Lag-specific ABC probability divides events occurring in a defined lag bin by response anchors eligible for that complete bin. Use nonoverlapping bins, one timestamp anchor, and an explicit rule for the first event, repeated events, or event presence. Report each bin's raw count, denominator, and truncated anchors. The resulting timing profile describes sampled sequences rather than causation.

Define the anchor and exclusive lag bins

A lag-specific ABC probability begins with a named anchor, such as response onset, and asks when a second event first occurs after it. Define the event, timestamp rule, total follow-up period, and bin endpoints before looking at the distribution. For example, use 0 through 5 seconds for lag 1 and more than 5 through 10 seconds for lag 2. An event at exactly 5.0 seconds belongs to lag 1 under that rule; an event just after 5.0 belongs to lag 2.

Decide whether the analysis scores first onset, any occurrence, count, or duration. An exclusive first-onset profile places each complete anchor in one bin or a no-event state. An "any event per bin" analysis may place one anchor in several bins and needs separate bin-specific denominators and wording. Do not combine these methods in one graph.

Build an anchor-level timing record

Create one row per candidate anchor. Retain anchor time, observation end, eligible follow-up, first qualifying event time, lag, no-event state, truncation, timestamp precision, setting, opportunity, observer, and source. Apply a predefined rule for overlapping anchors. A later response may reset follow-up, open another window, or be part of the same episode, depending on the question.

The row-level record should distinguish no event during a complete ten-second window from an incomplete window. The first is valid negative evidence. The second is truncated and cannot be placed in the no-event cell. Clock mismatch, delayed data entry, and uncertain event identity remain unresolved until reviewed.

Calculate Cleo's lag profile

Cleo has 10 response anchors with a complete ten-second follow-up. Attention first begins within 0 through 5 seconds after 6 anchors. It first begins more than 5 through 10 seconds after 2 anchors. No attention begins within ten seconds after the remaining 2 anchors.

Because the bins are exclusive and every anchor has complete follow-up, all three use the same denominator:

lag 1 probability = 6 / 10 = 0.60, or 60%.

lag 2 probability = 2 / 10 = 0.20, or 20%.

no event within 10 seconds = 2 / 10 = 0.20, or 20%.

The cells reconcile as 6 + 2 + 2 = 10 anchors and the probabilities sum to 1.00. This check would not apply to a nonexclusive any-occurrence method.

Check exposure and changing risk sets

Ten complete anchors are the valid cohort, but report how many anchors were planned or detected overall. Suppose two additional anchors occur eight seconds before the observation ends. They are eligible for lag 1 but not for a complete lag 2 or the ten-second no-event state. An exclusive full-window profile should exclude them from all outcome cells and report 10 of 12 complete-window coverage, or 83.3%.

A bin-specific risk-set method could use 12 eligible anchors for lag 1 and 10 for lag 2, but its probabilities answer separate questions and need separate denominators. Predeclare which approach serves the decision. Never keep a denominator of 12 while silently scoring the truncated anchors as no event.

Review clock precision and boundary rules

Lag bins should be wider than the meaningful timestamp uncertainty. Whole-second timestamps cannot reliably separate an onset at 5.0 from 5.4 seconds if both are stored as 5. Observer reaction time, device latency, unsynchronized clocks, and imported-event batching can create an artificial peak near a boundary. Test the recording workflow and document rounding before selecting narrow bins.

Audit events exactly at 0, 5, and 10 seconds, plus just beyond each boundary. State whether simultaneous timestamps qualify and how duration already underway at the anchor is treated. Preserve raw times at their actual precision. Additional decimal places should not imply precision the source system did not collect.

Handle no events, repeated events, and missing data

A complete anchor with no qualifying event has a valid no-event outcome. If every complete anchor has no event, the event-bin numerators are zero and the no-event probability is 1.0. If there are no eligible complete anchors, the profile is undefined. Uncertain onset identity and lost observation are missing states, not no-event outcomes.

For repeated attention events, Cleo's example uses the first qualifying onset. Later events remain in the raw record but do not enter another exclusive bin for the same anchor. When anchors overlap, one attention event could be linked to more than one response. Use a stated nearest-anchor, reset, episode, or multiple-link rule and evaluate how that choice affects interpretation.

Interpret timing without implying function

Cleo's profile shows that the defined attention onset appeared in the first five seconds after 60% of sampled complete anchors, the next five seconds after 20%, and not within ten seconds after 20%. It does not establish that attention caused or reinforced the response. Routine timing, staff proximity, competing events, anchor duration, and observation placement may contribute to the pattern.

Lag selection can change the apparent concentration. Combining the first two bins would yield 8/10 within ten seconds and hide the timing split. Dividing them into narrower bins could expose clock error rather than a clinical pattern. A qualified clinician should consider raw sequences, repeated samples, Cleo's perspective, health and safety context, and other assessment evidence before choosing a next step.

Graph the distribution and report its rules

For an exclusive profile, use a bar chart with lag 1, lag 2, and no event as categories. Put 6/10, 2/10, and 2/10 on the bars. Add complete-window coverage and timestamp precision in the caption. A raster plot showing anchor at time zero and event dots can reveal boundary clustering, repeated events, and long gaps that the bars suppress.

Report wording can be: "Among 10 response anchors with complete ten-second follow-up, attention first began within 0 to 5 seconds after 6 (60%), more than 5 to 10 seconds after 2 (20%), and did not begin within ten seconds after 2 (20%). Bins were mutually exclusive and used first onset. The timing profile is descriptive and does not establish function." Add truncation counts and contexts.

Conduct an accessible review with Cleo

Explain the event definitions, clock, bins, sample records, graph, and uncertainty using Cleo's established communication supports. Preserve access to AAC, interpreters, mobility, food, water, bathroom use, prescribed care, rest, relationships, and emergency help. ASHA's AAC guidance supports continuous access. Record Cleo's assent, dissent, corrections, discomfort, and priorities with source labels.

Do not delay urgent health, safety, or reporting action to complete a lag window. Limit identifiable raw-event access to the authorized team and separate direct observation, device events, partner report, and clinician inference.

Use current sources within their authority

Professional boundaries come from the BACB ethics resources, CASP guideline summary, and BCBA Test Content Outline. Work on antecedent and consequent predictors and contingency-space analysis supports preserving exposure and comparison cells. Lag-sequential research directly informs response-stimulus timing, while the precursor procedure shows why sequence direction matters. Comparative descriptive-method research supports the noncausal limit.

Clinician review checklist

For each lag-specific ABC probability, confirm the question, anchor, outcome event, timestamp rule, precision, exclusive or nonexclusive method, bin endpoints, boundary assignment, repeated-event rule, overlap rule, planned anchors, complete anchors, bin-specific eligibility if used, truncated and missing states, 6/10, 2/10, and 2/10 arithmetic, reconciliation, graph, report wording, accessible review, safety action, qualified owner, and review date.

Practical limits

A lag profile is sensitive to bin width, clock precision, follow-up eligibility, overlapping anchors, event definitions, and sample coverage. It cannot establish causality, function, treatment integrity, clinical importance, or future timing. Exclusive and nonexclusive methods are not interchangeable. Preserve raw timestamps and open a new labeled series when the anchor, event, bin, or linkage rule changes.

Related resources

Sources