1. Grouped versus Ungrouped Example XY 2.10.9 2.11 2.11.2 2.11.05 4.62 4.61.95 4.62.2 4.61.9 XY Low0.9 Low1 Low1.2 Low1.05 High2 High1.95 High2.2 High1.9 N = 8 K = 3 SSE = 0.09875 -2LL = -23.55 AIC c = -14.55 N = 8 K = 3 SSE = 0.09875 -2LL = -23.55 AIC c = -14.55 Continuous DataGrouped Data In this artificial example, we expect the analyses to yield equivalent results

2. Grouped versus Ungrouped Example Continuous DataGrouped Data XY 11.95 3.62 2.52.05 0.82.1 43.9 7.74.1 6.24.05 5.33.95 8.26 11.86.1 10.35.9 9.65.96 XY Low1.95 Low2 Low2.05 Low2.1 Med3.9 Med4.1 Med4.05 Med3.95 High6 High6.1 High5.9 High5.96 In this case, model selection should clearly favor the grouped data… N = 12 K = 3 SSE = 3.7138 -2LL = 19.98 AIC c = 28.98 w i = 0.000 N = 12 K = 4 SSE = 0.0587 -2LL = -29.79 AIC c = -16.07 w i = 1.000 … and it does

3. Grouped versus Ungrouped Example Continuous DataGrouped Data XY 11.8 22.7 32.3 43.2 56.0 65.3 76.3 87.2 99.7 109.3 1111.8 1211.1 XY Low1.8 Low2.7 Low2.3 Low3.2 Med6.0 Med5.3 Med6.3 Med7.2 High9.7 High9.3 High11.8 High11.1 These models appear to have similar quality of fit, with the continuous model fitting slightly better (and likely being more useful for predictive purposes). N = 12 K = 3 SSE = 6.7382 -2LL = 27.13 AIC c = 36.13 w i = 0.933 N = 12 K = 4 SSE = 7.0475 -2LL = 27.67 AIC c = 41.38 w i = 0.067 Model selection supports the continuous model