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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

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


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


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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