Modeling Intraindividual Change Over Time When There Is No Gold Standard

Tracking how a single person changes on some trait across time sounds simple until you try to measure it. The problem is that any single assessment carries error, and when you have nothing to check that assessment against, no definitive diagnostic test or absolute criterion, the errors ripple into whatever conclusions you draw about who got better and who got worse. This report by Raymond H. Baillargeon, Richard E. Tremblay, Doug Willms, Elisa Romano, Kyung-Hye Lee and Hong-Xing Wu set out to make those effects visible and to offer a way around them.

Three goals organized the work. The first was to demonstrate what independent classification errors do to estimates of incidence (people newly entering a condition) and remission (people leaving it). The second was to lay out a logit-based model built on time-specific latent variables that can separate two things usually tangled together: whether a person's hidden state persists or shifts from one measurement to the next, and how tightly the latent variables at different time points are linked. The third was to run this model on real data.

That data came from a representative sample of Canadian children drawn from the National Longitudinal Survey of Children and Youth. The children were measured on physical aggression at ages 8 to 9, then measured again two years later at ages 10 to 11. Physical aggression works well as a test case because children are not neatly sorted into aggressive and non-aggressive; they fall along a range, and whatever label a study assigns is itself an estimate rather than a fact.

The errors turned out to matter a great deal. Depending on how much misclassification crept in, estimates of the true incidence and remission rates could be badly inflated or badly deflated. Remission proved the more fragile of the two: even small amounts of classification error could throw its estimate off. Incidence was steadier under small errors but swung more wildly once the error levels climbed. So the two quantities fail in different ways, and a researcher who assumes clean measurement risks reporting numbers that bear little resemblance to reality.

When the latent model was applied, the off-diagonal cells of the transition probability matrix (the cells describing children who moved between states) showed no association beyond what chance would predict. In plainer terms, a child's latent aggression category at ages 8 to 9, whether low, medium or high, held about as steadily regardless of how severe it was. Stability did not scale with severity the way one might expect.

There was a second pattern worth stating. The chance of moving from one latent aggression status to another was roughly the same as the chance of moving back the other way. Shifts up and shifts down happened at comparable rates, so the transitions were close to symmetric rather than favoring one direction.