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Grouped versus Ungrouped ExamplePowerPoint Presentation

Grouped versus Ungrouped Example

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Grouped versus Ungrouped Example

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Grouped versus Ungrouped Example

Continuous Data

Grouped Data

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

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

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

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

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

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