lmer Demo

Norway Spruce and Larch Forest in Austrian Alps, https://ec.europa.eu/jrc/en/research-topic/forestry/qr-tree-project/norway-spruce

1 Get Data 🌲

Data are from von Guttenberg’s Norway spruce (Picea abies [L.] Karst) tree measurement data, from Robinson and Hamann (2020).

“The data are measures from 107 trees. The trees were selected as being of average size from healthy and well stocked stands in the Alps.”

library(FAwR) # Forest Analytics with R

data("gutten") # Von Guttenberg Tree Data

2 Variables 🌲

site Growth quality class of the tree’s habitat. 5 levels.

location Distinguishes tree location. 7 levels.

tree An identifier for the tree within location.

age.base The tree age taken at ground level.

height Tree height, m.

dbh.cm Tree diameter, cm.

volume Tree volume.

age.bh Tree age taken at 1.3 m.

tree.ID A factor uniquely identifying the tree.

3 Data Wrangling (Centering) 🌲

gutten$height.C <- gutten$height - mean(gutten$height)

gutten$age.base.C <- gutten$age.base - mean(gutten$age.base) 

4 Graph 🌲

library(ggplot2)

library(patchwork)

p_uncentered <- ggplot(gutten,
                       aes(x = age.base,
                           y = height,
                           color = tree.ID)) +
  geom_line() +
  labs(title = "Tree Height By Tree Age",
       subtitle = "Uncentered Data") +
  scale_color_viridis_d() +
  theme_minimal() +
  theme(legend.position = "none")

# p_uncentered

p_centered <- ggplot(gutten,
                     aes(x = age.base.C,
                         y = height.C,
                         color = tree.ID)) +
  geom_line() +
  labs(title = "Tree Height By Tree Age",
       subtitle = "Centered Data") +
  scale_color_viridis_d() +
  theme_minimal() +
  theme(legend.position = "none")

# p_centered

p_uncentered + p_centered 

Tree Height by Tree Age

5 lmer 🌲

library(lme4) # MLM

library(sjPlot) # nice tables for MLM

5.1 Unconditional Model 🌲

fit0 <- lmer(height ~ (1 | tree.ID), 
             data = gutten)

tab_model(fit0)

	height
Predictors	Estimates	CI	p
(Intercept)	17.23	16.35 – 18.11	<0.001
Random Effects
σ2	69.70
τ00 tree.ID	15.08
ICC	0.18
N tree.ID	107
Observations	1200
Marginal R2 / Conditional R2	0.000 / 0.178

5.2 One Independent Variable; Random Intercept Only 🌲

fit1 <- lmer(height ~ age.base + (1 | tree.ID), 
             data = gutten)

tab_model(fit1)

	height
Predictors	Estimates	CI	p
(Intercept)	2.10	1.07 – 3.13	<0.001
age base	0.21	0.21 – 0.22	<0.001
Random Effects
σ2	8.41
τ00 tree.ID	25.75
ICC	0.75
N tree.ID	107
Observations	1200
Marginal R2 / Conditional R2	0.654 / 0.915

5.3 One Independent Variable; Random Intercept and Random Slope (Correlated) 🌲

fit2 <- lmer(height ~ age.base + (1 + age.base | tree.ID), 
             data = gutten)

tab_model(fit2)

	height
Predictors	Estimates	CI	p
(Intercept)	1.20	0.76 – 1.65	<0.001
age base	0.24	0.23 – 0.25	<0.001
Random Effects
σ2	3.38
τ00 tree.ID	3.62
τ11 tree.ID.age.base	0.01
ρ01 tree.ID	-0.12
ICC	0.92
N tree.ID	107
Observations	1200
Marginal R2 / Conditional R2	0.657 / 0.972

5.4 One Independent Variable; Random Intercept and Random Slope (Uncorrelated) 🌲

Important

Converges only with grand mean centered independent variable.

fit3 <- lmer(height ~ age.base.C + (1 + age.base.C || tree.ID), 
             data = gutten)

tab_model(fit3)

	height
Predictors	Estimates	CI	p
(Intercept)	18.75	17.69 – 19.82	<0.001
age base C	0.24	0.23 – 0.26	<0.001
Random Effects
σ2	3.38
τ00 tree.ID	31.04
τ11 tree.ID.age.base.C	0.01
ρ01
ρ01
ICC	0.90
N tree.ID	107
Observations	1200
Marginal R2 / Conditional R2	0.703 / 0.971

References

Robinson, Andrew, and Jeff Hamann. 2020. FAwR: Functions and Datasets for "Forest Analytics with r". https://doi.org/10.32614/CRAN.package.FAwR.