.Source: Introduction · p. 3

The BePop calibration framework

• BePop jointly matches ACS demographic targets and ATUS behavioral-profile distributions conditional on socio-demographic strata through combined demographic and behavioral adjustment factors.Behavioral profiles are inferred by matching mobility sequences to ATUS-derived profiles, while unassigned sequences primarily identify low-quality traces or mislabeled locations.Source: Behavioral targets · pp. 5–6

Evaluating the effectiveness of BePop calibration

• Calibration improved time-use, activity-count, entropy, transition, and motif agreement, while reciprocity and turnover were already well aligned before calibration.Motif discrepancies decreased by 17.00% ± 0.16 despite motifs not being included in the embedding space.Source: Evaluating the effectiveness of BePop… · pp. 6–7
• BePop reduced mean Jensen–Shannon distance from ATUS by 9.71% ± 0.74 overall and improved alignment over demographic-only calibration by 10.44% ± 0.70.Improvements were 14.80% ± 0.09 for time use, 13.69% ± 0.25 for structural metrics, and 0.65% ± 2.21 for transitions.Source: Evaluating the effectiveness of BePop… · p. 7, Figure 2 · p. 7
• Across metropolitan areas, BePop effects were consistent but metric-specific, indicating that embedding design must be tailored when reproducing particular behavioral quantities geographically.The framework was evaluated in Phoenix, Boston, and New York using GPS traces alongside ACS and ATUS reference data.Source: The BePop calibration framework · p. 3, Evaluating the effectiveness of BePop… · p. 7

BePop calibration on longitudinal mobility data

• BePop reduced pre-pandemic weighted behavioral-profile distance from ATUS by 9.70% ± 0.61, but pandemic validation showed only a 0.64% ± 3.86 reduction with large uncertainty.The pandemic comparison provides external consistency rather than exact validation because the post-pandemic ATUS sample was substantially smaller.Source: BePop calibration on longitudinal… · p. 8
• The dominant behavioral profile accounted for more than 70% of users’ daily assignments, while unassigned classifications remained below 10% of evaluated user-days.Fixed reference-day assignments therefore captured persistent individual behavior while allowing weighted populations to shift with systemic changes, including pandemic-period changes consistent with independent ATUS data.Source: BePop calibration on longitudinal… · pp. 8–9
• BePop lowered radius-of-gyration estimates by 10.02% across cities before lockdown and 8.27% during lockdown, while changing business co-location estimates by 10.03% and 5.49%, respectively.Both approaches captured pandemic mobility contraction, but calibration changed estimated absolute levels and the magnitude of temporal change.Source: BePop calibration on longitudinal… · p. 10

• Demographic and geographic calibration can leave systematic activity-pattern discrepancies because it does not directly correct behavioral imbalances from heterogeneous device usage.The discussion therefore motivates explicit behavioral calibration for population-representative estimates of daily human behavior.Source: Discussion · p. 10
• BePop jointly aligns mobile-phone data with socio-demographic and behavioral benchmarks by combining census-derived margins with profiles from nationally representative time-use surveys.The framework extends traditional survey calibration to behavioral dimensions typically overlooked in mobility data.Source: Discussion · p. 11
• Across three metropolitan areas, BePop consistently improves agreement with representative distributions of time allocation, activity sequences, transitions, and behavioral motifs.Calibration also affects radius of gyration and workplace co-location estimates before and during the COVID-19 pandemic.Source: Discussion · p. 11
• BePop is data-agnostic, assigning one weight per user-day while accommodating different datasets, spatial and temporal resolutions, demographic classifications, and behavioral benchmarks.Its design is consistent with established survey-calibration methodologies and is not tied to a particular dataset or country.Source: Discussion · pp. 11–12
• Application-specific behavioral embeddings perform best for their targeted dimensions because no single embedding optimizes every behavioral measure.Richer embeddings that capture multiple behavioral aspects may provide a practical compromise between generality and calibration performance.Source: Discussion · p. 12
• Calibration quality depends on reference-data representativeness, measurement quality, target sparsity, mobile-phone data quality, and temporal consistency, especially during abrupt behavioral changes.Persistent failures in behavioral-profile assignment may nevertheless serve as a quality-control signal for low-quality data.Source: Discussion · p. 12

Data overview

• BePop combines ACS age and income distributions, ATUS time-use patterns, and privacy-enhanced GPS data from Phoenix, Boston, and New York.ACS data assign users to demographic groups and define CBSA targets; ATUS provides weighted behavioral references from 2004–2019, with additional 2020 diaries for longitudinal validation.Source: Data overview · pp. 12–13

Activity Sequences

• GPS traces are converted into activity sequences by identifying home, work, and POI-linked stops, mapping them to ATUS categories, and using 48 half-hour bins.Gaps between stops and ATUS Travel activities are assigned to Unspecified places to align the datasets.Source: Activity Sequences · p. 13

BePop Calibration Framework

• BePop jointly calibrates mobile-phone users across demographic and behavioral attributes to compute behavior-aware socio-demographic weights.Calibration attributes are assigned to users before combining sample information with representative population or survey targets.Source: BePop Calibration Framework · p. 13

Socio-demographic targets

• Demographic targets use four age groups and four income groups, with identical categorization required across ACS, ATUS, and mobile-phone data.Age groups are 18–24, 25–44, 45–66, and 67+; income groups are based on CBSA-specific quartiles.Source: Socio-demographic targets · pp. 13–14

Behavioral targets

• Behavioral targets are four ATUS-derived profiles formed by cosine-distance K-Medoids clustering of embedded activity sequences.Mobile sequences are assigned by majority consensus among k = 10 nearest ATUS neighbors, with ambiguous or overly distant sequences left unassigned.Source: Behavioral targets · p. 14

BePop weights construction

• BePop weights multiply demographic and within-stratum behavioral adjustments, preserving ACS composition while matching ATUS behavioral-profile distributions.The N/M factor scales weighted users to the target population, while unassigned low-quality sequences receive zero-weight calibration strata.Source: BePop weights construction · pp. 14–15

BePop longitudinal calibration

• Longitudinal BePop fixes each user’s demographic and behavioral assignments from one January–February 2020 user-day, then recomputes weights daily.The pre/post-pandemic analysis restricts users to a persistent cohort observed on both sides of March 11, 2020, which may introduce survivorship bias.Source: BePop longitudinal calibration · pp. 15–16

Building behavioral embeddings from activity sequences

• Behavioral embeddings combine structural sequence metrics, time-use allocation, and normalized transition frequencies into a flexible representation of daily behavior.Structural features include activity count, turnover, reciprocity, and entropy; time-use features cover Home, Work, POIs, and Unspecified categories.Source: Building behavioral embeddings from… · pp. 16–17

Author contributions statement

• L.L., S.C., N.A.G., and U.K. conceived the idea, planned and conducted the experiments, processed mobility data, created figures, and wrote the manuscript.N.A.G., U.K., S.C., L.L., E.L., and B.L. interpreted results, provided critical feedback, helped shape the manuscript, and substantively revised it.Source: Author contributions statement · p. 21

Data and Code availability

• Cuebiq GPS data, ATUS and ACS datasets, and the open-source BePop implementation are available through stated access portals, with further reproducibility information available from the lead contact.Cuebiq data access is subject to the Data for Good initiative’s conditions and limitations.Source: Data and Code availability · p. 21

A. American Time Use Survey (ATUS)

• ATUS is a nationally representative survey using 4:00 AM–to–4:00 AM time diaries that record each activity’s purpose, duration, location, and co-presence.The study uses location as a proxy for actual activity to align ATUS with mobile-phone GPS data.Source: A. American Time Use Survey (ATUS) · p. 24
• ATUS respondent weights produce nationally representative estimates and adjust weekday–weekend sampling so results represent a typical week.These data capture both the sequencing and duration of daily activities.Source: A. American Time Use Survey (ATUS) · p. 24
• The ATUS sample covers Boston, New York, and Phoenix from 2004–2019, totaling about 13,600 respondents.Approximate respondent counts are 2.6k for Boston, 9k for New York, and 2k for Phoenix.Source: A. American Time Use Survey (ATUS) · p. 24

B. American Community Survey (ACS)

• The ACS B01001 and B19001 tables provide Census Block Group age and income population estimates for probabilistic assignment, while corresponding CBSA-level tables provide target marginals for age and income variables.Source: B. American Community Survey (ACS) · p. 24

C. Mobile phone GPS data

• Privacy-enhanced, opt-in Cuebiq GPS data comply with CCPA and GDPR, while home and work locations are obfuscated to Census Block Group centroids.Sensitive POIs are excluded in accordance with Cuebiq’s policy.Source: C. Mobile phone GPS data · p. 25
• Stop events are defined by GPS coordinates within ∆s = 65 m for a minimum ∆t = 5 min, clustered with DBSCAN at ε = ∆s + 5 m (70 m), and associated with OpenStreetMap POIs within 65 meters.The cited passage specifies exclusion of sensitive POIs, including religious places.Source: C. Mobile phone GPS data · p. 25
• The GPS dataset spans January–June 2020 in Boston, Phoenix, and New York and contains approximately 760,000 consistently active anonymous users.City totals are approximately 96k Boston, 140k Phoenix, and 527k New York users.Source: C. Mobile phone GPS data · p. 25

• ATUS locations are mapped to OSM-attributed stop locations, with sensitive POIs excluded under Cuebiq policies and transportation modes collapsed into a single category.The final mapping is documented in Table S1, and stops around policy-designated sensitive POIs are explicitly excluded.Source: D. Constructing common activity space… · pp. 26–27, Table S1 · p. 27
• Individual POI visits are aggregated into one general POI category because they are a small share of daily stops and would otherwise add unnecessary variability to sequence representations.This aggregation keeps behavioral profiles driven primarily by major routine components such as home and work.Source: D. Constructing common activity space… · p. 26
• Daily sequences follow a 4 AM-to-4 AM circadian cycle divided into 30-minute activity intervals, matching the ATUS survey structure.Source: D. Constructing common activity space… · p. 26
• Mobility gaps, including non-stay episodes, travel, and missing data, are imputed as Unspecified place, while ATUS travel is coded as Transportation.This provides a consistent representation of travel and incomplete observations across the two datasets.Source: D. Constructing common activity space… · pp. 26–27

E. Constructing daily motifs

• Motif distributions are compared between ATUS and mobility data to assess whether BePop recovers daily-routine structure beyond the behavioral dimensions used for embeddings.The analysis focuses on the most prevalent ATUS motifs because many motifs are rare.Source: E. Constructing daily motifs · pp. 27–28
• Daily activity sequences are represented as directed graphs whose nodes are visited location categories and whose edges encode consecutive transitions.This captures the structural organization of routines independently of time spent at each location.Source: E. Constructing daily motifs · p. 27
• Graphs are grouped into structural motifs by isomorphism, retaining transition connectivity while ignoring the identities of location categories.Each equivalence class represents a structural pattern of daily mobility.Source: E. Constructing daily motifs · p. 28

S2. FRAMEWORK IMPLEMENTATION DETAILS

• The implementation constructs demographic and behavioral calibration attributes, including probabilistic demographic assignments and behavioral profiles extracted from daily activity sequences.These steps are needed because the mobility data do not contain the relevant demographic characteristics.Source: S2. FRAMEWORK IMPLEMENTATION DETAILS · p. 28
• Calibration weights are estimated in two stages, first aligning the mobility sample with demographic targets from ACS and then with behavioral targets from ATUS.The resulting weights align the sample with the reference data.Source: S2. FRAMEWORK IMPLEMENTATION DETAILS · p. 28
• The calibrated-weight implementation also accounts for uncertainty in the constructed attributes.This component supplements the alignment of mobility data with demographic and behavioral reference distributions.Source: S2. FRAMEWORK IMPLEMENTATION DETAILS · p. 28

A. Part I: Design

• Calibration is performed separately for each CBSA, a common geographic unit for U.S. mobility analysis.The framework uses inferred home CBGs to support local individual-level inferences and connect users with CBSA-level attributes.Source: A. Part I: Design · p. 29

2. Constructing behavioral profiles

• Behavioral profiles represent activity sequences with embeddings that jointly capture durations, transition patterns, and overall sequence structure.The feature choice affects behavioral profiles and calibration performance and can be tailored to specific behavioral needs.Source: A. Part I: Design · p. 29
• Each mobility sequence is assigned to an ATUS behavioral profile only when at least half of its k = 10 nearest neighbors agree, with an additional 99th-percentile medoid-distance filter excluding outliers.Sequences without a majority profile or sufficiently close medoid remain unassigned, reducing ambiguous and unreliable matches.Source: A. Part I: Design · pp. 29–30

1. Assigning demographic information to mobility individuals

• The demographic calibration uses age and income strata, assigning mobility users probabilistically from CBG-level ACS marginal distributions.Age is grouped into 18–24, 25–44, 45–66, and 67+, while income is divided into CBSA-specific quartile groups; age and income are sampled independently because their joint CBG distribution is unavailable.Source: A. Part I: Design · pp. 30–31

2. Constructing behavioral profiles

• ATUS activity sequences are clustered into discrete behavioral profiles using K-Medoids, with clustering performance evaluated across K values from 2 to 10.Source: A. Part I: Design · p. 31

Cluster evaluation

• Cluster evaluation combined weighted silhouette, K-Medoids objective, cluster compactness, and medoid separation to assess within-cluster coherence and between-cluster distinctiveness.Compactness measures average within-cluster dissimilarity to the medoid, while medoid separation measures distances between cluster medoids.Source: A. Part I: Design · p. 32

Cluster selection

• K = 4 was selected because larger solutions showed diminishing returns, declining medoid separation, and increasingly specific subgroups that reduced interpretability.The choice balanced cluster quality, separation, model complexity, and practical interpretability.Source: A. Part I: Design · pp. 32–33, Figure S1 · p. 33

Behavioral profiles

• The four profiles were almost identical across Phoenix, Boston, and New York, supporting a consistent behavioral typology across metropolitan areas.Profiles 1–4 represent home-only days, working days, mostly home-based days with activity in unspecified places or points of interest, and more varied working-day behavior, respectively.Source: A. Part I: Design · pp. 33–34, Figure S2 · p. 34

B. Part II: Weight creation

• The final weights simultaneously reproduce ACS demographic and ATUS behavioral distributions, with ATUS profile alignment preserved within every demographic stratum.ACS alignment uses observed joint distributions when available or IPF-fitted age and income margins; ATUS adjustment then calibrates conditional behavioral-profile distributions, and the final weights are scaled to represent the CBSA population.Source: B. Part II: Weight creation · pp. 36–37

C. Handling of unassigned mobility users

• Users without credible behavioral-profile assignments receive zero final weight, while their demographic weights are redistributed among assigned users in the same stratum without altering stratum-level population constraints.Unassigned users often exhibit unrealistic sequences, such as spending most of the day at an unspecified place and little time at home; complete redistribution is the main treatment, while partial redistribution offers a trade-off between excluding poorly represented behavior and retaining atypical patterns.Source: C. Handling of unassigned mobility users · pp. 37–38

D. Use of replicate weights

• Replicate-specific interim and final weights resample probabilistically assigned demographic attributes, enabling uncertainty propagation into downstream variance estimation.Demographic assignments based on home Census Block Group ACS distributions are inherently stochastic because individual characteristics are unknown.Source: D. Use of replicate weights · p. 39
• Replicate calibration independently resamples users’ daily sequences and demographic attributes, producing replicate-specific weights that quantify both sources of uncertainty across R = 50 replicates.Replicate estimates support variance estimation and confidence intervals for weighted mobility characteristics.Source: D. Use of replicate weights · p. 40

S3. USING TAILORED EMBEDDINGS

• Full embeddings provide consistently strong alignment across metrics, whereas tailored embeddings align most strongly with the behavioral dimensions they encode.Time-use-only embeddings perform best for time-use metrics but less well for structural metrics and transitions; motifs align well with full, transition-only, and time-use-only embeddings.Source: S3. USING TAILORED EMBEDDINGS · p. 41

A. Impact of ACS alignment

• Demographic-only calibration aligns demographic distributions but produces little or no behavioral improvement over the unweighted sample, including mobility metrics before and after lockdown.Probabilistic demographic assignment weakens the association between demographic characteristics and mobility behavior, motivating behavioral reference distributions alongside demographic ones.Source: A. Impact of ACS alignment · p. 42

B. Impact of ATUS alignment

• Behavioral-only ATUS calibration achieves alignment comparable to full calibration but cannot recover the underlying CBSA’s demographic composition.The method aligns behavioral-profile marginals to ATUS independently of users’ assigned sociodemographic characteristics.Source: B. Impact of ATUS alignment · p. 44

C. Improvement in demographic representativeness by calibration stages

• BePop’s combined, sequential strategy aligns the sample across demographic and behavioral metrics, whereas calibrating one metric set alone does not guarantee improvement on others.The behavioral-only calibration aligned closely with ATUS behavioral attributes but could not improve demographic alignment.Source: C. Improvement in demographic… · p. 45, Figure S9 · p. 45
• Relative differences were below 1% for every joint age–income group after BePop calibration, while ATUS-only adjustment did not systematically improve alignment and sometimes moved cells farther from reference.The uncalibrated sample was not well aligned; applying ATUS after ACS did not undo demographic alignment.Source: C. Improvement in demographic… · p. 45, Figure S10 · p. 46

S5. CALIBRATION DIAGNOSTICS

• All calibrated statistics in Phoenix were within 1 percentage point of their targets, confirming that the framework can align multiple distributions.The diagnostic evaluated income, age, and behavioral-pattern marginals before and after calibration.Source: S5. CALIBRATION DIAGNOSTICS · p. 47
• Pattern 4’s MAPE fell from 42.8% before calibration to 0.6% after calibration, while low-income under-representation and high-income over-representation were also identified before calibration.The uncalibrated sample had 12.5% MAPE for low-income individuals and 12.8% for high-income individuals.Source: S5. CALIBRATION DIAGNOSTICS · p. 47
• The final Phoenix weights had mean 33.6, median 30.8, coefficient of variation 0.47, design effect 1.22, and effective size 90,519, about 65% of the original sample.Approximately 21.1% of the sample was excluded because users could not be clearly assigned to a representative behavioral pattern.Source: S5. CALIBRATION DIAGNOSTICS · pp. 47–48
• Across 50 replicates, income and age distributions showed no detectable differences, with p = 0.36 and p = 0.53, respectively, and χ2/df ≈1.0.These results indicate consistency with metropolitan-area population characteristics at the aggregate level.Source: S5. CALIBRATION DIAGNOSTICS · p. 48
• Although approximately 72% of users had within-individual weight CV above 0.50 across replicates, the weights are intended for aggregate sample-level estimates averaged over replicates.Individuals can receive different demographic strata or behavioral patterns across replicates because selected sequence days vary.Source: S5. CALIBRATION DIAGNOSTICS · p. 48

S6. CITY-WISE CALIBRATION RESULTS

• Calibration improves alignment with ATUS users’ behavior in all three cities, with closer alignment in Phoenix and Boston than in New York.The city-wise results are reported for Phoenix, Boston, and New York.Source: S6. CITY-WISE CALIBRATION RESULTS · p. 48, Figure S11 · p. 49, Figure S12 · p. 49
• In New York, Reciprocity aligns less well than other metrics, while Transition disalignment also affects motif distributions.These results are more stable for Phoenix and Boston.Source: S6. CITY-WISE CALIBRATION RESULTS · p. 48
• New York’s larger population and metropolitan characteristics may require more specific data or parameters, including the number of behavioral profiles, to improve alignment.The paper presents this as a possible explanation for New York’s less stable results.Source: S6. CITY-WISE CALIBRATION RESULTS · p. 48

Longitudinal analysis

• Fixed demographic and reference behavioral assignments are retained, while daily behavioral profiles and weights are inferred or calibrated independently, allowing distributions to reflect population-level shifts.This preserves a common target population while making changes reflect daily behavioral assignments rather than changing underlying calibration weights.Source: S7. LONGITUDINAL ANALYSIS WITH THE… · pp. 50–51
• Unassigned users retain their reference weights and comprise less than 10% of daily observations across cities, so they remain included in weighted profile distributions.Daily profile distributions therefore include users without an inferred daily behavioral profile.Source: S7. LONGITUDINAL ANALYSIS WITH THE… · p. 51
• During lockdown, behavioral profile 1, corresponding to stay-at-home behavior, increased in Boston and New York, while daily weighted distributions converged toward pandemic ATUS profiles.Pre-pandemic profiles showed high ATUS alignment and systematic weekday-weekend variation; the convergence occurred toward the end of the considered sampling period.Source: S7. LONGITUDINAL ANALYSIS WITH THE… · pp. 51–52
• 12.81% ± 0.59 pre-pandemic Boston and 19.34% ± 0.37 New York improvements in Jensen Shannon (JS) distance fell to −0.50% ± 0.61 and −2.53% ± 18.49 during the pandemic.The large pandemic-period standard errors prevent determining whether BePop’s improvement persists, so these results indicate external consistency rather than definitive persistence.Source: S7. LONGITUDINAL ANALYSIS WITH THE… · p. 52

Individual behavioral profile stability

• The dominant behavioral profile covered almost 75% of assigned days, while the remaining profiles collectively accounted for only around one quarter, demonstrating stability.Source: S7. LONGITUDINAL ANALYSIS WITH THE… · p. 53

Behavioral dimensions

• Time-use and structural metrics show the largest improvements, while transitions improve more modestly because their representation may dilute behavioral information.Including all location combinations increases transition dimensionality and may weaken the behavioral information captured by the profiles.Source: S8. SUPPORTING TESTS FOR BEHAVIORAL… · p. 54

Behavioral alignment

• BePop significantly reduces both JS distance and KL divergence across behavioral dimensions and motifs, unlike demographic calibration, which is nearly identical to the uncalibrated sample.Figure S16 evaluates embedded behavioral dimensions, while Figure S17 shows the same pattern for motifs excluded from the embeddings.Source: S8. SUPPORTING TESTS FOR BEHAVIORAL… · p. 54, Figure S16 · p. 55, Figure S17 · p. 55

Relative improvement

• 9.71%±0.74 combined JS-distance reduction is achieved by BePop relative to the uncalibrated sample.Table S4 reports mean and standard deviation across bootstrap samples.Source: S8. SUPPORTING TESTS FOR BEHAVIORAL… · p. 54, Table S4 · p. 56

Motif distributions

• 17.00% ± 0.16 relative reduction is observed for motif distributions, exceeding the improvement across combined embedding dimensions.The larger motif gain likely reflects greater initial misalignment between uncalibrated mobility and ATUS motif distributions, and remains similar using demographic calibration as baseline.Source: S8. SUPPORTING TESTS FOR BEHAVIORAL… · p. 54, Table S4 · p. 56