21 Exercise 4: Linear Mixed Effects Model
Learning Objectives
By the end of this activity, you should be able to:
- Identify clustered and hierarchical data structures
- Specify linear mixed models with multiple random effects
- Implement PROC MIXED in SAS
- Interpret fixed and random effects
- Understand interaction + mixed effects
21.1 Dataset: Multi-Location Crop Yield Study
We now consider a more complex dataset:
- 5 locations (randomly sampled farms)
- 2 machine types (draper, stripper)
- 2 crop varieties
- multiple observations per combination
21.2 SAS Dataset
DATA crop;
INPUT location $ machine $ variety $ yield;
DATALINES;
A draper v1 35.2
A draper v2 34.8
A stripper v1 38.5
A stripper v2 39.1
B draper v1 30.5
B draper v2 31.2
B stripper v1 34.0
B stripper v2 35.5
C draper v1 28.9
C draper v2 29.5
C stripper v1 32.1
C stripper v2 33.0
D draper v1 36.0
D draper v2 35.7
D stripper v1 40.2
D stripper v2 41.0
E draper v1 33.3
E draper v2 34.1
E stripper v1 37.5
E stripper v2 38.0
;
RUN;21.3 Step 1: Identify Model Structure
21.3.1 Task 1
Identify:
- Response variable: ________
- Fixed effects: ________
- Random effects: ________
21.4 Step 2: Write the Full Model
\[ Y = \beta_0 + \beta_1 \text{machine} + \beta_2 \text{variety} + \beta_3 (machine \times variety) + u_{location} + \epsilon \]
21.5 Step 3: Implement in SAS
PROC MIXED DATA=crop;
CLASS location machine variety;
MODEL yield = machine variety machine*variety;
RANDOM location;
RUN;21.5.1 Step 4: Interpretation
Suppose:
- machine effect = 3.2
- interaction = 1.1
Interpret:
- machine effect: ____________________
- interaction: _______________________
21.5.2 Step 5: Model Comparison
| Model | AIC |
|---|---|
| No random effect | 210 |
| With random effect | 165 |
Which is better? Why?
22 Key Takeaways
- Mixed models handle clustered data
- Random effects capture variability across groups
- Interaction allows flexible modeling