1. Using R for multilevel modeling of salmon habitat
Yasmin Lucero, Statistical Consultant
Kelly Burnett, PNW Research Station, USFS
Kelly Christiansen, PNW Research Station, USFS
E. Ashley Steel, PNW Research Station, USFS
Eli Holmes, NW Fisheries Science Center, NOAA
Acknowledgements:
NRC-RAP, National Academy of Sciences
ISEMP Monitoring Program, NOAA

2. Outline
• Background on fish ecology and the data
• Background on multilevel modeling
• Demo of lme4 package in R

3. The big goal: measure effect of stream
habitat quality on fish survival
Photo by David Wolman
Schooling Juvenile Coho Salmon

4. Land Area Affected by
Endangered Species
Act Listings of Salmon
& Steelhead
* 28 distinct population segments:
6 endangered, 22 threatened
* 176,000 sq. miles in Washington,
Oregon, Idaho & California study area
* 61% of Washington’s land area,
55% of Oregon’s, 26% of Idaho’s, &
32% of California’s
February 2008

5. The Data
~266 study sites
Oregon coastal region
juvenile coho salmon habitat
sparsely sampled, longitudinal
study design Oregon
12 year time series
35 data layers
~100 landscape level variates
~22 habitat level variates

6. Abundance increases over time due to variation in
Ocean conditions (i.e. external to our analysis)
coho.obs coho.obs
●
1.0
●
●
●
8 ●
0.8
●
●
●
●
● ●
6 ●
●
coefficient
●
0.6
●
fs.coho.obs
●
● ● ●
● ●
●
● ●
●
4 ● ● ●
●
● ●
● ● ● ● ●
● ●
0.4
●
● ●
● ●
● ● ●
●
●
● ● ●
● ●
●
● ● ●
● ●
● ●
● ●
2 ● ●
●
●
●
●
0.2
● ●
● ●
●
● ●
●
● ●
● ●
●
●
●
0 1998 2000 2002 2004 2006 2008
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 year
fs.year

7. Sparsely sampled longitudinal data
• Only fish data has time 3.0
17100201010102 17100202030201 17100203020501 17100203020902
component 2.5
2.0 ●
• year effects exogenous
1.5
1.0 ● ● ● ●
● ● ● ● ●
0.5 ●
• Landscape data everywhere
● ● ● ● ● ● ● ● ● ●
● ● ●
●
● ● ● ● ● ● ● ● ● ●
0.0 ● ● ●
• Habitat data some places
17100203040402 17100203040602 17100203070101 17100203090101
3.0 ●
2.5
• Fish data some places
●
2.0 ●
●
1.5 ●
• Not always same places
●
●
1.0 ●
●
●
fs.coho.obs 0.5 ● ● ●
●
0.0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
17100204050303 17100205040105 17100205070202 17100206010504
3.0
2.5
2.0
1.5 ● ● ●
●
●
1.0 ● ● ● ●
●
0.5
● ● ● ●
●
0.0 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
17100206010603 17100303080202 17100304010604 17100305060202
3.0
2.5
2.0 ●
1.5
1.0 ●
0.5 ● ● ● ● ●
Figure Legend. Mean density of coho at
● ● ● ●
● ● ● ● ● ●
● ● ● ● ● ●
●
0.0 ● ● ● ● ● ● ● ● ● ● ●
16 frequently visited sites for 1998–2009 1998 2002 2006 1998 2002 2006 1998 2002 2006 1998 2002 2006
2000 2004 2008 2000 2004 2008 2000 2004 2008 2000 2004 2008
year

8. How the landscape data is acquired
summarize across area surrounding
GIS map layers
study site

9. habitat level data is collected by survey visits:
labor intensive to collect/therefore less abundant
gradient
pool density
debris
flow rates
drainage area high structure: rocks and woody debris
channel width
etc.
shallow, highly channelized

10. Multilevel structure for two reasons

11. Multi-level structure for two reasons:
(1) longitudinal sampling design
(2) varying scales of predictors
landscape
habitat
fish

12. Generalized linear mixed models
(aka hierarchical, multilevel, or random effects models)
canonical example: school test scores
class class class
class class class
class class class
school school school
state
student_score ~ class_average + school_average + state_average

13. state level predictors Norm(0, σstate )
2
state
school level predictors Norm(µstate1 , σschool )
2
school 1 school 2 school 3 school 4
class level predictors Norm(µschool1 , σclass )
2
class 1 class 2 class 3 class 4
student level predictors Norm(µclass3 , σstudent )
2
student 1 student 2 student 3 student 4

14. Our model structure is not so complicated
global
landscape level predictors
site 1 site 2 site 3 site 4
habitat level predictors
& year effects
obs 1 obs 2 obs 3 obs 4

15. Modeling presence/absence of fish:
logistic mixed model with site and year effects
year effects
γ ∗ year
logit(Pr{yi = 1}) = βyear xy + β1 xh1 + β1 xh2 + αsite
+ βh1 xh1 + βh2 xh2 + ...
+ αsite habitat level
predictors
site effects
αsite ∼ Norm(βl1 xl1 + βl2 xl2 + ... , σsite )
2
landscape level
predictors

16. Fit a lot of models, some predictors rose to the top
1300
m3
m18
m5
m6
m13
m11
m17
m15
m1m4
m9
m2
m21
Best predictors:
m8
m12
m7
gradient
1250
debris level
drainage area
1200
AIC
m14
mean elevation
1150
m10
m32
m30
m33
m34
1100
m16
m29
m31
m25
m20
m26
m28
m27
m19
m23 m22
m24
−620 −600 −580 −560 −540 −520
logLik

17. Overall model performance is strong at some
things, weak at others
fitted probabilities
1.0
●
●
●
●
●
●
●
●
●
●
●
0.8
800 ●
●
●
●
●
●
●
●
●
●
●
●
●
fitted probability
●
●
fitted probabilities
●
●
●
0.6
600 ●
●
●
●
●
●
●
●
●
●
●
●
count
0.4
●
●
400 ●
0.2
●
●
200 ●
●
0.0
0
0 1
0.0 0.2 0.4 0.6 0.8 1.0
fitted(models.ls$m24)
absence presence
histogram of fitted probabilities

18. Another look at model fit: some heavy outliers
~
pa.obs
s.year + (fs.grad.rs + fs.cfs.down.rs + fs.vol.len.rs + el.mean.rs | catchment
p/a of coho obs (data)
0.8
1998 2004
1999 2005
2000 2006
2001 2007
0.4
2002 2008
2003 2009
0.0
0.0 0.2 0.4 0.6 0.8 1.0
fitted

19. conclusions
• site matters
• we can explain about half of the variation in why site matters
with 4-5 predictors
• habitat data more valuable than landscape data
• small number of predictions are very wrong, and we can’t seem
to improve them

20. Thanks. yasmin.lucero@gmail.com

21. Model predicted probabilities given presence/
absence with and without site effects
m0 m1
1.0
1.0
●
●
●
●
● ●
● ●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
0.8
0.8
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Pr{coho present}
Pr{coho present}
●
●
●
0.6
0.6
●
●
●
●
●
●
●
●
●
●
●
0.4
0.4
●
●
●
●
●
●
●
●
●
0.2
0.2
●
●
0.0
0.0
FALSE TRUE FALSE TRUE
coho presence coho presence