Typifying developmental trajectories: a decision-making perspective

Alexander von Eye, Eun Young Mun, and Alka Indurkhya take up a problem that shows up whenever researchers track the same people over time. A developmental trajectory is just a curve drawn through repeated measurements. The trouble is that no two people produce the same curve. One person starts high, another starts low. Some speed up early and level off; others pick up momentum only late. Curves differ in elevation, in overall shape, in how much they scatter around a trend, and in exactly when any acceleration or slowdown kicks in.

Given all that variation, how do you sort individuals into meaningful types? That is the question the article sets out to answer, and it does so by laying out the methods available and the tradeoffs attached to each.

The authors split the approaches into two families. The first takes trajectories that already exist as categories and asks how many people fall into each pattern. This is where Configural Frequency Analysis comes in: you count the individuals whose data reflect a given natural grouping and test whether those counts depart from what chance would predict. The second family does not assume the groups in advance. Instead it uses cluster analysis to let the groupings emerge from the data themselves.

Picking a clustering method is not a single choice but a string of them. Von Eye and colleagues walk through ten characteristics that have to be settled before you run anything. Should clusters be disjoint or allowed to overlap? Hierarchical or flat? Built up by agglomeration or carved out by division? Must every case be classified, or can some be left aside? Is the procedure stochastic or deterministic? Does it work from correlations or from distances? Are the clusters assumed convex or can they take irregular shapes? Does the similarity measure treat pairs symmetrically or not? Is classification monothetic, resting on a single defining attribute, or polythetic, resting on a profile of them? And finally, are you clustering on the variables as observed or on latent variables behind them?

Each of those forks sends you toward a different algorithm with its own strengths and weaknesses, so the paper reviews the common methods and uses worked examples to show where one choice pays off and another costs you.

Once the groups are in hand, there is still the matter of what to do with them. Here the authors point to discriminant analysis and logistic regression as ways to characterize the groupings after the fact, checking which variables separate the clusters and how reliably membership can be predicted.

To keep the discussion concrete, the examples run on two kinds of data. Some are artificial, constructed to make a method's behavior visible. The others are empirical, drawn from research on how cigarette smoking develops in male adolescents.