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This paper is the primary citation for TRACK CHANGES. See FAQ & Citation for the full reference.

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You have the question and the longitudinal data. Whether it is symptom dynamics in a clinical trial, skill development in an educational study, performance metrics in an organizational dataset, or behavioral outcomes in a public health cohort — if you are asking how things change over time and what drives that change, TRACK CHANGES was built for you.

Upload your data, configure your constructs, and get back a complete answer: which variables drive change in the others, how the system is organized, when the dynamics shifted, and which discrete pathways your participants followed — with publication-ready output and a fully interactive report. No code required.

You know the models. You may have taught them. And you know what running one from scratch actually involves: hours of syntax, a nested model ladder tracked manually, assumption testing with no standardized workflow, custom visualization code, and an interpretation step where sign, significance, and valence interact in ways that are genuinely easy to misread.

TRACK CHANGES automates every stage — model selection, syntax generation, estimation, diagnostics, visualization, interpretation — while exporting complete lavaan and Mplus code so you can inspect and teach from every decision it makes.

Custom analysis and modeling from data cleaning through publication-ready output — and we do not stop at the statistics. We write it up too. Full results sections, interpretation, tables, and figures, so you can focus on the science. Especially powerful for TRACK CHANGES-based analyses, where we handle the entire workflow end-to-end.

Expertise in SEM, longitudinal methods, mixed models, dyadic data analysis, network analysis, dynamic systems modeling, conditional process modeling, and categorical data analysis.

Also available: custom analyses for methodological extensions not yet implemented in TRACK CHANGES — including multiple-group B-DLCS models, latent trajectory analysis, latent transition analysis, longitudinal conditional process models, and fluid vulnerability models.

Power analysis, sample size justification, analytic plans, and biostatistics sections for NIH, DoD, PCORI, VA, NSF, and private foundation proposals. Contributing to a lifetime funding rate approaching 30% across submitted applications.

Grant deadlines are firm. Proposal biostatistics support typically requires 2–4 weeks minimum. Reach out early — we will give you an honest timeline and make it work.

Tell us about your project, timeline, and goals. No commitment required. We will tell you honestly whether and how we can help.

We outline scope, deliverables, and timeline. Pricing is flexible — hourly, project-based, and retainer arrangements available depending on your needs.

We get to work. You stay in the loop at every stage. Deliverables are publication-ready — not just output dumps that leave you to figure out the rest.

Use MOMENTS to find the session where the system destabilized before your patient improved. Use BRIDGES to identify what drove that improvement — and in which direction.

Use BRIDGES to model the relationship between two key constructs. Use CHORDS when you have five and need to know which one is the hub the whole system revolves around.

Use STREAMS to identify which participants were on a recovery trajectory and which were chronic. Use BRIDGES within each group to see if the coupling dynamics differ.

Use MOMENTS to detect when a critical transition occurred in intensive data. Use STREAMS to classify whether that transition reflected a stable state change or a temporary fluctuation.

Core Capabilities

Initiates change in the system. Drivers exert strong outgoing influence on other constructs while being relatively insulated from incoming influence. Moving a driver produces the broadest downstream effects.

Absorbs influence from the system without propagating it forward. Sinks are outcome variables — they respond to what other constructs do but don't generate movement elsewhere. They're where the system's effects land.

Transmits influence through the system. Relays receive meaningful incoming influence and pass comparable influence forward — neither initiating nor absorbing dynamics but carrying them through. Intervening on a relay doesn't start things, but blocking a relay can break the chain.

Drives the system AND compounds its own dynamics over time. Amplifiers have both strong outgoing influence on other constructs AND positive self-amplifying within-construct dynamics (positive β or γ). They initiate change and intensify it simultaneously.

With two variables you can say A affects B more than B affects A. You cannot say anything about what function A plays in a system, because there is no system — there’s just a pair. With three or more variables simultaneously estimated, CHORDS computes outgoing and incoming influence across the full coupling matrix and classifies each construct’s role. Driver, Sink, Relay, Amplifier — these are properties of a node in a network, not properties of a directed relationship. They require a network to exist.

BRIDGES tells you whether a pair is asymmetric, bidirectional, or independent. CHORDS tells you how the whole system is organized — whether influence concentrates in a hub-and-spoke pattern around one dominant driver, flows sequentially through a chain, circulates reciprocally with no clear driver, or is largely fragmented. These are topological properties of the full coupling matrix. They emerge from the pattern of all relationships simultaneously, not from any individual pair.

With two variables you can describe whether they move together or in opposition. With three or more, CHORDS characterizes how the whole system coordinates — whether variables predominantly move in-phase (concordant system-wide movement), anti-phase (push-pull dynamics), or in patterns that vary by pair. Valence-adjusted clinical interpretation tells you whether each coupling relationship is working for or against recovery. Cascade tendency — whether influence propagates sequentially through the system like dominoes — is a system-wide signal with no bivariate analogue. It tells you whether a treatment gain in one variable is likely to reverberate, or whether it stops at the next node.

The two-level architecture + subtype framework, the 16-cell subtype taxonomy, and a complete worked example are on the BRIDGES features page.

Core Capabilities

Neither method alone gives you the full picture. DARCI identifies when the transition happened but doesn’t tell you what the dynamics looked like before it. Moving-window EWS detects rising autocorrelation but needs a principled transition definition to test whether the signal actually preceded something. TVP-AR models how the dynamics evolved but doesn’t classify the transition type or test its reliability. MOMENTS runs all three in sequence — DARCI defines the transition, TVP-AR models the evolution, moving-window EWS tests whether the system announced the shift before it happened.

Autocorrelation (β_t) drops sharply within the first 1–2 weeks and remains low. The system rapidly reorganizes into a low-inertia, high-resilience state and stays there. These are the cleanest treatment responders.

Autocorrelation declines incrementally across the full treatment period with no discrete transition point. The person is improving — but the improvement is a continuous reorganization rather than a phase shift. DARCI classifies this as a 3–4 week gradual improvement.

The person’s dynamics remain flat for an extended period, then reorganize rapidly and hold in the new state. A clear discrete transition — detectable as both a DARCI sudden gain and an abrupt shift in the TVP-AR parameter trajectory. Often preceded by rising autocorrelation.

Symptom levels improve and DARCI confirms a reliable transition — but autocorrelation (β_t) remains elevated throughout. The system reached a lower symptom set point but retained high inertia. These patients look like treatment successes on symptom measures. They are at elevated relapse risk.

Neither symptom levels nor autocorrelation change meaningfully over the treatment period. DARCI detects no reliable transition. β_t trajectory is flat. This is not the same as gradual improvement — the dynamics are genuinely unchanged. Treatment mechanism may not have engaged.

Multiple DARCI-detected transitions across the study period, alternating between higher and lower symptom states without settling. β_t fluctuates accordingly. These patients are not stalled — their system is genuinely reorganizing repeatedly. They are the highest-complexity responders and the hardest to categorize by symptom slope alone.

One model per variable. Anxiety gets its own β_t trajectory. Rumination gets its own. Depression gets its own. They run in parallel — separate Kalman filters, separate parameter trajectories, separate early warning signal tests. The “system” is a collection of individual pictures laid next to each other.

One model for the whole system. Yesterday’s anxiety, rumination, avoidance, and depression all simultaneously predict today’s anxiety — and simultaneously predict today’s rumination, avoidance, and depression. Every cross-lagged coupling strength is time-varying. The coupling between anxiety and rumination can strengthen in weeks 4–6 and dissolve in weeks 10–12. That’s a dynamic network, not four separate timelines.

Cross-lagged coupling between variables that evolves over time. Did the anxiety→rumination connection strengthen before the crisis? Did the depression→avoidance edge dissolve after the sudden gain? These are questions about how the network reorganized — not about any single variable’s trajectory.

CHORDS estimates a static coupling architecture from wave-level data — the average δ and φ across the whole study period. TVP-VAR estimates how that architecture changed moment to moment from intensive data. Same constructs. Different timescale. Different question. They’re complementary, not redundant.

With four variables, a standard VAR has 20 parameters. Make all 20 time-varying and you’re estimating 20 evolving trajectories from a single person’s data. That requires longer series (100+ observations minimum), more computational time, and more careful regularization. The Phase 1 univariate approach is validated and interpretable. Phase 2 builds on that foundation.

Core Capabilities

STREAMS is most powerful in combination with the other modules. BRIDGES or CHORDS detect significant slope variance in a continuous change model — evidence that the population isn’t following a single trajectory. STREAMS then characterizes what those multiple trajectories actually look like as discrete streams and maps the flows between them. The continuous and categorical perspectives converge on the same data from different angles: one tells you how much people changed, the other tells you which type of changer each person was.

Moves consistently through adjacent streams in the improving direction across every transition interval — Severe to Moderate to Low — without reversal. The model's ideal responder. High transition probability across every adjacent pair in the improving direction.

Remains in the same stream for multiple consecutive intervals, then transitions directly to a substantially different stream in a single interval, and holds there. The stream-based equivalent of a DARCI-detected sudden gain — but identified here by transition probability patterns rather than symptom magnitude.

Extremely high stability probability in the same stream across every transition interval — typically the most severe or most impaired stream. Not a slow responder on a continuous trajectory. A person for whom the treatment mechanism never engaged at the level required to produce stream change.

Successfully transitions to a lower-severity or more functional stream, maintains that position for one or more intervals, then returns to a higher-severity stream. The relapse pattern. Distinguished from an Oscillator by the presence of a sustained improvement phase before the return.

Multiple transitions across the study period without settling into a stable stream. Unlike the Fragile Improver, there is no sustained improvement phase — the person cycles between streams at nearly every interval. High off-diagonal transition probabilities in multiple directions simultaneously.

Remains in the initial stream for the first half or more of the study period, then successfully transitions to a better stream in the later intervals. Not a non-responder — a delayed responder whose treatment mechanism took longer to engage. Missed by analyses that only examine early change.

A PHQ-9 of 12 and a PHQ-9 of 13 are not meaningfully different on a continuous scale. But one person might be solidly in the Moderate stream and another might be in the Severe stream with a particularly good day. Continuous models treat these as adjacent points on a number line. STREAMS treats them as potentially different categories with different profiles, different transition probabilities, and different prognoses. The clinical question “is this patient in remission?” is a categorical question. It deserves a categorical model.

The probability of moving from Low to Severe (relapse) is not the inverse of the probability of moving from Severe to Low (recovery). Continuous models impose a symmetry that the data often violates. The transition matrix is asymmetric by nature — and that asymmetry is clinically meaningful. If recovery has a 0.40 probability and relapse has a 0.25 probability, the system is biased toward improvement. If those numbers are reversed, extended monitoring is indicated regardless of what the symptom slope suggests.

Running separate LTA models on depression and anxiety and comparing results misses the most important question: do depression stream transitions predict anxiety stream transitions, or do the two constructs move independently? Parallel process LTA estimates joint stream profiles — High Depression × High Anxiety, High Depression × Low Anxiety, and so on — and models cross-construct transition effects directly. If being in the Severe Anxiety stream at T significantly reduces the probability of transitioning out of the Severe Depression stream at T+1, that’s a treatment planning finding that no bivariate comparison can produce.

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