Using Repeated Measures in Statistical Analysis McKenzie Kuhn, Ben Bourrie, & Deanna Pepin Pseudoreplication in ecological studies Simple (subsamples) Temporal (repeated measures) A1 A2 A1 A2 A3 A4 A2 A3 A4 B1 B2 B3 B4 B1 B2 B3 B4 TIME
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Using Repeated Measures in Statistical AnalysisMcKenzie Kuhn, Ben Bourrie, & Deanna Pepin
Pseudoreplication in ecological studies
Simple (subsamples) Temporal (repeated measures)
A1
A2
A1 A2 A3 A4
A2
A3
A4
B1
B2
B3
B4B1 B2 B3 B4
TIME
Benefits of Repeated Measures
More statistical power
Fewer subjects
The solution: multilevel mixed effects modeling
Litter A
Cage1 Cage 2
Litter B
Cage3 Cage 4
Fixed Factor
Random
Bird 1
T1 T2 T3
Bird 2
T1 T2 T3
Bird 3
T1 T2 T3
Bird 4
T1 T2 T3
Bird 5
T1 T2 T3
Bird 6
T1 T2 T3
Bird 7
T1 T2 T3
Bird 8
T1 T2 T3
Bird 9
T1 T2 T3
Bird 10
T1 T2 T3
Bird 11
T1 T2 T3
Bird 12
T1 T2 T3
Random
Goal: look at effects of litter type and time (day) on weight gain
• Missing Data:
• Multivariate approach: Sample dropped
• Mixed approach: Time point dropped
• Post hoc tests:
Why Use a Mixed Effect Model?
• Post hoc tests:
• Repeated measures
• Mixed approach
Important R packages
nmle, car, multcomp
Limitations
Data must be normal & group sizes equal
No method for multivariate repeated measures (yet!)
Resources for pseudoreplication and mixed models
Davies, G. M., & Gray, A. (2015). Don't let spurious accusations of pseudoreplication limit our ability to learn from natural experiments (and other messy kinds of ecological monitoring). Ecology and Evolution, 5(22), 5295-5304.
Hurlbert, S. H. (1984). Pseudoreplication and the design of ecological field Hurlbert, S. H. (1984). Pseudoreplication and the design of ecological field experiments. Ecological monographs, 54(2), 187-211.
Zuur, A. F., Ieno, E. N., Walker, N. J., Saveliev, A. A., & Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. Gail M, Krickeberg
K, Samet JM, Tsiatis A, Wong W, editors. New York, NY: Spring Science and Business Media.
http://rpsychologist.com/r-guide-longitudinal-lme-lmer
Thanks!
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