# How can I correct for non-indepence without individual tracking?

I have some data taken at multiple time points from a set of individuals, but without tracking the individuals.

For example, at each of six time points, the heights of all individuals are recorded -- but there is no information on which height came from which individual. (This is similar to the R builtin data-set Loblolly if you ignore the Seed column which tracks individuals.)

I am trying to run a linear regression to analyze growth, and I know that the lack of independence is problematic for over-confidence in estimates of group differences and for adding excessive noise to the model. However, I am not sure how to go about correcting for those impacts.

In the simplest case, there would be just one group in which I am trying to model growth by predicting height by age. In more complicated cases, I will have two or more groups and will want to predict height by the interaction of age and group. The groups generally start as randomized and relatively homogenous, so the main expected difference is in growth rate. (Occasionally, I may need to handle differences in starting groups, but I think that is beyond the scope of this question.)

Yes: the correct answer is that I should track individuals and include them in the model. I am working on that. However, the production environment I am working in does not make that easy, and I don't have a Delorean to go back and get them from past experiments. So, I am forced to find at least a bit of guidance on correction methods, even if they are just back-of-the-envelope/rule-of-thumb guiding principles to let me know how much salt I should take with the results.

Here is the output from the R Loblolly dataset for those working in other systems that want a starting point (may just be too much time on StackOverflow, but I know it sometimes helps).

 height age Seed
4.51   3  301
10.89   5  301
28.72  10  301
41.74  15  301
52.70  20  301
60.92  25  301
4.55   3  303
10.92   5  303
29.07  10  303
42.83  15  303
53.88  20  303
63.39  25  303
4.79   3  305
11.37   5  305
30.21  10  305
44.40  15  305
55.82  20  305
64.10  25  305
3.91   3  307
9.48   5  307
25.66  10  307
39.07  15  307
50.78  20  307
59.07  25  307
4.81   3  309
11.20   5  309
28.66  10  309
41.66  15  309
53.31  20  309
63.05  25  309
3.88   3  311
9.40   5  311
25.99  10  311
39.55  15  311
51.46  20  311
59.64  25  311
4.32   3  315
10.43   5  315
27.16  10  315
40.85  15  315
51.33  20  315
60.07  25  315
4.57   3  319
10.57   5  319
27.90  10  319
41.13  15  319
52.43  20  319
60.69  25  319
3.77   3  321
9.03   5  321
25.45  10  321
38.98  15  321
49.76  20  321
60.28  25  321
4.33   3  323
10.79   5  323
28.97  10  323
42.44  15  323
53.17  20  323
61.62  25  323
4.38   3  325
10.48   5  325
27.93  10  325
40.20  15  325
50.06  20  325
58.49  25  325
4.12   3  327
9.92   5  327
26.54  10  327
37.82  15  327
48.43  20  327
56.81  25  327
3.93   3  329
9.34   5  329
26.08  10  329
37.79  15  329
48.31  20  329
56.43  25  329
3.46   3  331
9.05   5  331
25.85  10  331
39.15  15  331
49.12  20  331
59.49  25  331

• What variables are in the regression? – user0 Dec 28 '16 at 21:40
• Edited to add model description. Looking to predict height by age (with interaction with group sometimes) – Mark Peterson Dec 28 '16 at 21:57