Longitudinal Models & Time-Series Structure¶

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Abstractions about temporal trends, lags, survival timing, latent growth, measurement invariance, discounting, symmetry, and model fit over time.

8 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

Accelerated failure time model — Model covariates as multiplying an event-time scale—equivalently shifting log survival time—so coefficients are interpreted through time ratios rather than the constant hazard ratios of proportional-hazards regression.
Directional symmetry (time series) — A forecast-accuracy statistic equal to the percentage of successive periods in which predicted and observed changes have the same sign.
Discount function — Map delay to a present weight applied to future utility, payoff, or value, making timing assumptions explicit and distinguishing exponential consistency from nonexponential patterns.
Distributed lag — A time-series regression structure in which the current response depends on present and multiple lagged values of an explanatory variable through a lag-weight sequence.
Lack-of-Fit Sum of Squares — Decompose regression residual variation at replicated predictor settings into irreducible within-setting pure error and systematic discrepancy between fitted values and setting means.
Latent growth modeling — A longitudinal structural-equation framework that represents individual repeated measures through latent intercept and slope factors, estimating average trajectories and between-person variation.
Measurement Invariance — Establish that an instrument relates latent construct values to observed responses by the same measurement rule across specified groups, occasions, or conditions before interpreting their score differences.
Trend-stationary process — A nonstationary time series that becomes stationary after subtracting a deterministic time trend.