Apart from causality, the arguably most fundamental idea about modelling choice is the bias-variance trade-off, which applies regardless of whether we are interested in causal effects or predictive models. The idea is the following:
The more variables / complexity we include in the model, the better it can (in principle) adjust to the true relationship, thus reducing model error from bias.
The more variables / complexity we include in the model, the larger our error (variance) on the fitted coefficients, thus increasing model error from variance. This means, the model adopts to the given data but no longer to the underlying relationship.
If we sum both terms up, we see that at the total error of a model that is too simple will be dominated by bias (underfitting), and the total error of a model that is too complex will be dominated by variance (overfitting):
Let’s confirm this with a small simulation - let’s assume I have a simple relationship between x and y:
set.seed(123)x =runif(100)y =0.25* x +rnorm(100, sd =0.3)summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-0.67139 -0.18397 -0.00592 0.17890 0.66517
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.002688 0.058816 -0.046 0.964
x 0.223051 0.102546 2.175 0.032 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2908 on 98 degrees of freedom
Multiple R-squared: 0.04605, Adjusted R-squared: 0.03632
F-statistic: 4.731 on 1 and 98 DF, p-value: 0.03203
As you see, the effect is significant. Now, I add 80 new variables to the model which are just noise
xNoise =matrix(runif(8000), ncol =80)dat =data.frame(y=y,x=x, xNoise)fullModel =lm(y~., data = dat)summary(fullModel)
The effect estimates are relatively unchanged, but the CI has increased, and the p-values are n.s.
Precision variables
We have learned that adding variables increases the complexity of the model and thus the variance/uncertainty of the model. However, there are so-called precision variables that, when added to the model, actually reduce the variance/uncertainty of the model! Technically, they explain the response variable so well that they help to improve the overall fit of the model and thus help to reduce the overall variance of the model.
Call:
lm(formula = Y ~ X)
Residuals:
Min 1Q Median 3Q Max
-5.3935 -2.7579 0.3701 2.2876 4.8379
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.3465 0.5826 9.177 7.39e-15 ***
X 0.4364 0.9639 0.453 0.652
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.896 on 98 degrees of freedom
Multiple R-squared: 0.002088, Adjusted R-squared: -0.008095
F-statistic: 0.205 on 1 and 98 DF, p-value: 0.6517
Effect of X is n.s. (standard error = 0.96)
With the precision variable (P):
summary(lm(Y~X+P))
Call:
lm(formula = Y ~ X + P)
Residuals:
Min 1Q Median 3Q Max
-0.97608 -0.28268 0.00618 0.27548 1.38684
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.04947 0.12646 -0.391 0.697
X 0.75999 0.15197 5.001 2.54e-06 ***
P 10.05137 0.16200 62.045 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.4563 on 97 degrees of freedom
Multiple R-squared: 0.9755, Adjusted R-squared: 0.975
F-statistic: 1929 on 2 and 97 DF, p-value: < 2.2e-16
The effect of X on Y is now significant (standard error = 0.15)!
8.2 Model Selection Methods
Because of the bias-variance trade-off, we cannot just fit the most complex model that we can imagine. Of course, such a model would have the lowest possible bias, but we would loose all power to see effects. Therefore, we must put bounds on model complexity. There are many methods to do so, but I would argue that three of them stand out
Test whether there is evidence for going to a more complex model -> Likelihood Ratio Tests
Optimize a penalized fit to the data -> AIC selection
Specify a preference for parameter estimates to be small -> shrinkage estimation
Let’s go through them one by one
8.2.1 Likelihood-ratio tests
A likelihood-ratio test (LRT) is a hypothesis test that can be used to compare 2 nested models. Nested means that the simpler of the 2 models is included in the more complex model.
The more complex model will always fit the data better, i.e. have a higher likelihood. This is the reason why you shouldn’t use fit or residual patterns for model selection. The likelihood-ratio test tests whether this improvement in likelihood is significantly larger than one would expect if the simpler model is the correct model.
Likelihood-ratio tests are used to get the p-values in an R ANOVA, and thus you can also use the anova function to perform an likelihood-ratio test between 2 models (Note: For simple models, this will run an F-test, which is technically not exactly a likelihood-ratio test, but the principle is the same):
# Model 1m1 =lm(Ozone ~ Wind , data = airquality)# Model 2m2 =lm(Ozone ~ Wind + Temp, data = airquality)# LRTanova(m1, m2)
Analysis of Variance Table
Model 1: Ozone ~ Wind
Model 2: Ozone ~ Wind + Temp
Res.Df RSS Df Sum of Sq F Pr(>F)
1 114 79859
2 113 53973 1 25886 54.196 3.149e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
8.2.2 AIC model selection
Another method for model selection, and probably the most widely used, also because it does not require that models are nested, is the AIC = Akaike Information Criterion.
The AIC is defined as \(2 \ln(\text{likelihood}) + 2k\), where \(k\) = number of parameters.
Essentially, this means AIC = Fit - Penalty for complexity.
Lower AIC is better!
m1 =lm(Ozone ~ Temp, data = airquality)m2 =lm(Ozone ~ Temp + Wind, data = airquality)AIC(m1)
[1] 1067.706
AIC(m2)
[1] 1049.741
Note 1: It can be shown that AIC is asymptotically identical to leave-one-out cross-validation, so what AIC is optimizing is essentially the predictive error of the model on new data.
Note 2: There are other information criteria, such as BIC, DIC, WAIC etc., as well as sample-size corrected versions of either of them (e.g. AICc). The difference between the methods is beyond the scope of this course. For the most common one (BIC), just the note that this penalizes more strongly for large data sets, and thus corrects a tendency of AIC to overfit for large data sets.
Exercise
Compare results of AIC with likelihood-ratio tests. Discuss: When to use one or the other?
Solution
8.2.3 Shrinkage estimation
A third option option for model selection are shrinkage estimators. These include the LASSO and ridge, but also random-effects could be seen as shrinkage estimators.
The basic idea behind these estimators is not to reduce the number of parameters, but to reduce the flexibility of the model by introducing a penalty on the regression coefficients that code a preference for smaller or zero coefficient values. Effectively, this can either amount to model selection (because some coefficients are shrunk directly to zero), or it can mean that we can fit very large models while still being able to do good predictions, or avoid overfitting.
To put a ridge penalty on the standard lm, we can use
Family: gaussian ( identity )
Formula: Ozone ~ (0 + Wind + Temp + Solar.R || group)
Data: airquality
AIC BIC logLik deviance df.resid
1020.3 1025.8 -508.2 1016.3 109
Random effects:
Conditional model:
Groups Name Variance Std.Dev. Corr
group Wind 1.0 1.00
Temp 1.0 1.00 0.00
Solar.R 1.0 1.00 0.00 0.00
Residual 452.3 21.27
Number of obs: 111, groups: group, 1
Dispersion estimate for gaussian family (sigma^2): 452
Conditional model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -80.27 20.90 -3.841 0.000122 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(ridgeGlmmTMB10)
Family: gaussian ( identity )
Formula: Ozone ~ (0 + Wind + Temp + Solar.R || group)
Data: airquality
AIC BIC logLik deviance df.resid
1069.1 1074.6 -532.6 1065.1 109
Random effects:
Conditional model:
Groups Name Variance Std.Dev. Corr
group Wind 4.852e+08 22026.47
Temp 4.852e+08 22026.47 0.00
Solar.R 4.852e+08 22026.47 0.00 0.00
Residual 4.445e+02 21.08
Number of obs: 111, groups: group, 1
Dispersion estimate for gaussian family (sigma^2): 444
Conditional model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -64.34 22.95 -2.804 0.00505 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: The (…||…) syntax will model the individual random slopes individually (the default is to fit a covariance matrix between the random effects).
We can use the map and the start arguments to a) mark the variances of the random slopes as constant and b) to set them so specific values (smaller values mean higher regularization).
Random effects are now our slopes:
ranef(ridgeGlmmTMB1)[[1]]$g
Wind Temp Solar.R
1 -2.426747 1.736524 0.06169567
ranef(ridgeGlmmTMB10)[[1]]$g
Wind Temp Solar.R
1 -3.333591 1.652093 0.05982059
For higher variances they are stronger biased to 0.
Adaptive shrinkage
The next obvious step would be to let the model and the data decide on the variance estimate (the amount of shrinkage), which is called adaptive shrinkage.
We still get a convergence issue, but this is related to the very small variance estimates of the other predictors (glmmTMB tries to calculate standard errors based on the hessian, however, the hessian has very small elements on its diagonal, which makes it impossible to calculate its inverse).
8.2.4 P-hacking
The most dubious model selection strategy, actually considered scientific misconduct, is p-hacking. The purpose of this exercises is to show you how not to do model selection, i.e, that by playing around with the variables, you can make any outcome significant. That is why your hypothesis needs to be fixed before looking at the data, ideally through pre-registration, based on an experimental plan or a causal analysis. Here is the example:
p-hacking exercise
We have (simulated) measurements of plant performance. The goal of the analysis was to find out if Gen1 has an effect on Performance. Various other variables are measured. As you can see, the way I simulated the data, none of the variables has an effect on the response, so this is pure noise
When you run summary(fullModel), you will see that there is no significant effect of of Gen1. Task for you: P-hack the analysis, i.e. make an effect appear, by trying around (systematically, e.g. with selecting with data, model selection, or by hand to find a model combination that has an effect). Popular strategies for p-hacking include changing the mdoel, but also sub-selecting particualr data. The group who finds the model with the highest significance for Gen1 wins!
Possible solution
summary(lm(Performance ~ Gen1 * Humidity, data = dat[20:30,]))
Call:
lm(formula = Performance ~ Gen1 * Humidity, data = dat[20:30,
])
Residuals:
Min 1Q Median 3Q Max
-0.71665 -0.39627 -0.05915 0.28044 0.91257
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.5248 0.2277 -2.304 0.05465 .
Gen1 0.8657 0.2276 3.804 0.00668 **
Humidity 0.6738 0.2544 2.649 0.03298 *
Gen1:Humidity -0.5480 0.1756 -3.122 0.01680 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6102 on 7 degrees of freedom
Multiple R-squared: 0.7004, Adjusted R-squared: 0.572
F-statistic: 5.454 on 3 and 7 DF, p-value: 0.03
Model selection works great to generate predictive models. The big problem with model selection is when we want interpret effect estimates. Here, we have two problems
Model selection doesn’t respect causal relationships
Model selection methods often lead to wrong p-values, CIs etc.
Let’s look at them 1 by one:
8.3.1 Causality
In general, model selection does NOT solve the problem of estimating causal effects. Quite the contrary: most model selection methods act against estimating causal effects. Consider the following example, where we create a response that causally depends on two collinear predictors, both with an effect size of 1
Given the structure of the data, we should run a multiple regression, and the multiple regression will get it roughly right: both effects are n.s., but estimates are roughly right and true values are in the 95% CI.
m1 =lm(y ~ x1 + x2)summary(m1)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
Min 1Q Median 3Q Max
-1.8994 -0.6821 -0.1086 0.5749 3.3663
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1408 0.2862 -0.492 0.624
x1 1.2158 1.5037 0.809 0.421
x2 0.8518 1.8674 0.456 0.649
Residual standard error: 0.9765 on 97 degrees of freedom
Multiple R-squared: 0.237, Adjusted R-squared: 0.2212
F-statistic: 15.06 on 2 and 97 DF, p-value: 2.009e-06
A model selection (more on the method later) will remove one of the variables and consequently overestimates the effect size (effect size too high, true causal value outside the 95% CI).
m2 = MASS::stepAIC(m1)
summary(m2)
Call:
lm(formula = y ~ x1)
Residuals:
Min 1Q Median 3Q Max
-1.9047 -0.6292 -0.1019 0.6077 3.3394
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.04633 0.19670 -0.236 0.814
x1 1.88350 0.34295 5.492 3.13e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9725 on 98 degrees of freedom
Multiple R-squared: 0.2353, Adjusted R-squared: 0.2275
F-statistic: 30.16 on 1 and 98 DF, p-value: 3.134e-07
If you understand what AIC model selection is doing, you wouldn’t be concerned - this is actually not a bug, but rather, the method is doing exactly what it is designed for. However, it was not designed to estimate causal effects. Let’s do another simulation: here, x1,x2 and x3 all have the same effect on the response, but x1 and x2 are highly collinear, while x3 is independent
Analysis of Variance Table
Model 1: y ~ x1
Model 2: y ~ x1 + x2
Res.Df RSS Df Sum of Sq F Pr(>F)
1 98 96.548
2 97 94.066 1 2.4817 2.5591 0.1129
AIC(m2)
[1] 285.6705
The same for the comparison of x1 to x1 + x3
m3 =lm(y ~ x1 + x3)anova(m1, m3)
Analysis of Variance Table
Model 1: y ~ x1
Model 2: y ~ x1 + x3
Res.Df RSS Df Sum of Sq F Pr(>F)
1 98 96.548
2 97 86.848 1 9.6998 10.834 0.001391 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AIC(m3)
[1] 277.6868
What we see is that the model selection methods are far more enthusiastic about including x3. And with good reason: x3 is an independent predictor, so adding x3 improves the model a lot. The effect of x2, however, is mostly already included in x1, so adding x2 will only slightly improve the model. Thus, from the point of view of how good the data is explained, it doesn’t pay off to add x2. From the causal viewpoint, however, adding x3 is irrelevant, because it is not a confounder, while adding x2 is crucial (assuming the causal direction is such that it is a confounder).
8.3.2 P-values
The second problem with model selection is the calibration of p-values. Let’s revisit our simulation example from the bias-variance trade-off, where we added 80 noisy predictors with no effect to a situation where we had one variable with an effect.
set.seed(123)x =runif(100)y =0.25* x +rnorm(100, sd =0.3)xNoise =matrix(runif(8000), ncol =80)dat =data.frame(y=y,x=x, xNoise)fullModel =lm(y~., data = dat)
We saw before that the y~x effect is n.s. after adding all 80 predictors. Let’s use AIC in a stepwise model selection procedure to reduce model complexity
Tip
Systematic LRT or AIC model selections are often used stepwise or global. Stepwise means that start with the most simple (forward) or the most comples (backward) model, and then run a chain of model selection steps (AIC or LRT) adding (forward) or removing (backward) complexity until we arrive at an optimum. Global means that we run immediately all possible models and compare their AIC. The main function for stepwise selection is MASS::StepAIC, for global selection MuMIn::dredge. There was a lot of discussion about step-wise vs. global selection in the literature, that mostly revolved around the fact that a stepwise selection is faster, but will not always find the global optimum. However, compared to the other problems discussed here (causality, p-values), I do not consider this a serious problem. Thus, if you can, run a global selection by all means, but if this is computationally prohibitive, stepwise selections are also fine.
library(MASS)reduced =stepAIC(fullModel)
Note
When you inspect the output of stepAIC, you can see that the function calculates at each step the AIC improvement for each predictor that could be removed, and then chooses to remove the predictor that leads to the strongest AIC improvement first.
The result ist good and bad. Good is that we now get the effect of y ~ x significant. Bad is that a lot of the other noisy variables are also significant, and the rate at which this occurs is much higher than we should expect (22/80 random predictors significant is much higher than the expected type I error rate).
The phenomenon is well-known in the stats literature, and the reason is that performing a stepwise / global selection + calculating a regression table for the selected model is hidden multiple testing and has inflated Type I error rates! Remember, you are implicitly trying out hundreds or thousand of models, and are taking the one that is showing the strongest effects.
There are methods to correct for the problem (keyword: post-selection inference), but none of them are readily available in R, and also, mostly those corrected p-values have lower power than the full model.
8.4 Non-parametric R2 - cross-validation
Cross-validation is the non-parametric alternative to AIC. Note that AIC is asymptotically equal to leave-one-out cross-validation.
For most advanced models, you will have to program the cross-validation by hand, but here an example for glm, using the cv.glm function:
library(boot)# Leave-one-out and 6-fold cross-validation prediction error for the mammals data set.data(mammals, package="MASS")mammals.glm =glm(log(brain) ~log(body), data = mammals)cv.err =cv.glm(mammals, mammals.glm, K =5)$delta# As this is a linear model we could calculate the leave-one-out # cross-validation estimate without any extra model-fitting.muhat =fitted(mammals.glm)mammals.diag =glm.diag(mammals.glm)(cv.err =mean((mammals.glm$y - muhat)^2/(1- mammals.diag$h)^2))
[1] 0.491865
# Leave-one-out and 11-fold cross-validation prediction error for # the nodal data set. Since the response is a binary variable an# appropriate cost function iscost =function(r, pi =0){ mean(abs(r - pi) >0.5) }nodal.glm =glm(r ~ stage+xray+acid, binomial, data = nodal)(cv.err =cv.glm(nodal, nodal.glm, cost, K =nrow(nodal))$delta)
[1] 0.1886792 0.1886792
(cv.11.err =cv.glm(nodal, nodal.glm, cost, K =11)$delta)
[1] 0.2641509 0.2570310
Note that cross-validation requires independence of data points. For non-independent data, it is possible to block the cross-validation, see Roberts, David R., et al. “Cross‐validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure.” Ecography 40.8 (2017): 913-929., methods implemented in package blockCV, see https://cran.r-project.org/web/packages/blockCV/vignettes/BlockCV_for_SDM.html.
8.5 Case studies
8.5.1 Exercise: Global Plant Trait Analysis #3
Excercise
Revisit exercises our previous analyses of the dataset plantHeight, and discuss / analyze:
Which would be the appropriate model, if we want to get a predictive model for plant height, based on all the variables in the data set? Note: some text-based variables may need to be included, so probably it’s the easiest if you start with a large model that you specify by hand. You can also include interactions. The syntax:
fit <-lm((x1 + x2 + x3)^2)
includes all possible 2nd-order interactions between the variables in your model. You can extend this to x3, x4 but I would not recommend it, your model will get too large.
Solution
library(EcoData)library(MASS)head(plantHeight)## sort_number site Genus_species Family growthform height## 1 1402 193 Acer_macryophyllum Sapindaceae Tree 28.0## 2 25246 103 Quararibea_cordata Malvaceae Tree 26.6## 3 11648 54 Eragrostis_dielsii Poaceae Herb 0.3## 4 8168 144 Cistus_salvifolius Cistaceae Shrub 1.6## 5 22422 178 Phlox_bifida Polemoniaceae Herb 0.2## 6 15925 59 Homalium_betulifolium Salicaceae Shrub 1.7## loght Country Site lat long entered.by alt## 1 1.4471580 USA Oregon - McDun 44.600 -123.334 Angela 179## 2 1.4248816 Peru Manu 12.183 -70.550 Angela 386## 3 -0.5228787 Australia Central Australia 23.800 133.833 Michelle 553## 4 0.2041200 Israel Hanadiv 32.555 34.938 Angela 115## 5 -0.6989700 USA Indiana Dunes 41.617 -86.950 Michelle 200## 6 0.2304489 New Caledonia <NA> 21.500 165.500 Laura 95## temp diurn.temp isotherm temp.seas temp.max.warm temp.min.cold temp.ann.range## 1 10.8 11.8 4.4 5.2 27.0 0.3 26.7## 2 24.5 10.8 7.4 0.9 31.2 16.7 14.5## 3 20.9 16.3 4.8 6.0 37.0 3.6 33.4## 4 19.9 9.7 4.4 4.9 30.7 8.7 22.0## 5 9.7 10.7 2.8 9.7 28.6 -9.5 38.1## 6 22.6 7.4 5.4 2.2 29.0 15.5 13.5## temp.mean.wetqr temp.mean.dryqr temp.mean.warmqr temp.mean.coldqr rain## 1 4.9 17.4 17.6 4.5 1208## 2 25.1 23.2 25.3 23.1 3015## 3 28.1 14.8 28.1 12.8 278## 4 13.6 25.3 25.7 13.6 598## 5 21.6 -3.3 21.6 -3.3 976## 6 25.4 20.4 25.4 19.7 1387## rain.wetm rain.drym rain.seas rain.wetqr rain.dryqr rain.warmqr rain.coldqr## 1 217 13 69 601 68 75 560## 2 416 99 45 1177 340 928 359## 3 37 9 42 109 35 109 42## 4 159 0 115 408 0 2 408## 5 104 44 23 299 165 299 165## 6 216 59 46 600 186 600 212## LAI NPP hemisphere## 1 2.51 572 1## 2 4.26 1405 -1## 3 1.32 756 -1## 4 1.01 359 1## 5 3.26 1131 1## 6 6.99 1552 -1fullModel <-lm(loght ~ (growthform + Family + lat + long + alt + temp + NPP )^2, data = plantHeight)selectedModel =stepAIC(fullModel, trace =0)summary(selectedModel)## ## Call:## lm(formula = loght ~ growthform + Family + lat + long + alt + ## temp + NPP + growthform:Family + growthform:lat + growthform:long + ## growthform:NPP + Family:lat + Family:long + Family:alt + ## Family:temp + lat:long + lat:temp + lat:NPP + long:alt + ## long:temp + long:NPP + alt:temp + temp:NPP, data = plantHeight)## ## Residuals:## Min 1Q Median 3Q Max ## -0.1897 0.0000 0.0000 0.0000 0.1998 ## ## Coefficients: (521 not defined because of singularities)## Estimate Std. Error t value## (Intercept) -1.612e+01 2.152e+01 -0.749## growthformHerb 1.598e+02 1.822e+02 0.877## growthformHerb/Shrub -2.013e-01 3.854e+00 -0.052## growthformShrub -1.992e+02 2.590e+02 -0.769## growthformShrub/Tree -1.126e+02 1.952e+02 -0.577## growthformTree 2.053e+01 1.530e+01 1.342## FamilyAsteraceae -3.562e+02 1.352e+02 -2.636## FamilyAtherospermataceae -2.866e+01 2.295e+01 -1.248## FamilyBalsaminaceae 1.530e+02 1.927e+02 0.794## FamilyBetulaceae -3.010e+01 1.056e+02 -0.285## FamilyBrassicaceae -1.271e+02 1.910e+02 -0.665## FamilyCactaceae 2.620e+02 2.820e+02 0.929## FamilyCasuarinaceae 1.995e+02 2.582e+02 0.773## FamilyChloranthaceae 7.419e-01 9.460e-01 0.784## FamilyChrysobalanaceae 5.392e+00 8.314e+00 0.649## FamilyCistaceae 1.999e+02 2.586e+02 0.773## FamilyCornaceae 3.361e+02 4.220e+02 0.796## FamilyCrassulaceae 1.954e+02 2.551e+02 0.766## FamilyCunoniaceae 1.716e-01 3.008e-01 0.571## FamilyCupressaceae -3.435e+01 3.185e+01 -1.079## FamilyCyperaceae -1.814e+01 2.054e+01 -0.883## FamilyDennstaedtiaceae NA NA NA## FamilyDicksoniaceae 1.878e+02 2.490e+02 0.754## FamilyDipterocarpaceae 4.334e+00 4.919e+00 0.881## FamilyEbenaceae 5.281e+00 5.975e+00 0.884## FamilyElaeocarpaceae 5.440e-01 5.242e-01 1.038## FamilyEricaceae 2.186e+02 2.792e+02 0.783## FamilyEuphorbiaceae 3.472e+00 4.301e+00 0.807## FamilyFabaceae - C 2.644e+00 3.387e+00 0.781## FamilyFabaceae - M -2.768e+00 2.238e+00 -1.237## FamilyFabaceae - P 5.128e+01 5.128e+01 1.000## FamilyFagaceae -2.036e+00 7.802e+00 -0.261## FamilyGentianaceae -1.963e+02 2.264e+02 -0.867## FamilyHeliconiaceae -1.193e+02 1.413e+02 -0.845## FamilyJuglandaceae -2.223e+01 2.069e+01 -1.074## FamilyJuncaginaceae 2.855e+02 3.596e+02 0.794## FamilyLamiaceae 1.876e+02 2.522e+02 0.744## FamilyLauraceae -2.595e+00 4.184e+00 -0.620## FamilyMaesaceae 2.097e+02 2.652e+02 0.791## FamilyMalvaceae 3.153e+00 4.933e+00 0.639## FamilyMelastomataceae 2.135e+02 2.701e+02 0.790## FamilyMoraceae -5.805e+00 6.329e+00 -0.917## FamilyMyristicaceae 8.819e-01 8.987e-01 0.981## FamilyMyrsinaceae -9.893e+00 1.109e+01 -0.892## FamilyMyrtaceae -3.193e+01 1.040e+01 -3.070## FamilyOchnaceae 2.125e+02 2.692e+02 0.789## FamilyOnagraceae NA NA NA## FamilyOrobanchaceae -1.075e+02 1.752e+02 -0.613## FamilyPhyllanthaceae -1.211e+01 1.357e+01 -0.892## FamilyPicrodendraceae -1.256e+01 1.307e+01 -0.961## FamilyPinaceae 1.522e+01 8.029e+00 1.895## FamilyPoaceae 1.059e+02 1.625e+02 0.652## FamilyPolemoniaceae -1.369e+02 1.613e+02 -0.849## FamilyPolygonaceae -1.292e+02 1.622e+02 -0.796## FamilyProteaceae 1.685e+01 9.511e+00 1.772## FamilyRanunculaceae 1.136e+02 1.438e+02 0.790## FamilyRhamnaceae 1.944e+02 2.570e+02 0.756## FamilyRosaceae 1.148e+01 3.983e+00 2.883## FamilyRubiaceae 2.165e+02 2.702e+02 0.801## FamilyRutaceae 1.979e+02 2.555e+02 0.774## FamilySalicaceae 2.326e+02 2.849e+02 0.816## FamilySapindaceae 4.753e+00 8.974e+00 0.530## FamilySapotaceae -1.511e+01 1.313e+01 -1.151## FamilyScrophulariaceae 2.099e+02 2.660e+02 0.789## FamilyThymelaeaceae -9.324e+00 9.227e+00 -1.010## FamilyUlmaceae 1.783e+01 1.401e+01 1.273## FamilyUrticaceae 8.939e+00 8.901e+00 1.004## FamilyViolaceae 2.145e+02 2.712e+02 0.791## FamilyXanthorrhoeaceae 2.016e+02 2.596e+02 0.777## FamilyZygophyllaceae 1.871e+02 2.474e+02 0.756## lat 6.678e-01 6.451e-01 1.035## long 6.846e-03 3.808e-02 0.180## alt 5.440e-03 8.816e-03 0.617## temp -1.851e-01 2.343e-01 -0.790## NPP 2.978e-03 2.716e-03 1.097## growthformHerb:FamilyAsteraceae -1.535e+01 4.924e+01 -0.312## growthformHerb/Shrub:FamilyAsteraceae NA NA NA## growthformShrub:FamilyAsteraceae NA NA NA## growthformShrub/Tree:FamilyAsteraceae NA NA NA## growthformTree:FamilyAsteraceae NA NA NA## growthformHerb:FamilyAtherospermataceae NA NA NA## growthformHerb/Shrub:FamilyAtherospermataceae NA NA NA## growthformShrub:FamilyAtherospermataceae NA NA NA## growthformShrub/Tree:FamilyAtherospermataceae NA NA NA## growthformTree:FamilyAtherospermataceae NA NA NA## growthformHerb:FamilyBalsaminaceae NA NA NA## growthformHerb/Shrub:FamilyBalsaminaceae NA NA NA## growthformShrub:FamilyBalsaminaceae NA NA NA## growthformShrub/Tree:FamilyBalsaminaceae NA NA NA## growthformTree:FamilyBalsaminaceae NA NA NA## growthformHerb:FamilyBetulaceae NA NA NA## growthformHerb/Shrub:FamilyBetulaceae NA NA NA## growthformShrub:FamilyBetulaceae 2.035e+02 2.795e+02 0.728## growthformShrub/Tree:FamilyBetulaceae NA NA NA## growthformTree:FamilyBetulaceae NA NA NA## growthformHerb:FamilyBrassicaceae NA NA NA## growthformHerb/Shrub:FamilyBrassicaceae NA NA NA## growthformShrub:FamilyBrassicaceae NA NA NA## growthformShrub/Tree:FamilyBrassicaceae NA NA NA## growthformTree:FamilyBrassicaceae NA NA NA## growthformHerb:FamilyCactaceae NA NA NA## growthformHerb/Shrub:FamilyCactaceae NA NA NA## growthformShrub:FamilyCactaceae NA NA NA## growthformShrub/Tree:FamilyCactaceae NA NA NA## growthformTree:FamilyCactaceae NA NA NA## growthformHerb:FamilyCasuarinaceae NA NA NA## growthformHerb/Shrub:FamilyCasuarinaceae NA NA NA## growthformShrub:FamilyCasuarinaceae NA NA NA## growthformShrub/Tree:FamilyCasuarinaceae NA NA NA## growthformTree:FamilyCasuarinaceae NA NA NA## growthformHerb:FamilyChloranthaceae NA NA NA## growthformHerb/Shrub:FamilyChloranthaceae NA NA NA## growthformShrub:FamilyChloranthaceae NA NA NA## growthformShrub/Tree:FamilyChloranthaceae NA NA NA## growthformTree:FamilyChloranthaceae NA NA NA## growthformHerb:FamilyChrysobalanaceae NA NA NA## growthformHerb/Shrub:FamilyChrysobalanaceae NA NA NA## growthformShrub:FamilyChrysobalanaceae NA NA NA## growthformShrub/Tree:FamilyChrysobalanaceae NA NA NA## growthformTree:FamilyChrysobalanaceae NA NA NA## growthformHerb:FamilyCistaceae NA NA NA## growthformHerb/Shrub:FamilyCistaceae NA NA NA## growthformShrub:FamilyCistaceae NA NA NA## growthformShrub/Tree:FamilyCistaceae NA NA NA## growthformTree:FamilyCistaceae NA NA NA## growthformHerb:FamilyCornaceae NA NA NA## growthformHerb/Shrub:FamilyCornaceae NA NA NA## growthformShrub:FamilyCornaceae NA NA NA## growthformShrub/Tree:FamilyCornaceae NA NA NA## growthformTree:FamilyCornaceae NA NA NA## growthformHerb:FamilyCrassulaceae NA NA NA## growthformHerb/Shrub:FamilyCrassulaceae NA NA NA## growthformShrub:FamilyCrassulaceae NA NA NA## growthformShrub/Tree:FamilyCrassulaceae NA NA NA## growthformTree:FamilyCrassulaceae NA NA NA## growthformHerb:FamilyCunoniaceae NA NA NA## growthformHerb/Shrub:FamilyCunoniaceae NA NA NA## growthformShrub:FamilyCunoniaceae NA NA NA## growthformShrub/Tree:FamilyCunoniaceae 2.124e+02 2.694e+02 0.789## growthformTree:FamilyCunoniaceae NA NA NA## growthformHerb:FamilyCupressaceae NA NA NA## growthformHerb/Shrub:FamilyCupressaceae NA NA NA## growthformShrub:FamilyCupressaceae 2.214e+02 2.802e+02 0.790## growthformShrub/Tree:FamilyCupressaceae NA NA NA## growthformTree:FamilyCupressaceae NA NA NA## growthformHerb:FamilyCyperaceae NA NA NA## growthformHerb/Shrub:FamilyCyperaceae NA NA NA## growthformShrub:FamilyCyperaceae NA NA NA## growthformShrub/Tree:FamilyCyperaceae NA NA NA## growthformTree:FamilyCyperaceae NA NA NA## growthformHerb:FamilyDennstaedtiaceae NA NA NA## growthformHerb/Shrub:FamilyDennstaedtiaceae NA NA NA## growthformShrub:FamilyDennstaedtiaceae NA NA NA## growthformShrub/Tree:FamilyDennstaedtiaceae NA NA NA## growthformTree:FamilyDennstaedtiaceae NA NA NA## growthformHerb:FamilyDicksoniaceae NA NA NA## growthformHerb/Shrub:FamilyDicksoniaceae NA NA NA## growthformShrub:FamilyDicksoniaceae NA NA NA## growthformShrub/Tree:FamilyDicksoniaceae NA NA NA## growthformTree:FamilyDicksoniaceae NA NA NA## growthformHerb:FamilyDipterocarpaceae NA NA NA## growthformHerb/Shrub:FamilyDipterocarpaceae NA NA NA## growthformShrub:FamilyDipterocarpaceae NA NA NA## growthformShrub/Tree:FamilyDipterocarpaceae NA NA NA## growthformTree:FamilyDipterocarpaceae NA NA NA## growthformHerb:FamilyEbenaceae NA NA NA## growthformHerb/Shrub:FamilyEbenaceae NA NA NA## growthformShrub:FamilyEbenaceae NA NA NA## growthformShrub/Tree:FamilyEbenaceae NA NA NA## growthformTree:FamilyEbenaceae NA NA NA## growthformHerb:FamilyElaeocarpaceae NA NA NA## growthformHerb/Shrub:FamilyElaeocarpaceae NA NA NA## growthformShrub:FamilyElaeocarpaceae NA NA NA## growthformShrub/Tree:FamilyElaeocarpaceae NA NA NA## growthformTree:FamilyElaeocarpaceae NA NA NA## growthformHerb:FamilyEricaceae NA NA NA## growthformHerb/Shrub:FamilyEricaceae NA NA NA## growthformShrub:FamilyEricaceae -1.611e+00 4.441e+00 -0.363## growthformShrub/Tree:FamilyEricaceae NA NA NA## growthformTree:FamilyEricaceae NA NA NA## growthformHerb:FamilyEuphorbiaceae NA NA NA## growthformHerb/Shrub:FamilyEuphorbiaceae NA NA NA## growthformShrub:FamilyEuphorbiaceae 2.201e+02 2.766e+02 0.796## growthformShrub/Tree:FamilyEuphorbiaceae NA NA NA## growthformTree:FamilyEuphorbiaceae NA NA NA## growthformHerb:FamilyFabaceae - C NA NA NA## growthformHerb/Shrub:FamilyFabaceae - C NA NA NA## growthformShrub:FamilyFabaceae - C NA NA NA## growthformShrub/Tree:FamilyFabaceae - C NA NA NA## growthformTree:FamilyFabaceae - C NA NA NA## growthformHerb:FamilyFabaceae - M NA NA NA## growthformHerb/Shrub:FamilyFabaceae - M NA NA NA## growthformShrub:FamilyFabaceae - M NA NA NA## growthformShrub/Tree:FamilyFabaceae - M 2.338e+02 2.857e+02 0.818## growthformTree:FamilyFabaceae - M NA NA NA## growthformHerb:FamilyFabaceae - P 1.161e+02 1.357e+02 0.855## growthformHerb/Shrub:FamilyFabaceae - P NA NA NA## growthformShrub:FamilyFabaceae - P 2.457e+02 3.020e+02 0.814## growthformShrub/Tree:FamilyFabaceae - P NA NA NA## growthformTree:FamilyFabaceae - P NA NA NA## growthformHerb:FamilyFagaceae NA NA NA## growthformHerb/Shrub:FamilyFagaceae NA NA NA## growthformShrub:FamilyFagaceae 2.144e+02 2.735e+02 0.784## growthformShrub/Tree:FamilyFagaceae NA NA NA## growthformTree:FamilyFagaceae NA NA NA## growthformHerb:FamilyGentianaceae NA NA NA## growthformHerb/Shrub:FamilyGentianaceae NA NA NA## growthformShrub:FamilyGentianaceae NA NA NA## growthformShrub/Tree:FamilyGentianaceae NA NA NA## growthformTree:FamilyGentianaceae NA NA NA## growthformHerb:FamilyHeliconiaceae NA NA NA## growthformHerb/Shrub:FamilyHeliconiaceae NA NA NA## growthformShrub:FamilyHeliconiaceae NA NA NA## growthformShrub/Tree:FamilyHeliconiaceae NA NA NA## growthformTree:FamilyHeliconiaceae NA NA NA## growthformHerb:FamilyJuglandaceae NA NA NA## growthformHerb/Shrub:FamilyJuglandaceae NA NA NA## growthformShrub:FamilyJuglandaceae NA NA NA## growthformShrub/Tree:FamilyJuglandaceae NA NA NA## growthformTree:FamilyJuglandaceae NA NA NA## growthformHerb:FamilyJuncaginaceae NA NA NA## growthformHerb/Shrub:FamilyJuncaginaceae NA NA NA## growthformShrub:FamilyJuncaginaceae NA NA NA## growthformShrub/Tree:FamilyJuncaginaceae NA NA NA## growthformTree:FamilyJuncaginaceae NA NA NA## growthformHerb:FamilyLamiaceae NA NA NA## growthformHerb/Shrub:FamilyLamiaceae NA NA NA## growthformShrub:FamilyLamiaceae NA NA NA## growthformShrub/Tree:FamilyLamiaceae NA NA NA## growthformTree:FamilyLamiaceae NA NA NA## growthformHerb:FamilyLauraceae NA NA NA## growthformHerb/Shrub:FamilyLauraceae NA NA NA## growthformShrub:FamilyLauraceae NA NA NA## growthformShrub/Tree:FamilyLauraceae NA NA NA## growthformTree:FamilyLauraceae NA NA NA## growthformHerb:FamilyMaesaceae NA NA NA## growthformHerb/Shrub:FamilyMaesaceae NA NA NA## growthformShrub:FamilyMaesaceae NA NA NA## growthformShrub/Tree:FamilyMaesaceae NA NA NA## growthformTree:FamilyMaesaceae NA NA NA## growthformHerb:FamilyMalvaceae NA NA NA## growthformHerb/Shrub:FamilyMalvaceae NA NA NA## growthformShrub:FamilyMalvaceae NA NA NA## growthformShrub/Tree:FamilyMalvaceae NA NA NA## growthformTree:FamilyMalvaceae NA NA NA## growthformHerb:FamilyMelastomataceae NA NA NA## growthformHerb/Shrub:FamilyMelastomataceae NA NA NA## growthformShrub:FamilyMelastomataceae NA NA NA## growthformShrub/Tree:FamilyMelastomataceae NA NA NA## growthformTree:FamilyMelastomataceae NA NA NA## growthformHerb:FamilyMoraceae NA NA NA## growthformHerb/Shrub:FamilyMoraceae NA NA NA## growthformShrub:FamilyMoraceae NA NA NA## growthformShrub/Tree:FamilyMoraceae NA NA NA## growthformTree:FamilyMoraceae NA NA NA## growthformHerb:FamilyMyristicaceae NA NA NA## growthformHerb/Shrub:FamilyMyristicaceae NA NA NA## growthformShrub:FamilyMyristicaceae NA NA NA## growthformShrub/Tree:FamilyMyristicaceae NA NA NA## growthformTree:FamilyMyristicaceae NA NA NA## growthformHerb:FamilyMyrsinaceae NA NA NA## growthformHerb/Shrub:FamilyMyrsinaceae NA NA NA## growthformShrub:FamilyMyrsinaceae NA NA NA## growthformShrub/Tree:FamilyMyrsinaceae 2.252e+02 2.829e+02 0.796## growthformTree:FamilyMyrsinaceae NA NA NA## growthformHerb:FamilyMyrtaceae NA NA NA## growthformHerb/Shrub:FamilyMyrtaceae NA NA NA## growthformShrub:FamilyMyrtaceae 2.171e+02 2.710e+02 0.801## growthformShrub/Tree:FamilyMyrtaceae NA NA NA## growthformTree:FamilyMyrtaceae NA NA NA## growthformHerb:FamilyOchnaceae NA NA NA## growthformHerb/Shrub:FamilyOchnaceae NA NA NA## growthformShrub:FamilyOchnaceae NA NA NA## growthformShrub/Tree:FamilyOchnaceae NA NA NA## growthformTree:FamilyOchnaceae NA NA NA## growthformHerb:FamilyOnagraceae NA NA NA## growthformHerb/Shrub:FamilyOnagraceae NA NA NA## growthformShrub:FamilyOnagraceae NA NA NA## growthformShrub/Tree:FamilyOnagraceae NA NA NA## growthformTree:FamilyOnagraceae NA NA NA## growthformHerb:FamilyOrobanchaceae NA NA NA## growthformHerb/Shrub:FamilyOrobanchaceae NA NA NA## growthformShrub:FamilyOrobanchaceae NA NA NA## growthformShrub/Tree:FamilyOrobanchaceae NA NA NA## growthformTree:FamilyOrobanchaceae NA NA NA## growthformHerb:FamilyPhyllanthaceae NA NA NA## growthformHerb/Shrub:FamilyPhyllanthaceae NA NA NA## growthformShrub:FamilyPhyllanthaceae NA NA NA## growthformShrub/Tree:FamilyPhyllanthaceae NA NA NA## growthformTree:FamilyPhyllanthaceae NA NA NA## growthformHerb:FamilyPicrodendraceae NA NA NA## growthformHerb/Shrub:FamilyPicrodendraceae NA NA NA## growthformShrub:FamilyPicrodendraceae NA NA NA## growthformShrub/Tree:FamilyPicrodendraceae NA NA NA## growthformTree:FamilyPicrodendraceae NA NA NA## growthformHerb:FamilyPinaceae NA NA NA## growthformHerb/Shrub:FamilyPinaceae NA NA NA## growthformShrub:FamilyPinaceae NA NA NA## growthformShrub/Tree:FamilyPinaceae NA NA NA## growthformTree:FamilyPinaceae NA NA NA## growthformHerb:FamilyPoaceae -2.601e+02 3.246e+02 -0.801## growthformHerb/Shrub:FamilyPoaceae NA NA NA## growthformShrub:FamilyPoaceae NA NA NA## growthformShrub/Tree:FamilyPoaceae NA NA NA## growthformTree:FamilyPoaceae NA NA NA## growthformHerb:FamilyPolemoniaceae NA NA NA## growthformHerb/Shrub:FamilyPolemoniaceae NA NA NA## growthformShrub:FamilyPolemoniaceae NA NA NA## growthformShrub/Tree:FamilyPolemoniaceae NA NA NA## growthformTree:FamilyPolemoniaceae NA NA NA## growthformHerb:FamilyPolygonaceae NA NA NA## growthformHerb/Shrub:FamilyPolygonaceae NA NA NA## growthformShrub:FamilyPolygonaceae NA NA NA## growthformShrub/Tree:FamilyPolygonaceae NA NA NA## growthformTree:FamilyPolygonaceae NA NA NA## growthformHerb:FamilyProteaceae NA NA NA## growthformHerb/Shrub:FamilyProteaceae NA NA NA## growthformShrub:FamilyProteaceae 2.174e+02 2.714e+02 0.801## growthformShrub/Tree:FamilyProteaceae NA NA NA## growthformTree:FamilyProteaceae NA NA NA## growthformHerb:FamilyRanunculaceae NA NA NA## growthformHerb/Shrub:FamilyRanunculaceae NA NA NA## growthformShrub:FamilyRanunculaceae NA NA NA## growthformShrub/Tree:FamilyRanunculaceae NA NA NA## growthformTree:FamilyRanunculaceae NA NA NA## growthformHerb:FamilyRhamnaceae NA NA NA## growthformHerb/Shrub:FamilyRhamnaceae NA NA NA## growthformShrub:FamilyRhamnaceae NA NA NA## growthformShrub/Tree:FamilyRhamnaceae NA NA NA## growthformTree:FamilyRhamnaceae NA NA NA## growthformHerb:FamilyRosaceae 3.723e+02 4.458e+02 0.835## growthformHerb/Shrub:FamilyRosaceae NA NA NA## growthformShrub:FamilyRosaceae 2.126e+02 2.715e+02 0.783## growthformShrub/Tree:FamilyRosaceae NA NA NA## growthformTree:FamilyRosaceae NA NA NA## growthformHerb:FamilyRubiaceae NA NA NA## growthformHerb/Shrub:FamilyRubiaceae NA NA NA## growthformShrub:FamilyRubiaceae 6.243e+00 3.379e+00 1.848## growthformShrub/Tree:FamilyRubiaceae NA NA NA## growthformTree:FamilyRubiaceae NA NA NA## growthformHerb:FamilyRutaceae NA NA NA## growthformHerb/Shrub:FamilyRutaceae NA NA NA## growthformShrub:FamilyRutaceae NA NA NA## growthformShrub/Tree:FamilyRutaceae NA NA NA## growthformTree:FamilyRutaceae NA NA NA## growthformHerb:FamilySalicaceae NA NA NA## growthformHerb/Shrub:FamilySalicaceae NA NA NA## growthformShrub:FamilySalicaceae 9.252e+00 6.665e+00 1.388## growthformShrub/Tree:FamilySalicaceae NA NA NA## growthformTree:FamilySalicaceae NA NA NA## growthformHerb:FamilySapindaceae NA NA NA## growthformHerb/Shrub:FamilySapindaceae NA NA NA## growthformShrub:FamilySapindaceae NA NA NA## growthformShrub/Tree:FamilySapindaceae NA NA NA## growthformTree:FamilySapindaceae NA NA NA## growthformHerb:FamilySapotaceae NA NA NA## growthformHerb/Shrub:FamilySapotaceae NA NA NA## growthformShrub:FamilySapotaceae NA NA NA## growthformShrub/Tree:FamilySapotaceae NA NA NA## growthformTree:FamilySapotaceae NA NA NA## growthformHerb:FamilyScrophulariaceae NA NA NA## growthformHerb/Shrub:FamilyScrophulariaceae NA NA NA## growthformShrub:FamilyScrophulariaceae NA NA NA## growthformShrub/Tree:FamilyScrophulariaceae NA NA NA## growthformTree:FamilyScrophulariaceae NA NA NA## growthformHerb:FamilyThymelaeaceae NA NA NA## growthformHerb/Shrub:FamilyThymelaeaceae NA NA NA## growthformShrub:FamilyThymelaeaceae NA NA NA## growthformShrub/Tree:FamilyThymelaeaceae NA NA NA## growthformTree:FamilyThymelaeaceae NA NA NA## growthformHerb:FamilyUlmaceae NA NA NA## growthformHerb/Shrub:FamilyUlmaceae NA NA NA## growthformShrub:FamilyUlmaceae NA NA NA## growthformShrub/Tree:FamilyUlmaceae NA NA NA## growthformTree:FamilyUlmaceae NA NA NA## growthformHerb:FamilyUrticaceae NA NA NA## growthformHerb/Shrub:FamilyUrticaceae NA NA NA## growthformShrub:FamilyUrticaceae NA NA NA## growthformShrub/Tree:FamilyUrticaceae NA NA NA## growthformTree:FamilyUrticaceae NA NA NA## growthformHerb:FamilyViolaceae NA NA NA## growthformHerb/Shrub:FamilyViolaceae NA NA NA## growthformShrub:FamilyViolaceae NA NA NA## growthformShrub/Tree:FamilyViolaceae NA NA NA## growthformTree:FamilyViolaceae NA NA NA## growthformHerb:FamilyXanthorrhoeaceae NA NA NA## growthformHerb/Shrub:FamilyXanthorrhoeaceae NA NA NA## growthformShrub:FamilyXanthorrhoeaceae NA NA NA## growthformShrub/Tree:FamilyXanthorrhoeaceae NA NA NA## growthformTree:FamilyXanthorrhoeaceae NA NA NA## growthformHerb:FamilyZygophyllaceae NA NA NA## growthformHerb/Shrub:FamilyZygophyllaceae NA NA NA## growthformShrub:FamilyZygophyllaceae NA NA NA## growthformShrub/Tree:FamilyZygophyllaceae NA NA NA## growthformTree:FamilyZygophyllaceae NA NA NA## growthformHerb:lat -7.667e+00 9.125e+00 -0.840## growthformHerb/Shrub:lat NA NA NA## growthformShrub:lat 7.514e-02 3.299e-02 2.278## growthformShrub/Tree:lat -4.602e+00 4.806e+00 -0.957## growthformTree:lat NA NA NA## growthformHerb:long 3.209e-02 3.417e-02 0.939## growthformHerb/Shrub:long NA NA NA## growthformShrub:long -6.040e-03 1.358e-02 -0.445## growthformShrub/Tree:long NA NA NA## growthformTree:long NA NA NA## growthformHerb:NPP 4.933e-04 4.811e-04 1.025## growthformHerb/Shrub:NPP NA NA NA## growthformShrub:NPP 6.473e-04 3.846e-04 1.683## growthformShrub/Tree:NPP NA NA NA## growthformTree:NPP NA NA NA## FamilyAsteraceae:lat 9.729e+00 8.577e+00 1.134## FamilyAtherospermataceae:lat NA NA NA## FamilyBalsaminaceae:lat NA NA NA## FamilyBetulaceae:lat -5.249e-01 1.875e+00 -0.280## FamilyBrassicaceae:lat 6.681e+00 9.160e+00 0.729## FamilyCactaceae:lat -1.966e+00 8.672e-01 -2.267## FamilyCasuarinaceae:lat NA NA NA## FamilyChloranthaceae:lat NA NA NA## FamilyChrysobalanaceae:lat -7.988e-01 1.363e+00 -0.586## FamilyCistaceae:lat NA NA NA## FamilyCornaceae:lat NA NA NA## FamilyCrassulaceae:lat NA NA NA## FamilyCunoniaceae:lat NA NA NA## FamilyCupressaceae:lat NA NA NA## FamilyCyperaceae:lat NA NA NA## FamilyDennstaedtiaceae:lat NA NA NA## FamilyDicksoniaceae:lat NA NA NA## FamilyDipterocarpaceae:lat NA NA NA## FamilyEbenaceae:lat -2.703e-01 3.089e-01 -0.875## FamilyElaeocarpaceae:lat NA NA NA## FamilyEricaceae:lat -8.632e-01 6.646e-01 -1.299## FamilyEuphorbiaceae:lat -7.697e-01 7.758e-01 -0.992## FamilyFabaceae - C:lat -6.439e-01 7.319e-01 -0.880## FamilyFabaceae - M:lat NA NA NA## FamilyFabaceae - P:lat -2.849e+00 2.838e+00 -1.004## FamilyFagaceae:lat -6.391e-01 6.767e-01 -0.944## FamilyGentianaceae:lat 7.953e+00 9.600e+00 0.828## FamilyHeliconiaceae:lat NA NA NA## FamilyJuglandaceae:lat NA NA NA## FamilyJuncaginaceae:lat NA NA NA## FamilyLamiaceae:lat NA NA NA## FamilyLauraceae:lat NA NA NA## FamilyMaesaceae:lat NA NA NA## FamilyMalvaceae:lat -5.759e-01 7.352e-01 -0.783## FamilyMelastomataceae:lat NA NA NA## FamilyMoraceae:lat NA NA NA## FamilyMyristicaceae:lat NA NA NA## FamilyMyrsinaceae:lat NA NA NA## FamilyMyrtaceae:lat -2.630e-01 6.091e-01 -0.432## FamilyOchnaceae:lat NA NA NA## FamilyOnagraceae:lat NA NA NA## FamilyOrobanchaceae:lat 6.419e+00 8.683e+00 0.739## FamilyPhyllanthaceae:lat NA NA NA## FamilyPicrodendraceae:lat NA NA NA## FamilyPinaceae:lat -1.017e+00 6.698e-01 -1.518## FamilyPoaceae:lat 7.161e+00 8.523e+00 0.840## FamilyPolemoniaceae:lat 6.911e+00 8.461e+00 0.817## FamilyPolygonaceae:lat 6.776e+00 8.505e+00 0.797## FamilyProteaceae:lat -1.078e+00 6.906e-01 -1.560## FamilyRanunculaceae:lat NA NA NA## FamilyRhamnaceae:lat NA NA NA## FamilyRosaceae:lat -8.875e-01 5.851e-01 -1.517## FamilyRubiaceae:lat -1.008e+00 7.723e-01 -1.305## FamilyRutaceae:lat NA NA NA## FamilySalicaceae:lat -1.327e+00 1.062e+00 -1.249## FamilySapindaceae:lat -7.032e-01 7.657e-01 -0.918## FamilySapotaceae:lat NA NA NA## FamilyScrophulariaceae:lat NA NA NA## FamilyThymelaeaceae:lat NA NA NA## FamilyUlmaceae:lat -1.490e+00 1.311e+00 -1.137## FamilyUrticaceae:lat -1.170e+00 1.217e+00 -0.962## FamilyViolaceae:lat NA NA NA## FamilyXanthorrhoeaceae:lat NA NA NA## FamilyZygophyllaceae:lat NA NA NA## FamilyAsteraceae:long 3.953e-02 8.917e-03 4.433## FamilyAtherospermataceae:long NA NA NA## FamilyBalsaminaceae:long NA NA NA## FamilyBetulaceae:long 1.284e+00 1.382e+00 0.929## FamilyBrassicaceae:long NA NA NA## FamilyCactaceae:long 3.726e-02 2.427e-02 1.535## FamilyCasuarinaceae:long NA NA NA## FamilyChloranthaceae:long NA NA NA## FamilyChrysobalanaceae:long NA NA NA## FamilyCistaceae:long NA NA NA## FamilyCornaceae:long NA NA NA## FamilyCrassulaceae:long NA NA NA## FamilyCunoniaceae:long NA NA NA## FamilyCupressaceae:long NA NA NA## FamilyCyperaceae:long NA NA NA## FamilyDennstaedtiaceae:long NA NA NA## FamilyDicksoniaceae:long NA NA NA## FamilyDipterocarpaceae:long NA NA NA## FamilyEbenaceae:long NA NA NA## FamilyElaeocarpaceae:long NA NA NA## FamilyEricaceae:long 6.409e-02 2.972e-02 2.156## FamilyEuphorbiaceae:long 4.371e-02 4.554e-02 0.960## FamilyFabaceae - C:long NA NA NA## FamilyFabaceae - M:long NA NA NA## FamilyFabaceae - P:long NA NA NA## FamilyFagaceae:long NA NA NA## FamilyGentianaceae:long NA NA NA## FamilyHeliconiaceae:long NA NA NA## FamilyJuglandaceae:long NA NA NA## FamilyJuncaginaceae:long NA NA NA## FamilyLamiaceae:long NA NA NA## FamilyLauraceae:long NA NA NA## FamilyMaesaceae:long NA NA NA## FamilyMalvaceae:long 3.701e-02 4.705e-02 0.787## FamilyMelastomataceae:long NA NA NA## FamilyMoraceae:long NA NA NA## FamilyMyristicaceae:long NA NA NA## FamilyMyrsinaceae:long NA NA NA## FamilyMyrtaceae:long 5.316e-02 3.216e-02 1.653## FamilyOchnaceae:long NA NA NA## FamilyOnagraceae:long NA NA NA## FamilyOrobanchaceae:long NA NA NA## FamilyPhyllanthaceae:long NA NA NA## FamilyPicrodendraceae:long NA NA NA## FamilyPinaceae:long 1.006e-03 3.483e-02 0.029## FamilyPoaceae:long NA NA NA## FamilyPolemoniaceae:long NA NA NA## FamilyPolygonaceae:long NA NA NA## FamilyProteaceae:long 3.544e-02 2.338e-02 1.516## FamilyRanunculaceae:long NA NA NA## FamilyRhamnaceae:long NA NA NA## FamilyRosaceae:long 6.083e-02 5.503e-02 1.105## FamilyRubiaceae:long NA NA NA## FamilyRutaceae:long NA NA NA## FamilySalicaceae:long NA NA NA## FamilySapindaceae:long 4.512e-02 2.639e-02 1.710## FamilySapotaceae:long NA NA NA## FamilyScrophulariaceae:long NA NA NA## FamilyThymelaeaceae:long NA NA NA## FamilyUlmaceae:long NA NA NA## FamilyUrticaceae:long NA NA NA## FamilyViolaceae:long NA NA NA## FamilyXanthorrhoeaceae:long NA NA NA## FamilyZygophyllaceae:long NA NA NA## FamilyAsteraceae:alt 2.977e-02 1.249e-02 2.384## FamilyAtherospermataceae:alt NA NA NA## FamilyBalsaminaceae:alt NA NA NA## FamilyBetulaceae:alt NA NA NA## FamilyBrassicaceae:alt NA NA NA## FamilyCactaceae:alt -4.211e-03 9.104e-03 -0.463## FamilyCasuarinaceae:alt NA NA NA## FamilyChloranthaceae:alt NA NA NA## FamilyChrysobalanaceae:alt NA NA NA## FamilyCistaceae:alt NA NA NA## FamilyCornaceae:alt NA NA NA## FamilyCrassulaceae:alt NA NA NA## FamilyCunoniaceae:alt NA NA NA## FamilyCupressaceae:alt NA NA NA## FamilyCyperaceae:alt NA NA NA## FamilyDennstaedtiaceae:alt NA NA NA## FamilyDicksoniaceae:alt NA NA NA## FamilyDipterocarpaceae:alt NA NA NA## FamilyEbenaceae:alt NA NA NA## FamilyElaeocarpaceae:alt NA NA NA## FamilyEricaceae:alt 2.057e-03 9.530e-03 0.216## FamilyEuphorbiaceae:alt NA NA NA## FamilyFabaceae - C:alt NA NA NA## FamilyFabaceae - M:alt NA NA NA## FamilyFabaceae - P:alt NA NA NA## FamilyFagaceae:alt NA NA NA## FamilyGentianaceae:alt NA NA NA## FamilyHeliconiaceae:alt NA NA NA## FamilyJuglandaceae:alt NA NA NA## FamilyJuncaginaceae:alt NA NA NA## FamilyLamiaceae:alt NA NA NA## FamilyLauraceae:alt NA NA NA## FamilyMaesaceae:alt NA NA NA## FamilyMalvaceae:alt NA NA NA## FamilyMelastomataceae:alt NA NA NA## FamilyMoraceae:alt NA NA NA## FamilyMyristicaceae:alt NA NA NA## FamilyMyrsinaceae:alt NA NA NA## FamilyMyrtaceae:alt -2.001e-03 8.486e-03 -0.236## FamilyOchnaceae:alt NA NA NA## FamilyOnagraceae:alt NA NA NA## FamilyOrobanchaceae:alt NA NA NA## FamilyPhyllanthaceae:alt NA NA NA## FamilyPicrodendraceae:alt NA NA NA## FamilyPinaceae:alt -7.229e-03 8.920e-03 -0.810## FamilyPoaceae:alt -3.846e-03 8.857e-03 -0.434## FamilyPolemoniaceae:alt NA NA NA## FamilyPolygonaceae:alt NA NA NA## FamilyProteaceae:alt -8.882e-03 8.984e-03 -0.989## FamilyRanunculaceae:alt NA NA NA## FamilyRhamnaceae:alt NA NA NA## FamilyRosaceae:alt NA NA NA## FamilyRubiaceae:alt NA NA NA## FamilyRutaceae:alt NA NA NA## FamilySalicaceae:alt NA NA NA## FamilySapindaceae:alt NA NA NA## FamilySapotaceae:alt NA NA NA## FamilyScrophulariaceae:alt NA NA NA## FamilyThymelaeaceae:alt NA NA NA## FamilyUlmaceae:alt NA NA NA## FamilyUrticaceae:alt NA NA NA## FamilyViolaceae:alt NA NA NA## FamilyXanthorrhoeaceae:alt NA NA NA## FamilyZygophyllaceae:alt NA NA NA## FamilyAsteraceae:temp 9.741e+00 2.649e+00 3.678## FamilyAtherospermataceae:temp NA NA NA## FamilyBalsaminaceae:temp NA NA NA## FamilyBetulaceae:temp NA NA NA## FamilyBrassicaceae:temp NA NA NA## FamilyCactaceae:temp NA NA NA## FamilyCasuarinaceae:temp NA NA NA## FamilyChloranthaceae:temp NA NA NA## FamilyChrysobalanaceae:temp NA NA NA## FamilyCistaceae:temp NA NA NA## FamilyCornaceae:temp NA NA NA## FamilyCrassulaceae:temp NA NA NA## FamilyCunoniaceae:temp NA NA NA## FamilyCupressaceae:temp NA NA NA## FamilyCyperaceae:temp NA NA NA## FamilyDennstaedtiaceae:temp NA NA NA## FamilyDicksoniaceae:temp NA NA NA## FamilyDipterocarpaceae:temp NA NA NA## FamilyEbenaceae:temp NA NA NA## FamilyElaeocarpaceae:temp NA NA NA## FamilyEricaceae:temp NA NA NA## FamilyEuphorbiaceae:temp NA NA NA## FamilyFabaceae - C:temp NA NA NA## FamilyFabaceae - M:temp NA NA NA## FamilyFabaceae - P:temp NA NA NA## FamilyFagaceae:temp NA NA NA## FamilyGentianaceae:temp NA NA NA## FamilyHeliconiaceae:temp NA NA NA## FamilyJuglandaceae:temp NA NA NA## FamilyJuncaginaceae:temp NA NA NA## FamilyLamiaceae:temp NA NA NA## FamilyLauraceae:temp NA NA NA## FamilyMaesaceae:temp NA NA NA## FamilyMalvaceae:temp NA NA NA## FamilyMelastomataceae:temp NA NA NA## FamilyMoraceae:temp NA NA NA## FamilyMyristicaceae:temp NA NA NA## FamilyMyrsinaceae:temp NA NA NA## FamilyMyrtaceae:temp 1.113e+00 3.408e-01 3.266## FamilyOchnaceae:temp NA NA NA## FamilyOnagraceae:temp NA NA NA## FamilyOrobanchaceae:temp NA NA NA## FamilyPhyllanthaceae:temp NA NA NA## FamilyPicrodendraceae:temp NA NA NA## FamilyPinaceae:temp NA NA NA## FamilyPoaceae:temp 6.425e-01 2.770e-01 2.320## FamilyPolemoniaceae:temp NA NA NA## FamilyPolygonaceae:temp NA NA NA## FamilyProteaceae:temp NA NA NA## FamilyRanunculaceae:temp NA NA NA## FamilyRhamnaceae:temp NA NA NA## FamilyRosaceae:temp NA NA NA## FamilyRubiaceae:temp NA NA NA## FamilyRutaceae:temp NA NA NA## FamilySalicaceae:temp NA NA NA## FamilySapindaceae:temp NA NA NA## FamilySapotaceae:temp NA NA NA## FamilyScrophulariaceae:temp NA NA NA## FamilyThymelaeaceae:temp NA NA NA## FamilyUlmaceae:temp NA NA NA## FamilyUrticaceae:temp NA NA NA## FamilyViolaceae:temp NA NA NA## FamilyXanthorrhoeaceae:temp NA NA NA## FamilyZygophyllaceae:temp NA NA NA## lat:long -4.850e-04 3.239e-04 -1.497## lat:temp -5.288e-03 1.011e-03 -5.231## lat:NPP -4.384e-05 4.734e-05 -0.926## long:alt -1.635e-06 2.683e-06 -0.609## long:temp -1.650e-03 5.755e-04 -2.868## long:NPP 7.363e-06 2.523e-06 2.918## alt:temp -5.835e-05 1.708e-05 -3.416## temp:NPP -1.631e-04 8.021e-05 -2.034## Pr(>|t|) ## (Intercept) 0.471210 ## growthformHerb 0.401018 ## growthformHerb/Shrub 0.959364 ## growthformShrub 0.459650 ## growthformShrub/Tree 0.576973 ## growthformTree 0.209409 ## FamilyAsteraceae 0.024915 * ## FamilyAtherospermataceae 0.240297 ## FamilyBalsaminaceae 0.445806 ## FamilyBetulaceae 0.781378 ## FamilyBrassicaceae 0.520831 ## FamilyCactaceae 0.374789 ## FamilyCasuarinaceae 0.457542 ## FamilyChloranthaceae 0.451076 ## FamilyChrysobalanaceae 0.531209 ## FamilyCistaceae 0.457466 ## FamilyCornaceae 0.444251 ## FamilyCrassulaceae 0.461491 ## FamilyCunoniaceae 0.580889 ## FamilyCupressaceae 0.306038 ## FamilyCyperaceae 0.397873 ## FamilyDennstaedtiaceae NA ## FamilyDicksoniaceae 0.468095 ## FamilyDipterocarpaceae 0.398966 ## FamilyEbenaceae 0.397522 ## FamilyElaeocarpaceae 0.323838 ## FamilyEricaceae 0.451810 ## FamilyEuphorbiaceae 0.438290 ## FamilyFabaceae - C 0.453083 ## FamilyFabaceae - M 0.244394 ## FamilyFabaceae - P 0.340876 ## FamilyFagaceae 0.799425 ## FamilyGentianaceae 0.406314 ## FamilyHeliconiaceae 0.418080 ## FamilyJuglandaceae 0.307939 ## FamilyJuncaginaceae 0.445752 ## FamilyLamiaceae 0.474074 ## FamilyLauraceae 0.548932 ## FamilyMaesaceae 0.447295 ## FamilyMalvaceae 0.537119 ## FamilyMelastomataceae 0.447635 ## FamilyMoraceae 0.380649 ## FamilyMyristicaceae 0.349574 ## FamilyMyrsinaceae 0.393440 ## FamilyMyrtaceae 0.011832 * ## FamilyOchnaceae 0.448174 ## FamilyOnagraceae NA ## FamilyOrobanchaceae 0.553364 ## FamilyPhyllanthaceae 0.393311 ## FamilyPicrodendraceae 0.359305 ## FamilyPinaceae 0.087314 . ## FamilyPoaceae 0.529061 ## FamilyPolemoniaceae 0.415849 ## FamilyPolygonaceae 0.444282 ## FamilyProteaceae 0.106800 ## FamilyRanunculaceae 0.447850 ## FamilyRhamnaceae 0.466950 ## FamilyRosaceae 0.016301 * ## FamilyRubiaceae 0.441496 ## FamilyRutaceae 0.456598 ## FamilySalicaceae 0.433258 ## FamilySapindaceae 0.607885 ## FamilySapotaceae 0.276654 ## FamilyScrophulariaceae 0.448464 ## FamilyThymelaeaceae 0.336091 ## FamilyUlmaceae 0.231765 ## FamilyUrticaceae 0.338942 ## FamilyViolaceae 0.447326 ## FamilyXanthorrhoeaceae 0.455414 ## FamilyZygophyllaceae 0.467051 ## lat 0.325004 ## long 0.860913 ## alt 0.550965 ## temp 0.447922 ## NPP 0.298512 ## growthformHerb:FamilyAsteraceae 0.761650 ## growthformHerb/Shrub:FamilyAsteraceae NA ## growthformShrub:FamilyAsteraceae NA ## growthformShrub/Tree:FamilyAsteraceae NA ## growthformTree:FamilyAsteraceae NA ## growthformHerb:FamilyAtherospermataceae NA ## growthformHerb/Shrub:FamilyAtherospermataceae NA ## growthformShrub:FamilyAtherospermataceae NA ## growthformShrub/Tree:FamilyAtherospermataceae NA ## growthformTree:FamilyAtherospermataceae NA ## growthformHerb:FamilyBalsaminaceae NA ## growthformHerb/Shrub:FamilyBalsaminaceae NA ## growthformShrub:FamilyBalsaminaceae NA ## growthformShrub/Tree:FamilyBalsaminaceae NA ## growthformTree:FamilyBalsaminaceae NA ## growthformHerb:FamilyBetulaceae NA ## growthformHerb/Shrub:FamilyBetulaceae NA ## growthformShrub:FamilyBetulaceae 0.483172 ## growthformShrub/Tree:FamilyBetulaceae NA ## growthformTree:FamilyBetulaceae NA ## growthformHerb:FamilyBrassicaceae NA ## growthformHerb/Shrub:FamilyBrassicaceae NA ## growthformShrub:FamilyBrassicaceae NA ## growthformShrub/Tree:FamilyBrassicaceae NA ## growthformTree:FamilyBrassicaceae NA ## growthformHerb:FamilyCactaceae NA ## growthformHerb/Shrub:FamilyCactaceae NA ## growthformShrub:FamilyCactaceae NA ## growthformShrub/Tree:FamilyCactaceae NA ## growthformTree:FamilyCactaceae NA ## growthformHerb:FamilyCasuarinaceae NA ## growthformHerb/Shrub:FamilyCasuarinaceae NA ## growthformShrub:FamilyCasuarinaceae NA ## growthformShrub/Tree:FamilyCasuarinaceae NA ## growthformTree:FamilyCasuarinaceae NA ## growthformHerb:FamilyChloranthaceae NA ## growthformHerb/Shrub:FamilyChloranthaceae NA ## growthformShrub:FamilyChloranthaceae NA ## growthformShrub/Tree:FamilyChloranthaceae NA ## growthformTree:FamilyChloranthaceae NA ## growthformHerb:FamilyChrysobalanaceae NA ## growthformHerb/Shrub:FamilyChrysobalanaceae NA ## growthformShrub:FamilyChrysobalanaceae NA ## growthformShrub/Tree:FamilyChrysobalanaceae NA ## growthformTree:FamilyChrysobalanaceae NA ## growthformHerb:FamilyCistaceae NA ## growthformHerb/Shrub:FamilyCistaceae NA ## growthformShrub:FamilyCistaceae NA ## growthformShrub/Tree:FamilyCistaceae NA ## growthformTree:FamilyCistaceae NA ## growthformHerb:FamilyCornaceae NA ## growthformHerb/Shrub:FamilyCornaceae NA ## growthformShrub:FamilyCornaceae NA ## growthformShrub/Tree:FamilyCornaceae NA ## growthformTree:FamilyCornaceae NA ## growthformHerb:FamilyCrassulaceae NA ## growthformHerb/Shrub:FamilyCrassulaceae NA ## growthformShrub:FamilyCrassulaceae NA ## growthformShrub/Tree:FamilyCrassulaceae NA ## growthformTree:FamilyCrassulaceae NA ## growthformHerb:FamilyCunoniaceae NA ## growthformHerb/Shrub:FamilyCunoniaceae NA ## growthformShrub:FamilyCunoniaceae NA ## growthformShrub/Tree:FamilyCunoniaceae 0.448590 ## growthformTree:FamilyCunoniaceae NA ## growthformHerb:FamilyCupressaceae NA ## growthformHerb/Shrub:FamilyCupressaceae NA ## growthformShrub:FamilyCupressaceae 0.447817 ## growthformShrub/Tree:FamilyCupressaceae NA ## growthformTree:FamilyCupressaceae NA ## growthformHerb:FamilyCyperaceae NA ## growthformHerb/Shrub:FamilyCyperaceae NA ## growthformShrub:FamilyCyperaceae NA ## growthformShrub/Tree:FamilyCyperaceae NA ## growthformTree:FamilyCyperaceae NA ## growthformHerb:FamilyDennstaedtiaceae NA ## growthformHerb/Shrub:FamilyDennstaedtiaceae NA ## growthformShrub:FamilyDennstaedtiaceae NA ## growthformShrub/Tree:FamilyDennstaedtiaceae NA ## growthformTree:FamilyDennstaedtiaceae NA ## growthformHerb:FamilyDicksoniaceae NA ## growthformHerb/Shrub:FamilyDicksoniaceae NA ## growthformShrub:FamilyDicksoniaceae NA ## growthformShrub/Tree:FamilyDicksoniaceae NA ## growthformTree:FamilyDicksoniaceae NA ## growthformHerb:FamilyDipterocarpaceae NA ## growthformHerb/Shrub:FamilyDipterocarpaceae NA ## growthformShrub:FamilyDipterocarpaceae NA ## growthformShrub/Tree:FamilyDipterocarpaceae NA ## growthformTree:FamilyDipterocarpaceae NA ## growthformHerb:FamilyEbenaceae NA ## growthformHerb/Shrub:FamilyEbenaceae NA ## growthformShrub:FamilyEbenaceae NA ## growthformShrub/Tree:FamilyEbenaceae NA ## growthformTree:FamilyEbenaceae NA ## growthformHerb:FamilyElaeocarpaceae NA ## growthformHerb/Shrub:FamilyElaeocarpaceae NA ## growthformShrub:FamilyElaeocarpaceae NA ## growthformShrub/Tree:FamilyElaeocarpaceae NA ## growthformTree:FamilyElaeocarpaceae NA ## growthformHerb:FamilyEricaceae NA ## growthformHerb/Shrub:FamilyEricaceae NA ## growthformShrub:FamilyEricaceae 0.724294 ## growthformShrub/Tree:FamilyEricaceae NA ## growthformTree:FamilyEricaceae NA ## growthformHerb:FamilyEuphorbiaceae NA ## growthformHerb/Shrub:FamilyEuphorbiaceae NA ## growthformShrub:FamilyEuphorbiaceae 0.444658 ## growthformShrub/Tree:FamilyEuphorbiaceae NA ## growthformTree:FamilyEuphorbiaceae NA ## growthformHerb:FamilyFabaceae - C NA ## growthformHerb/Shrub:FamilyFabaceae - C NA ## growthformShrub:FamilyFabaceae - C NA ## growthformShrub/Tree:FamilyFabaceae - C NA ## growthformTree:FamilyFabaceae - C NA ## growthformHerb:FamilyFabaceae - M NA ## growthformHerb/Shrub:FamilyFabaceae - M NA ## growthformShrub:FamilyFabaceae - M NA ## growthformShrub/Tree:FamilyFabaceae - M 0.432247 ## growthformTree:FamilyFabaceae - M NA ## growthformHerb:FamilyFabaceae - P 0.412368 ## growthformHerb/Shrub:FamilyFabaceae - P NA ## growthformShrub:FamilyFabaceae - P 0.434788 ## growthformShrub/Tree:FamilyFabaceae - P NA ## growthformTree:FamilyFabaceae - P NA ## growthformHerb:FamilyFagaceae NA ## growthformHerb/Shrub:FamilyFagaceae NA ## growthformShrub:FamilyFagaceae 0.451214 ## growthformShrub/Tree:FamilyFagaceae NA ## growthformTree:FamilyFagaceae NA ## growthformHerb:FamilyGentianaceae NA ## growthformHerb/Shrub:FamilyGentianaceae NA ## growthformShrub:FamilyGentianaceae NA ## growthformShrub/Tree:FamilyGentianaceae NA ## growthformTree:FamilyGentianaceae NA ## growthformHerb:FamilyHeliconiaceae NA ## growthformHerb/Shrub:FamilyHeliconiaceae NA ## growthformShrub:FamilyHeliconiaceae NA ## growthformShrub/Tree:FamilyHeliconiaceae NA ## growthformTree:FamilyHeliconiaceae NA ## growthformHerb:FamilyJuglandaceae NA ## growthformHerb/Shrub:FamilyJuglandaceae NA ## growthformShrub:FamilyJuglandaceae NA ## growthformShrub/Tree:FamilyJuglandaceae NA ## growthformTree:FamilyJuglandaceae NA ## growthformHerb:FamilyJuncaginaceae NA ## growthformHerb/Shrub:FamilyJuncaginaceae NA ## growthformShrub:FamilyJuncaginaceae NA ## growthformShrub/Tree:FamilyJuncaginaceae NA ## growthformTree:FamilyJuncaginaceae NA ## growthformHerb:FamilyLamiaceae NA ## growthformHerb/Shrub:FamilyLamiaceae NA ## growthformShrub:FamilyLamiaceae NA ## growthformShrub/Tree:FamilyLamiaceae NA ## growthformTree:FamilyLamiaceae NA ## growthformHerb:FamilyLauraceae NA ## growthformHerb/Shrub:FamilyLauraceae NA ## growthformShrub:FamilyLauraceae NA ## growthformShrub/Tree:FamilyLauraceae NA ## growthformTree:FamilyLauraceae NA ## growthformHerb:FamilyMaesaceae NA ## growthformHerb/Shrub:FamilyMaesaceae NA ## growthformShrub:FamilyMaesaceae NA ## growthformShrub/Tree:FamilyMaesaceae NA ## growthformTree:FamilyMaesaceae NA ## growthformHerb:FamilyMalvaceae NA ## growthformHerb/Shrub:FamilyMalvaceae NA ## growthformShrub:FamilyMalvaceae NA ## growthformShrub/Tree:FamilyMalvaceae NA ## growthformTree:FamilyMalvaceae NA ## growthformHerb:FamilyMelastomataceae NA ## growthformHerb/Shrub:FamilyMelastomataceae NA ## growthformShrub:FamilyMelastomataceae NA ## growthformShrub/Tree:FamilyMelastomataceae NA ## growthformTree:FamilyMelastomataceae NA ## growthformHerb:FamilyMoraceae NA ## growthformHerb/Shrub:FamilyMoraceae NA ## growthformShrub:FamilyMoraceae NA ## growthformShrub/Tree:FamilyMoraceae NA ## growthformTree:FamilyMoraceae NA ## growthformHerb:FamilyMyristicaceae NA ## growthformHerb/Shrub:FamilyMyristicaceae NA ## growthformShrub:FamilyMyristicaceae NA ## growthformShrub/Tree:FamilyMyristicaceae NA ## growthformTree:FamilyMyristicaceae NA ## growthformHerb:FamilyMyrsinaceae NA ## growthformHerb/Shrub:FamilyMyrsinaceae NA ## growthformShrub:FamilyMyrsinaceae NA ## growthformShrub/Tree:FamilyMyrsinaceae 0.444600 ## growthformTree:FamilyMyrsinaceae NA ## growthformHerb:FamilyMyrtaceae NA ## growthformHerb/Shrub:FamilyMyrtaceae NA ## growthformShrub:FamilyMyrtaceae 0.441684 ## growthformShrub/Tree:FamilyMyrtaceae NA ## growthformTree:FamilyMyrtaceae NA ## growthformHerb:FamilyOchnaceae NA ## growthformHerb/Shrub:FamilyOchnaceae NA ## growthformShrub:FamilyOchnaceae NA ## growthformShrub/Tree:FamilyOchnaceae NA ## growthformTree:FamilyOchnaceae NA ## growthformHerb:FamilyOnagraceae NA ## growthformHerb/Shrub:FamilyOnagraceae NA ## growthformShrub:FamilyOnagraceae NA ## growthformShrub/Tree:FamilyOnagraceae NA ## growthformTree:FamilyOnagraceae NA ## growthformHerb:FamilyOrobanchaceae NA ## growthformHerb/Shrub:FamilyOrobanchaceae NA ## growthformShrub:FamilyOrobanchaceae NA ## growthformShrub/Tree:FamilyOrobanchaceae NA ## growthformTree:FamilyOrobanchaceae NA ## growthformHerb:FamilyPhyllanthaceae NA ## growthformHerb/Shrub:FamilyPhyllanthaceae NA ## growthformShrub:FamilyPhyllanthaceae NA ## growthformShrub/Tree:FamilyPhyllanthaceae NA ## growthformTree:FamilyPhyllanthaceae NA ## growthformHerb:FamilyPicrodendraceae NA ## growthformHerb/Shrub:FamilyPicrodendraceae NA ## growthformShrub:FamilyPicrodendraceae NA ## growthformShrub/Tree:FamilyPicrodendraceae NA ## growthformTree:FamilyPicrodendraceae NA ## growthformHerb:FamilyPinaceae NA ## growthformHerb/Shrub:FamilyPinaceae NA ## growthformShrub:FamilyPinaceae NA ## growthformShrub/Tree:FamilyPinaceae NA ## growthformTree:FamilyPinaceae NA ## growthformHerb:FamilyPoaceae 0.441587 ## growthformHerb/Shrub:FamilyPoaceae NA ## growthformShrub:FamilyPoaceae NA ## growthformShrub/Tree:FamilyPoaceae NA ## growthformTree:FamilyPoaceae NA ## growthformHerb:FamilyPolemoniaceae NA ## growthformHerb/Shrub:FamilyPolemoniaceae NA ## growthformShrub:FamilyPolemoniaceae NA ## growthformShrub/Tree:FamilyPolemoniaceae NA ## growthformTree:FamilyPolemoniaceae NA ## growthformHerb:FamilyPolygonaceae NA ## growthformHerb/Shrub:FamilyPolygonaceae NA ## growthformShrub:FamilyPolygonaceae NA ## growthformShrub/Tree:FamilyPolygonaceae NA ## growthformTree:FamilyPolygonaceae NA ## growthformHerb:FamilyProteaceae NA ## growthformHerb/Shrub:FamilyProteaceae NA ## growthformShrub:FamilyProteaceae 0.441738 ## growthformShrub/Tree:FamilyProteaceae NA ## growthformTree:FamilyProteaceae NA ## growthformHerb:FamilyRanunculaceae NA ## growthformHerb/Shrub:FamilyRanunculaceae NA ## growthformShrub:FamilyRanunculaceae NA ## growthformShrub/Tree:FamilyRanunculaceae NA ## growthformTree:FamilyRanunculaceae NA ## growthformHerb:FamilyRhamnaceae NA ## growthformHerb/Shrub:FamilyRhamnaceae NA ## growthformShrub:FamilyRhamnaceae NA ## growthformShrub/Tree:FamilyRhamnaceae NA ## growthformTree:FamilyRhamnaceae NA ## growthformHerb:FamilyRosaceae 0.423206 ## growthformHerb/Shrub:FamilyRosaceae NA ## growthformShrub:FamilyRosaceae 0.451569 ## growthformShrub/Tree:FamilyRosaceae NA ## growthformTree:FamilyRosaceae NA ## growthformHerb:FamilyRubiaceae NA ## growthformHerb/Shrub:FamilyRubiaceae NA ## growthformShrub:FamilyRubiaceae 0.094423 . ## growthformShrub/Tree:FamilyRubiaceae NA ## growthformTree:FamilyRubiaceae NA ## growthformHerb:FamilyRutaceae NA ## growthformHerb/Shrub:FamilyRutaceae NA ## growthformShrub:FamilyRutaceae NA ## growthformShrub/Tree:FamilyRutaceae NA ## growthformTree:FamilyRutaceae NA ## growthformHerb:FamilySalicaceae NA ## growthformHerb/Shrub:FamilySalicaceae NA ## growthformShrub:FamilySalicaceae 0.195221 ## growthformShrub/Tree:FamilySalicaceae NA ## growthformTree:FamilySalicaceae NA ## growthformHerb:FamilySapindaceae NA ## growthformHerb/Shrub:FamilySapindaceae NA ## growthformShrub:FamilySapindaceae NA ## growthformShrub/Tree:FamilySapindaceae NA ## growthformTree:FamilySapindaceae NA ## growthformHerb:FamilySapotaceae NA ## growthformHerb/Shrub:FamilySapotaceae NA ## growthformShrub:FamilySapotaceae NA ## growthformShrub/Tree:FamilySapotaceae NA ## growthformTree:FamilySapotaceae NA ## growthformHerb:FamilyScrophulariaceae NA ## growthformHerb/Shrub:FamilyScrophulariaceae NA ## growthformShrub:FamilyScrophulariaceae NA ## growthformShrub/Tree:FamilyScrophulariaceae NA ## growthformTree:FamilyScrophulariaceae NA ## growthformHerb:FamilyThymelaeaceae NA ## growthformHerb/Shrub:FamilyThymelaeaceae NA ## growthformShrub:FamilyThymelaeaceae NA ## growthformShrub/Tree:FamilyThymelaeaceae NA ## growthformTree:FamilyThymelaeaceae NA ## growthformHerb:FamilyUlmaceae NA ## growthformHerb/Shrub:FamilyUlmaceae NA ## growthformShrub:FamilyUlmaceae NA ## growthformShrub/Tree:FamilyUlmaceae NA ## growthformTree:FamilyUlmaceae NA ## growthformHerb:FamilyUrticaceae NA ## growthformHerb/Shrub:FamilyUrticaceae NA ## growthformShrub:FamilyUrticaceae NA ## growthformShrub/Tree:FamilyUrticaceae NA ## growthformTree:FamilyUrticaceae NA ## growthformHerb:FamilyViolaceae NA ## growthformHerb/Shrub:FamilyViolaceae NA ## growthformShrub:FamilyViolaceae NA ## growthformShrub/Tree:FamilyViolaceae NA ## growthformTree:FamilyViolaceae NA ## growthformHerb:FamilyXanthorrhoeaceae NA ## growthformHerb/Shrub:FamilyXanthorrhoeaceae NA ## growthformShrub:FamilyXanthorrhoeaceae NA ## growthformShrub/Tree:FamilyXanthorrhoeaceae NA ## growthformTree:FamilyXanthorrhoeaceae NA ## growthformHerb:FamilyZygophyllaceae NA ## growthformHerb/Shrub:FamilyZygophyllaceae NA ## growthformShrub:FamilyZygophyllaceae NA ## growthformShrub/Tree:FamilyZygophyllaceae NA ## growthformTree:FamilyZygophyllaceae NA ## growthformHerb:lat 0.420417 ## growthformHerb/Shrub:lat NA ## growthformShrub:lat 0.045980 * ## growthformShrub/Tree:lat 0.360912 ## growthformTree:lat NA ## growthformHerb:long 0.369731 ## growthformHerb/Shrub:long NA ## growthformShrub:long 0.665856 ## growthformShrub/Tree:long NA ## growthformTree:long NA ## growthformHerb:NPP 0.329320 ## growthformHerb/Shrub:NPP NA ## growthformShrub:NPP 0.123317 ## growthformShrub/Tree:NPP NA ## growthformTree:NPP NA ## FamilyAsteraceae:lat 0.283138 ## FamilyAtherospermataceae:lat NA ## FamilyBalsaminaceae:lat NA ## FamilyBetulaceae:lat 0.785252 ## FamilyBrassicaceae:lat 0.482497 ## FamilyCactaceae:lat 0.046821 * ## FamilyCasuarinaceae:lat NA ## FamilyChloranthaceae:lat NA ## FamilyChrysobalanaceae:lat 0.570866 ## FamilyCistaceae:lat NA ## FamilyCornaceae:lat NA ## FamilyCrassulaceae:lat NA ## FamilyCunoniaceae:lat NA ## FamilyCupressaceae:lat NA ## FamilyCyperaceae:lat NA ## FamilyDennstaedtiaceae:lat NA ## FamilyDicksoniaceae:lat NA ## FamilyDipterocarpaceae:lat NA ## FamilyEbenaceae:lat 0.402213 ## FamilyElaeocarpaceae:lat NA ## FamilyEricaceae:lat 0.223129 ## FamilyEuphorbiaceae:lat 0.344510 ## FamilyFabaceae - C:lat 0.399668 ## FamilyFabaceae - M:lat NA ## FamilyFabaceae - P:lat 0.339143 ## FamilyFagaceae:lat 0.367245 ## FamilyGentianaceae:lat 0.426756 ## FamilyHeliconiaceae:lat NA ## FamilyJuglandaceae:lat NA ## FamilyJuncaginaceae:lat NA ## FamilyLamiaceae:lat NA ## FamilyLauraceae:lat NA ## FamilyMaesaceae:lat NA ## FamilyMalvaceae:lat 0.451583 ## FamilyMelastomataceae:lat NA ## FamilyMoraceae:lat NA ## FamilyMyristicaceae:lat NA ## FamilyMyrsinaceae:lat NA ## FamilyMyrtaceae:lat 0.675074 ## FamilyOchnaceae:lat NA ## FamilyOnagraceae:lat NA ## FamilyOrobanchaceae:lat 0.476749 ## FamilyPhyllanthaceae:lat NA ## FamilyPicrodendraceae:lat NA ## FamilyPinaceae:lat 0.159861 ## FamilyPoaceae:lat 0.420438 ## FamilyPolemoniaceae:lat 0.433041 ## FamilyPolygonaceae:lat 0.444087 ## FamilyProteaceae:lat 0.149712 ## FamilyRanunculaceae:lat NA ## FamilyRhamnaceae:lat NA ## FamilyRosaceae:lat 0.160271 ## FamilyRubiaceae:lat 0.221123 ## FamilyRutaceae:lat NA ## FamilySalicaceae:lat 0.240215 ## FamilySapindaceae:lat 0.380059 ## FamilySapotaceae:lat NA ## FamilyScrophulariaceae:lat NA ## FamilyThymelaeaceae:lat NA ## FamilyUlmaceae:lat 0.282140 ## FamilyUrticaceae:lat 0.358817 ## FamilyViolaceae:lat NA ## FamilyXanthorrhoeaceae:lat NA ## FamilyZygophyllaceae:lat NA ## FamilyAsteraceae:long 0.001268 ** ## FamilyAtherospermataceae:long NA ## FamilyBalsaminaceae:long NA ## FamilyBetulaceae:long 0.374743 ## FamilyBrassicaceae:long NA ## FamilyCactaceae:long 0.155711 ## FamilyCasuarinaceae:long NA ## FamilyChloranthaceae:long NA ## FamilyChrysobalanaceae:long NA ## FamilyCistaceae:long NA ## FamilyCornaceae:long NA ## FamilyCrassulaceae:long NA ## FamilyCunoniaceae:long NA ## FamilyCupressaceae:long NA ## FamilyCyperaceae:long NA ## FamilyDennstaedtiaceae:long NA ## FamilyDicksoniaceae:long NA ## FamilyDipterocarpaceae:long NA ## FamilyEbenaceae:long NA ## FamilyElaeocarpaceae:long NA ## FamilyEricaceae:long 0.056466 . ## FamilyEuphorbiaceae:long 0.359718 ## FamilyFabaceae - C:long NA ## FamilyFabaceae - M:long NA ## FamilyFabaceae - P:long NA ## FamilyFagaceae:long NA ## FamilyGentianaceae:long NA ## FamilyHeliconiaceae:long NA ## FamilyJuglandaceae:long NA ## FamilyJuncaginaceae:long NA ## FamilyLamiaceae:long NA ## FamilyLauraceae:long NA ## FamilyMaesaceae:long NA ## FamilyMalvaceae:long 0.449768 ## FamilyMelastomataceae:long NA ## FamilyMoraceae:long NA ## FamilyMyristicaceae:long NA ## FamilyMyrsinaceae:long NA ## FamilyMyrtaceae:long 0.129339 ## FamilyOchnaceae:long NA ## FamilyOnagraceae:long NA ## FamilyOrobanchaceae:long NA ## FamilyPhyllanthaceae:long NA ## FamilyPicrodendraceae:long NA ## FamilyPinaceae:long 0.977523 ## FamilyPoaceae:long NA ## FamilyPolemoniaceae:long NA ## FamilyPolygonaceae:long NA ## FamilyProteaceae:long 0.160569 ## FamilyRanunculaceae:long NA ## FamilyRhamnaceae:long NA ## FamilyRosaceae:long 0.294900 ## FamilyRubiaceae:long NA ## FamilyRutaceae:long NA ## FamilySalicaceae:long NA ## FamilySapindaceae:long 0.118118 ## FamilySapotaceae:long NA ## FamilyScrophulariaceae:long NA ## FamilyThymelaeaceae:long NA ## FamilyUlmaceae:long NA ## FamilyUrticaceae:long NA ## FamilyViolaceae:long NA ## FamilyXanthorrhoeaceae:long NA ## FamilyZygophyllaceae:long NA ## FamilyAsteraceae:alt 0.038360 * ## FamilyAtherospermataceae:alt NA ## FamilyBalsaminaceae:alt NA ## FamilyBetulaceae:alt NA ## FamilyBrassicaceae:alt NA ## FamilyCactaceae:alt 0.653610 ## FamilyCasuarinaceae:alt NA ## FamilyChloranthaceae:alt NA ## FamilyChrysobalanaceae:alt NA ## FamilyCistaceae:alt NA ## FamilyCornaceae:alt NA ## FamilyCrassulaceae:alt NA ## FamilyCunoniaceae:alt NA ## FamilyCupressaceae:alt NA ## FamilyCyperaceae:alt NA ## FamilyDennstaedtiaceae:alt NA ## FamilyDicksoniaceae:alt NA ## FamilyDipterocarpaceae:alt NA ## FamilyEbenaceae:alt NA ## FamilyElaeocarpaceae:alt NA ## FamilyEricaceae:alt 0.833476 ## FamilyEuphorbiaceae:alt NA ## FamilyFabaceae - C:alt NA ## FamilyFabaceae - M:alt NA ## FamilyFabaceae - P:alt NA ## FamilyFagaceae:alt NA ## FamilyGentianaceae:alt NA ## FamilyHeliconiaceae:alt NA ## FamilyJuglandaceae:alt NA ## FamilyJuncaginaceae:alt NA ## FamilyLamiaceae:alt NA ## FamilyLauraceae:alt NA ## FamilyMaesaceae:alt NA ## FamilyMalvaceae:alt NA ## FamilyMelastomataceae:alt NA ## FamilyMoraceae:alt NA ## FamilyMyristicaceae:alt NA ## FamilyMyrsinaceae:alt NA ## FamilyMyrtaceae:alt 0.818358 ## FamilyOchnaceae:alt NA ## FamilyOnagraceae:alt NA ## FamilyOrobanchaceae:alt NA ## FamilyPhyllanthaceae:alt NA ## FamilyPicrodendraceae:alt NA ## FamilyPinaceae:alt 0.436576 ## FamilyPoaceae:alt 0.673346 ## FamilyPolemoniaceae:alt NA ## FamilyPolygonaceae:alt NA ## FamilyProteaceae:alt 0.346160 ## FamilyRanunculaceae:alt NA ## FamilyRhamnaceae:alt NA ## FamilyRosaceae:alt NA ## FamilyRubiaceae:alt NA ## FamilyRutaceae:alt NA ## FamilySalicaceae:alt NA ## FamilySapindaceae:alt NA ## FamilySapotaceae:alt NA ## FamilyScrophulariaceae:alt NA ## FamilyThymelaeaceae:alt NA ## FamilyUlmaceae:alt NA ## FamilyUrticaceae:alt NA ## FamilyViolaceae:alt NA ## FamilyXanthorrhoeaceae:alt NA ## FamilyZygophyllaceae:alt NA ## FamilyAsteraceae:temp 0.004264 ** ## FamilyAtherospermataceae:temp NA ## FamilyBalsaminaceae:temp NA ## FamilyBetulaceae:temp NA ## FamilyBrassicaceae:temp NA ## FamilyCactaceae:temp NA ## FamilyCasuarinaceae:temp NA ## FamilyChloranthaceae:temp NA ## FamilyChrysobalanaceae:temp NA ## FamilyCistaceae:temp NA ## FamilyCornaceae:temp NA ## FamilyCrassulaceae:temp NA ## FamilyCunoniaceae:temp NA ## FamilyCupressaceae:temp NA ## FamilyCyperaceae:temp NA ## FamilyDennstaedtiaceae:temp NA ## FamilyDicksoniaceae:temp NA ## FamilyDipterocarpaceae:temp NA ## FamilyEbenaceae:temp NA ## FamilyElaeocarpaceae:temp NA ## FamilyEricaceae:temp NA ## FamilyEuphorbiaceae:temp NA ## FamilyFabaceae - C:temp NA ## FamilyFabaceae - M:temp NA ## FamilyFabaceae - P:temp NA ## FamilyFagaceae:temp NA ## FamilyGentianaceae:temp NA ## FamilyHeliconiaceae:temp NA ## FamilyJuglandaceae:temp NA ## FamilyJuncaginaceae:temp NA ## FamilyLamiaceae:temp NA ## FamilyLauraceae:temp NA ## FamilyMaesaceae:temp NA ## FamilyMalvaceae:temp NA ## FamilyMelastomataceae:temp NA ## FamilyMoraceae:temp NA ## FamilyMyristicaceae:temp NA ## FamilyMyrsinaceae:temp NA ## FamilyMyrtaceae:temp 0.008481 ** ## FamilyOchnaceae:temp NA ## FamilyOnagraceae:temp NA ## FamilyOrobanchaceae:temp NA ## FamilyPhyllanthaceae:temp NA ## FamilyPicrodendraceae:temp NA ## FamilyPinaceae:temp NA ## FamilyPoaceae:temp 0.042787 * ## FamilyPolemoniaceae:temp NA ## FamilyPolygonaceae:temp NA ## FamilyProteaceae:temp NA ## FamilyRanunculaceae:temp NA ## FamilyRhamnaceae:temp NA ## FamilyRosaceae:temp NA ## FamilyRubiaceae:temp NA ## FamilyRutaceae:temp NA ## FamilySalicaceae:temp NA ## FamilySapindaceae:temp NA ## FamilySapotaceae:temp NA ## FamilyScrophulariaceae:temp NA ## FamilyThymelaeaceae:temp NA ## FamilyUlmaceae:temp NA ## FamilyUrticaceae:temp NA ## FamilyViolaceae:temp NA ## FamilyXanthorrhoeaceae:temp NA ## FamilyZygophyllaceae:temp NA ## lat:long 0.165174 ## lat:temp 0.000384 ***## lat:NPP 0.376311 ## long:alt 0.555973 ## long:temp 0.016734 * ## long:NPP 0.015356 * ## alt:temp 0.006587 ** ## temp:NPP 0.069341 . ## ---## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ## Residual standard error: 0.14 on 10 degrees of freedom## (15 observations deleted due to missingness)## Multiple R-squared: 0.9981, Adjusted R-squared: 0.9695 ## F-statistic: 34.87 on 152 and 10 DF, p-value: 5.06e-07
R2 = 0.99 … very high. In general, AIC should not overfit. In practice, however, it can overfit if there are unmodelled correlations in the data, or if you use variables that are (indirectly) identical to your response.
8.5.2 Exercise: Life Satisfaction #3
Excercise
Revisit our previous analysis on life satisfaction in the chapter on causal inference. Now, build a predictive model of life satistisfaction. If you want, you can also tune this model in a validation or cross-validation split.
