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RQ3 — Temporal dynamics

How desire moves over a session and across sessions.

Vela·Reports·source: people-analyst/vela/docs/research/papers/rq3-temporal-dynamics.md

Paper scaffold — RQ3: Within-session desire trajectories and between-session stability

Status: Scaffold — not a submission draft
Source RQ: docs/RESEARCH-PROGRAM.md §II — How does desire shift within and across viewing sessions?
Target venues (choose one primary): Cognition and Emotion or Psychology of Aesthetics, Creativity, and the Arts (PACA)

Title (draft)

Warm-up, peak, and fatigue: Modeling aesthetic response trajectories in sequenced figurative viewing
(Alternative: Within-session growth curves and the stability of desire profiles across repeated engagement)

Abstract

Aesthetic experience unfolds in time, yet most studies treat ratings as exchangeable draws. Vela presents figurative images in editorially sequenced orders with explicit role metadata (entry, build, shift, peak, release, ground), enabling tests of whether ratings and approach behaviors follow predictable within-session trajectories (e.g., inverted-U shaped engagement) and whether between-session summaries of desire-relevant dimensions stabilize like traits or fluctuate like moods. We specify multilevel growth curve models (linear and quadratic time) for rating and log dwell nested within sessions and users, with session-level covariates including sequence role indicators. For cross-session stability, we estimate intraclass correlations (ICC) on dimension scores using append-only user_desire_profile_versions rows (post-ASN-572) or, where history is absent, acknowledge limits per validation report. Pre-registered minimum session and user counts apply; early data may support only within-session models. Results inform pacing in contemplative interfaces and the interpretability of adaptive profiles over time.

Word count: ~195

Introduction — prose prompts (~400 words)

  1. Temporal blind spot (1 paragraph). Cite appraisal dynamics (Silvia, 2005) and emotion time course work: why a single rating per image misses fatigue, warm-up, and context carried by sequence.

  2. Vela’s natural experiment (1 paragraph). Describe sequence roles as a designed rhythm—not fully orthogonal to content, so pre-register controls for unit difficulty (e.g., mean population rating) as level-2 covariates.

  3. Across-session stability (1 paragraph). Connect to psychometrics: profiles as soft traits. Acknowledge honest-N: docs/engine-room/02-instrument-validation.md states test-retest was not computable until versioned profiles exist—now reference user_desire_profile_versions migration 20260424143000_asn572_replay_provenance.sql.

  4. Contributions. (a) Growth parameters for aesthetic ratings in the wild; (b) first ICC estimates for Vela’s eight desire dimensions once N permits.

  5. Ethics. Brief consent / withdrawal framing.

Hypothesis (formal)

Let $y_{ist}$ be outcome (rating or log dwell) for user $i$ in session $s$ at within-session trial index $t \in {1,\ldots,T_{is}}$.

  • H1 (within-session shape): Quadratic time coefficient $\beta_{2i} < 0$ on average: concave-down trajectory (peak mid-session) after controlling for role indicators.

  • H2 (role alignment): Indicators for peak role associated with higher predicted $y$ than entry, holding time and unit covariates fixed (ordinal contrast test).

  • H3 (between-session ICC): For each desire dimension $d$, $\text{ICC}_d > .40$ across profile versions spaced ≥14 days apart, if ≥30 users contribute ≥3 snapshots each (pre-register exact window).

Methods

Data assembly

  • Sort responses by created_at within (user_hash, session_id).
  • Merge player_sessions for session boundaries and mode (learning / calibrated / guided).
  • Merge queue / role data: if player_session_queue (or equivalent) is exported, attach role per trial; else infer role from join to sequence_units / engine logs—pre-register inference path or restrict to sessions with explicit queue export.

Within-session growth model

Level 1 (trials):

$$ y_{ist} = \pi_{0is} + \pi_{1is} t_{ist} + \pi_{2is} t_{ist}^2 + \mathbf{w}{ist}^\top \boldsymbol{\delta} + e{ist} $$

Level 2 (sessions): $\pi_{0is} = \theta_{00} + u_{0is}$, etc., with optional level 3 (users).

Alternative: Piecewise linear splines at trial quantiles if quadratic misfits.

Software: R lme4, nlme, or Bayesian brms for full posterior on random curvature.

Between-session stability

  1. Pull user_desire_profile_versions (columns per migration: user_id hashed in export, profile_version, dimension_scores JSONB, created_at).
  2. Reshape to long format by dimension.
  3. Estimate ICC(1,1) or two-way random effects ANOVA for each dimension (Shrout & Fleiss, 1979) with time between observations as covariate sensitivity.

Vela data export path (by table)

TableUse
responsesTrial-level outcomes, timestamps, session_id
player_sessionsSession duration, mode, user link
user_desire_profile_versionsPrimary for longitudinal profile ICC
user_desire_profilesLatest snapshot fallback / join key
player_session_queueRole per position (if present in export pipeline — verify export-dataset.ts selects)

If queue is not yet exported, add a scoped engineering task before analysis freeze; note in Limitations.

Pre-registered analysis plan (OSF-ready)

  1. Primary: Random intercept + random linear time + fixed quadratic (population).
  2. Secondary: Same model with role indicators instead of raw time (compare AIC).
  3. Tertiary: ICC per dimension with pre-registered exclusion of users with <3 snapshots.
  4. Sensitivity: Exclude first session per user (novelty); exclude sessions <8 trials.

Power analysis

  • Growth models: Singer & Willett (2003) recommend ≥50 persons with ≥5 waves for individual growth variance; analog for ≥5 trials per session across ≥200 sessions for random curvature stability (simulation-based—use simr).
  • ICC: Nicewander (1991) and Adachi & Willoughby (2015) on sample size for reliability of ICC; target ≥100 profile snapshots across ≥30 users for rough stability.

Citation: Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press.

Data sources

Internal: As above; reincarnation_instrumentation optional for engine provenance when correlating profile updates to batch runs.

External: TODO(ASN-575) — cite emotion dynamics and aesthetic chills time-course literature.

Expected figures

#Sketch
F1Spaghetti + mean growth curve for z-scored rating vs trial index.
F2Marginal means by sequence role (entry…peak…).
F3ICC bar chart across eight dimensions with 95% CI (bootstrap).
F4Profile version timeline for exemplar users (anonymized IDs).

Limitations

  • Sequence confound: Role correlates with image difficulty; include unit-level random intercept or fe.
  • Sparse history: Early cohort may force within-session only paper; do not overclaim stability.
  • Mode changes: player_sessions.mode transitions complicate pooling—stratify or model as covariate.

Contribution statement

We articulate time as a first-class variable in digital aesthetic response, linking sequenced presentation roles to measurable trajectories and, when data allow, quantifying how stable algorithmically inferred desire profiles are across weeks. That stability boundary matters for both science (trait-like constructs) and product ethics (profiles that drift without user awareness).

References (seed list — TODO ASN-575)

  1. Adachi, T., & Willoughby, T. (2015). Interpreting parameter estimates from growth curve models. International Journal of Behavioral Development, 39(2), 101–114.
  2. Silvia, P. J. (2005). Emotional responses to art: From collation and arousal to cognition and emotion. Review of General Psychology, 9(4), 342–357.
  3. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis. Oxford University Press.
  4. Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420–428.
  5. Leder, H., Belke, B., Oeberst, A., & Augustin, D. (2004). A model of aesthetic appreciation and aesthetic judgments. British Journal of Psychology, 95(4), 489–508.
  6. Smith, J. K., & Smith, L. F. (2001). Spending time on art. Empirical Studies of the Arts, 19(2), 229–236. (museum dwell-time baseline)
  7. Nicewander, W. A. (1991). Sample size requirements for reliability coefficients. — cited in prose for ICC planning; confirm primary source at analysis freeze.

TODO(ASN-575): Add citations on fatigue in aesthetic judgment, aesthetic chills time-course, and recommender “sessionization.”