how to visualize within-individual change over time

[kangoh lee]

I have unbalanced panel data on cognitive functions over 12 years across about 200,000 older individuals. I would like to have a sense of a change in cognitive functions over time within individual. I would appreciate it if you could suggest a Stata code for a figure with x = wave and y = cognitive functions. I do not think a “demeaned” curve captures within-individual change. I do not have to have a figure but need a sense of within-individual change over time in the data. In a sense, I am sort of looking for how to visualize fixed-effect regression results over time in a figure, but fixed-effect regression results reflect all 12 years (there is only one coefficient) and cannot be presented over time.

Thanks,
Kangoh

[Nick Cox]

How is cognitive function quantified, with a few distinct values or as a more or less continuoius measurement? You might find plotting a few random samples as informative as plotting the complete dataset.

[kangoh lee]

Thanks, Nick.
It ranges from 0 to 27 and almost continuous.
I thought about your suggestion, but I wonder if there is any way to represent the data more broadly than a few random samples.

Thanks,
Kangoh

[Nick Cox]

As you imply yourself, wanting to get a sense of individual patterns is challenging with 200,000 individuals. Your desiderata seem contradictory therefore if you dismiss both looking at some individual trajectories and (it seems) summary statistics too.

[kangoh lee]

I agree, Nick.
The dilemma is this. It is not practical to include more than 10 individuals (their trajectories) in a figure, but how representative are 10 randomly-chosen individuals?

[Nick Cox]

The idea of a representative sample is strangely elusive if not incoherent, despite the frequent use of the term. It's hard to improve on the detailed dissection in

Kruskal, W. & Mosteller, F. 1979.. Representative sampling, I: Non-scientific literature. International Statistical Review 47: 13-24.
Kruskal, W. & Mosteller, F. 1979.. Representative sampling, II: Scientific literature, excluding statistics. International Statistical Review 47: 111-127.
Kruskal, W. & Mosteller, F. 1979.. Representative sampling, III: The current statistical literature. International Statistical Review 47: 245-265.
Kruskal, W. & Mosteller, F. 1980.. Representative sampling, IV: The history of the concept in statistics, 1895-1939..International Statistical Review 48: 169-195.

I don't get a clear sense of what other variables you have or what you're doing, but random sampling is the best you can do in the absence of other information.

I won't suggest code because I can't see any of your variable names. The need is to select panels randomly, not observations.

My suggestion was of a few random samples.

A 3 x 3 display each with say 30 series might be a terrible mess, in which case you can retreat to something simpler. It's usually a a waste of space to show a legend too.

search spaghetti, sj

will identity a couple of papers.

[Joseph Coveney]

It is not practical to include more than 10 individuals (their trajectories) in a figure, but how representative are 10 randomly-chosen individuals?

I second Nick's suggestions, and add that if you have other variables of predictive or associative interest, then you can stratify on those variables and randomly select samples (of ten each, or whatever) from within the strata.

If nothing else, then at least you can stratify on the starting (first-wave) values, blocking them by quantiles or other cut-points of theoretical interest, or in categories as suggested by the literature.

After stratified random sampling, you can apply the principle of small multiples in your line plots (spaghetti plots).