Glossary#

Domain terms#

autism class#: One of the four latent groups the reference model assigns each participant to, the classes of Litman et al. [1]: Social or behavioral, Mixed ASD with developmental delay, Moderate challenges, and Broadly affected. A class is a latent class of the general finite mixture model, not an observed label.
latent class#: A group that is not directly observed but inferred from the pattern across many measured features (a latent class). Each participant has a responsibilities vector giving the probability of belonging to each class rather than a hard assignment.
general finite mixture model#: The model behind the classes (GFMM): a fixed number of latent classes, each with its own class-conditional distribution over the measured features, mixed in the population by the prevalence weights (a finite mixture model). Fitted by expectation-maximization with StepMix [2], which estimates this family of models, and whose three-step methods run the prevalence test.
profile#: The class-conditional measurement parameters that define one class: the feature-level Gaussian means and variances, Bernoulli probabilities, and multinomial category probabilities. The invariance hypotheses ask whether the profiles move along an axis.
prevalence#: The share of the population in a class, also called the mixing proportion or latent class size. Whether the prevalences shift along an axis is tested separately from profile drift (\(H_0^B\)).
age at diagnosis#: The participant’s age in years when autism was first diagnosed. One of the two axes; the corroborating axis for the headline question.
diagnostic era#: The reconstructed calendar year of diagnosis, treated as a continuous axis. The axis for the headline question of whether the classes drift with diagnostic timing.
DSM-5 boundary#: The 2013 revision of the diagnostic manual, which merged the earlier autism sub-diagnoses into one spectrum. A candidate discontinuity in the diagnostic era axis: diagnoses from 2013 onward.
referent#: The time frame an instrument asks about. A current-state instrument (for example RBS-R, CBCL 6-18) reports the present; a retrospective or lifetime instrument (SCQ-Lifetime, developmental milestones) reports the past. The split separates a measurement-timing change from a change in the diagnosed population (\(H_0^G\)).
measurement lag#: The gap between the diagnosis and the parent-report measurement. A nuisance covariate the era analysis adjusts for, since a change in the lag could otherwise be mistaken for era drift.
seven phenotype categories#: The author-defined symptom groupings the features fall into: anxiety or mood, attention, disruptive behaviour, self-injury, social or communication, restricted or repetitive, and developmental. Drift is attributed across these categories (\(H_0^F\)).
Litman feature set#: The 238 parent-report features from Litman et al. [1] that the reference model is fitted over, the measurement set for every stability test on this site.
SPARK#: The Simons Foundation Powering Autism Research cohort, the primary parent-report dataset; the reference model is fitted to the SPARK cohort.
SSC#: The Simons Simplex Collection, a separate autism cohort used to check whether the reference classes replicate outside SPARK.

Method terms#

responsibilities#: The posterior class-membership probabilities the model assigns each participant, one per latent class, summing to one. The soft counterpart of a hard class label: the three-step estimator regresses on these rather than on a single assigned class.
expectation-maximization#: The iterative algorithm that fits the general finite mixture model (expectation-maximization): it alternates estimating the responsibilities given the parameters with re-estimating the parameters given the responsibilities.
measurement invariance#: The property that a measurement relates to the latent construct the same way across groups or along an axis (measurement invariance). The invariance nulls (\(H_0^A\)) state that the profile of each class is invariant to the axis.
score-based invariance test#: A test for measurement invariance that scans the per-participant model scores, ordered along the axis, for a systematic fluctuation. The generalisation to a continuous axis without pre-set subgroups is the Merkle and Zeileis score-based test [3]; it is built on an empirical fluctuation process and corroborates the effect-size read.
empirical fluctuation process#: The cumulative sum of the ordered model scores, which behaves like a Brownian bridge under the invariance null, so an unusual excursion signals a break along the axis.
Brownian bridge#: A Brownian motion pinned to zero at both ends. The reference process for the empirical fluctuation process under the null; at the full sample size its \(p\)-value saturates, so the read moves to the effect size.
family-clustered bootstrap#: A resampling scheme that draws whole families rather than individuals, so the intervals respect the dependence between related participants. The source of every confidence band on this site.
confidence band#: The band around an effect-size trajectory produced by the family-clustered bootstrap. A band sitting above the control level is the positive read for a specific drift.
false discovery rate#: The expected share of false positives among the rejected nulls. Controlled by the Benjamini-Hochberg procedure across the class-by-parameter tests within an axis.
Mahalanobis distance#: A distance between a point and a distribution that accounts for the covariance, so it reads in the natural units of the spread. Used to scale a centroid shift against the between-class separation.
linear discriminant analysis#: The projection that best separates the classes. Its plane defines the between-class separation; a capture fraction flags drift lying outside it.
between-class separation#: How far apart the classes sit: the mean distance between their centroids, measured as the full (un-averaged) standardised-Euclidean norm and averaged over class pairs. One separation unit is this mean inter-class gap. The trajectory figures scale every displacement by it using the same full norm, so numerator and denominator share a scale and a displacement reads directly as a fraction of a class gap: a value near one is a class that moved about as far as two classes are apart, and the whole-class endpoint drifts of a few tenths mean a few tenths of that gap. This is the single canonical convention across the effect-size trajectory, its controls, and the attribution decompositions. (The archived refit-based drift stage keeps its own averaged root-mean-square norm, self-consistent within that stage; the two are not compared.)
capture fraction#: The share of a class’s centroid drift that lies within the linear discriminant analysis plane. A low value flags drift in a direction the between-class axes do not span.
local structural equation modelling#: Re-estimating the model at each point on a continuous axis, weighting every proband by a kernel around that focal point so the class parameters come out as smooth trajectories rather than a handful of disjoint strata (LSEM [4]). The kernel bandwidth sets how local each fit is. The KernelWindows scheme in analysis.localise implements it.
multinomial logistic regression#: A regression of a categorical outcome with more than two levels on covariates. Used to regress latent class on an axis for the prevalence test.
three-step estimator#: A way to relate latent class to a covariate without refitting the mixture: fit the mixture, fix the classification-error matrix of the posteriors, then regress class on the covariate with that error accounted for. Removes the bias of regressing on hard labels.
differential item functioning#: A feature that relates to the latent class differently across groups or along an axis, net of the class itself. The direct-effect route for testing whether era drift survives adjustment for measurement lag (\(H_0^H\)).
likelihood-ratio test#: A test comparing two nested models by twice the difference in their log-likelihoods. Used for order selection (a bootstrap variant for the number of classes) and as an invariance cross-check.
cross-validated log-likelihood#: The held-out log-likelihood, averaged over folds. Its elbow selects the number of latent classes, in preference to the raw information criteria, which over-extract at this sample size (\(H_0^C\)).

Glossary#

Domain terms#

Method terms#

Sources#