Quantifies ecological memory with Random Forest.

Takes the output of prepareLaggedData to fit the following model with Random Forest:

\(p_{t} = p_{t-1} +...+ p_{t-n} + d_{t} + d_{t-1} +...+ d_{t-n} + r\)

where:

\(d\) is a driver (several drivers can be added).
\(t\) is the time of any given value of the response p.
\(t-1\) is the lag number 1 (in time units).
\(p_{t-1} +...+ p_{t-n}\) represents the endogenous component of ecological memory.
\(d_{t-1} +...+ d_{t-n}\) represents the exogenous component of ecological memory.
\(d_{t}\) represents the concurrent effect of the driver over the response.
\(r\) represents a column of random values, used to test the significance of the variable importance scores returned by Random Forest.

Usage

computeMemory(
  lagged.data = NULL,
  response = NULL,
  drivers = NULL,
  random.mode = "autocorrelated",
  repetitions = 10,
  subset.response = "none",
  num.threads = 2
)

Arguments

lagged.data: a lagged dataset resulting from prepareLaggedData. See palaeodataLagged as example. Default: NULL.
response: character string, name of the response variable. Not required if `lagged.data` was generated with [prepareLaggedData]. Default: NULL.
drivers: a character string or character vector with variables to be used as predictors in the model. Not required if `lagged.data` was generated with [prepareLaggedData]. Important: drivers names must not have the character "__" (double underscore). Default: NULL.
random.mode: either "none", "white.noise" or "autocorrelated". See details. Default: "autocorrelated".
repetitions: integer, number of random forest models to fit. Default: 10.
subset.response: character string with values "up", "down" or "none", triggers the subsetting of the input dataset. "up" only models memory on cases where the response's trend is positive, "down" selects cases with negative trends, and "none" selects all cases. Default: "none".
num.threads: integer, number of cores ranger can use for multithreading. Default: 2.

Value

A list with 5 slots:

response character, response variable name.
drivers character vector, driver variable names.
memory dataframe with six columns:
- median numeric, median importance across repetitions of the given variable according to Random Forest.
- sd numeric, standard deviation of the importance values of the given variable across repetitions.
- min and max numeric, percentiles 0.05 and 0.95 of importance values of the given variable across repetitions.
- variable character, names of the different variables used to model ecological memory.
- lag numeric, time lag values.
R2 vector, values of pseudo R-squared value obtained for the Random Forest model fitted on each repetition. Pseudo R-squared is the Pearson correlation between the observed and predicted data.
prediction dataframe, with the same columns as the dataframe in the slot memory, with the median and confidence intervals of the predictions of all random forest models fitted.

Details

This function uses the ranger package to fit Random Forest models. Please, check the help of the ranger function to better understand how Random Forest is parameterized in this package. This function fits the model explained above as many times as defined in the argument repetitions.

To test the statistical significance of the variable importance scores returned by random forest, on each repetition the model is fitted with a different r (random) term, unless random.mode = "none". If random.mode equals "autocorrelated", the random term will have a temporal autocorrelation, and if it equals "white.noise", it will be a pseudo-random sequence of numbers generated with rnorm, with no temporal autocorrelation. The importance of the random sequence in predicting the response is stored for each model run, and used as a benchmark to assess the importance of the other predictors.

Importance values of other predictors that are above the median of the importance of the random term should be interpreted as non-random, and therefore, significant.

References

Wright, M. N. & Ziegler, A. (2017). ranger: A fast implementation of random forests for high dimensional data in C++ and R. J Stat Softw 77:1-17. doi:10.18637/jss.v077.i01 .
Breiman, L. (2001). Random forests. Mach Learn, 45:5-32. doi:10.1023/A:1010933404324 .
Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning. Springer, New York. 2nd edition.

Author

Blas M. Benito <blasbenito@gmail.com>

Examples

# \donttest{
#loading data
data(palaeodataLagged)

# Simplified call - response and drivers auto-detected from attributes
memory.output <- computeMemory(
 lagged.data = palaeodataLagged,
 random.mode = "autocorrelated",
 repetitions = 10
)

str(memory.output)
#> List of 5
#>  $ response  : chr "pollen.pinus"
#>  $ drivers   : chr [1:2] "climate.temperatureAverage" "climate.rainfallAverage"
#>  $ memory    :'data.frame':	23 obs. of  6 variables:
#>   ..$ median  : num [1:23] 40 25 17.9 17.5 18.7 ...
#>   ..$ sd      : num [1:23] 0.941 0.498 0.631 1.063 1.615 ...
#>   ..$ min     : num [1:23] 39.6 24.4 17.2 16 16.5 ...
#>   ..$ max     : num [1:23] 42.1 25.8 18.9 19 21 ...
#>   ..$ variable: Factor w/ 4 levels "pollen.pinus",..: 1 1 1 1 1 2 2 2 2 2 ...
#>   ..$ lag     : num [1:23] 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 ...
#>  $ R2        : num [1:10] 0.991 0.991 0.991 0.991 0.991 ...
#>  $ prediction:'data.frame':	3988 obs. of  4 variables:
#>   ..$ median: num [1:3988] 3.66 5.02 7.83 11.15 13.86 ...
#>   ..$ sd    : num [1:3988] 0.212 0.144 0.177 0.234 0.239 ...
#>   ..$ min   : num [1:3988] 3.35 4.86 7.56 10.86 13.77 ...
#>   ..$ max   : num [1:3988] 3.95 5.25 8.02 11.51 14.38 ...
str(memory.output$memory)
#> 'data.frame':	23 obs. of  6 variables:
#>  $ median  : num  40 25 17.9 17.5 18.7 ...
#>  $ sd      : num  0.941 0.498 0.631 1.063 1.615 ...
#>  $ min     : num  39.6 24.4 17.2 16 16.5 ...
#>  $ max     : num  42.1 25.8 18.9 19 21 ...
#>  $ variable: Factor w/ 4 levels "pollen.pinus",..: 1 1 1 1 1 2 2 2 2 2 ...
#>  $ lag     : num  0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 ...

#plotting output
plotMemory(memory.output = memory.output)

# }