Table 2.

Median cross-validated AUC for all models applied to the simulated data, for the case when N=200, T_i is skewed, measurement error is present, and the outcome is binary. Models include seven functional models, five simple logistic regressions on the indicated summary statistic, and nine more complicated parametric or semi-parametric functions of the within-subject mean (X̄_i) and the domain width (T_i).

	β1(t, Ti)	β2(t, Ti)	β3(t, Ti)	β4(t, Ti)
Functional Models:
Untransformed	0.862	0.744	0.947	0.886
Lagged	0.863	0.746	0.946	0.887
DS (TPRS)	0.902	0.778	0.963	0.904
DS (TPBS)	0.900	0.775	0.933	0.905
DS (No Int)	0.905	0.602	0.948	0.790
DS (Lin)	0.901	0.716	0.964	0.866
DS (Quad)	0.897	0.767	0.959	0.872
Summary Statistic Models:
Mean	0.434	0.634	0.955	0.854
Median	0.436	0.637	0.949	0.847
Maximum	0.439	0.601	0.842	0.776
Cumulative	0.431	0.646	0.915	0.817
Slope	0.820	0.429	0.438	0.431
Additional Models:
β1X̄i + β2Ti	0.459	0.631	0.954	0.850
β1X̄i + f2(Ti)	0.466	0.628	0.951	0.846
f1(X̄i) + β2Ti	0.466	0.621	0.953	0.845
f1(X̄i) + f2(Ti)	0.472	0.620	0.949	0.842
f(X̄i, Ti)	0.465	0.720	0.938	0.865
β1X̄i + β2Ti + β3X̄iTi	0.458	0.636	0.958	0.864
β1X̄i + f2(Ti) + f3(X̄iTi)	0.468	0.647	0.953	0.856
f1(X̄i) + β2Ti + f3(X̄iTi)	0.472	0.650	0.955	0.857
f1(X̄i) + f2(Ti) + f3(X̄iTi)	0.475	0.649	0.952	0.852