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Grouped versus Ungrouped Example

Grouped versus Ungrouped Example. Continuous Data. Grouped Data. X Y 2.1 0.9 2.1 1 2.1 1.2 2.1 1.05 4.6 2 4.6 1.95 4.6 2.2 4.6 1.9. X Y Low 0.9 Low 1 Low 1.2 Low 1.05 High 2 High 1.95 High 2.2 High 1.9. N = 8 K = 3 SSE = 0.09875 -2LL = -23.55 AIC c = -14.55. N = 8 K = 3

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Grouped versus Ungrouped Example

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  1. Grouped versus Ungrouped Example Continuous Data Grouped Data X Y 2.1 0.9 2.1 1 2.1 1.2 2.1 1.05 4.6 2 4.6 1.95 4.6 2.2 4.6 1.9 X Y Low 0.9 Low 1 Low 1.2 Low 1.05 High 2 High 1.95 High 2.2 High 1.9 N = 8 K = 3 SSE = 0.09875 -2LL = -23.55 AICc = -14.55 N = 8 K = 3 SSE = 0.09875 -2LL = -23.55 AICc = -14.55 In this artificial example, we expect the analyses to yield equivalent results

  2. Grouped versus Ungrouped Example Continuous Data Grouped Data X Y 1 1.95 3.6 2 2.5 2.05 0.8 2.1 4 3.9 7.7 4.1 6.2 4.05 5.3 3.95 8.2 6 11.8 6.1 10.3 5.9 9.6 5.96 X Y Low 1.95 Low 2 Low 2.05 Low 2.1 Med 3.9 Med 4.1 Med 4.05 Med 3.95 High 6 High 6.1 High 5.9 High 5.96 N = 12 K = 3 SSE = 3.7138 -2LL = 19.98 AICc = 28.98 wi = 0.000 In this case, model selection should clearly favor the grouped data… N = 12 K = 4 SSE = 0.0587 -2LL = -29.79 AICc = -16.07 wi = 1.000 … and it does

  3. Grouped versus Ungrouped Example Continuous Data Grouped Data X Y 1 1.8 2 2.7 3 2.3 4 3.2 5 6.0 6 5.3 7 6.3 8 7.2 9 9.7 10 9.3 11 11.8 12 11.1 X Y Low 1.8 Low 2.7 Low 2.3 Low 3.2 Med 6.0 Med 5.3 Med 6.3 Med 7.2 High 9.7 High 9.3 High 11.8 High 11.1 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 AICc = 36.13 wi = 0.933 N = 12 K = 4 SSE = 7.0475 -2LL = 27.67 AICc = 41.38 wi = 0.067 Model selection supports the continuous model

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