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Mixed Models Example Data Sets ExampleType of Example data file: Example?.DAT SAS Example?.SAS R Example?.R 1. Apple SizeLinear (clustered longitudinal) (Schabenberger and Pierce 2002, page 464) Yes 2.Orange TreesNonlinear (balanced longitudinal) (Draper and Smith 1981, page 524) Yes 3. HT-DBHLinear (multi-level) (based on Robinson and Wykoff 2004) Yes 4. Yield By AgeNonlinear (unbalanced longitudinal)Yes 5. Yield By AgeNonlinear (clustered unbalanced longitudinal) NoYes

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Example 1: Apples (Schabenberger and Pierce 2002, page 464) Linear Mixed Model Clustered Longitudinal Data 3-12 apples per tree 10 trees 6 measurements (weekly) Yij = (Bo + boi) + (B1 + b1i)Xij + eij Y = apple diameter (inches) X = time (week)

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Example 2: Orange Trees (Draper and Smith 1981, page 524) Nonlinear Mixed Model Longitudinal Data (balanced) 5 orange trees 8 measurements Yi = (B1+b1i)/(1+exp(-(Xi-B2)/B3)) Y = tree circumference (mm) X = time (days)

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Example 3: HT imputation (based on Robinson and Wykoff 2004) Linear Mixed Model Multi-level Data 5 stands in compartment (j) 3-11 plots per stand (i) Multiple trees per plot (k) ln(Ykij-4.5) = (Bo + boi + boj) + (B1 + b1i + b1j)/(1+Xkij) + eij Y = Total Height (feet) X = DBH (inches)

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Example 4: Yield/Age Nonlinear Mixed Model Longitudinal Data (unbalanced) 9 installations (locations) 5-10 measurements Yi = (B1+b1i)/(1+exp(-(Xi-B2)/B3)) Y = Merchantable Cunits (ft3/acre) X = Total Age (years)

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Example 5: Yield/Age Nonlinear Mixed Model Clustered Longitudinal Data (unbalanced) 9 installations (locations) (j) 3 plots per installation (i) 5-10 measurements Yi = (B1+b1i+b1j)/(1+exp(-(Xi-B2)/B3)) Y = Merchantable Cunits (ft3/acre) X = Total Age (years)

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4x + 2y = 18 a. (1,8)4 + 16 = 18 a. 4(1) + 2(8) = 18 b. (3,3)20 = 18 b. 4(3) + 2(3) = 18 12 + 6 = 18 18 = 18 15x + 5y = 5 a. (-2,7) NoYes b. (-1,4) a.

4x + 2y = 18 a. (1,8)4 + 16 = 18 a. 4(1) + 2(8) = 18 b. (3,3)20 = 18 b. 4(3) + 2(3) = 18 12 + 6 = 18 18 = 18 15x + 5y = 5 a. (-2,7) NoYes b. (-1,4) a.

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