sjSDM (version 1.0.6)

DNN: Non-linear model (deep neural network) of environmental responses

Description

specify the model to be fitted

Usage

DNN(
  data = NULL,
  formula = NULL,
  hidden = c(10L, 10L, 10L),
  activation = "selu",
  bias = TRUE,
  lambda = 0,
  alpha = 0.5,
  dropout = 0
)

Value

An S3 class of type 'DNN' including the following components:

formula

Model matrix formula

X

Model matrix of covariates

data

Raw data

l1_coef

L1 regularization strength, can be -99 if lambda = 0.0

l2_coef

L2 regularization strength, can be -99 if lambda = 0.0

hidden

Integer vector of hidden neurons in the deep neural network. Length of vector corresponds to the number of hidden layers.

activation

Character vector of activation functions.

bias

Logical vector whether to use bias or not in each hidden layer.

Implemented S3 methods include print.DNN

Arguments

data

matrix of environmental predictors

formula

formula object for predictors

hidden

hidden units in layers, length of hidden corresponds to number of layers

activation

activation functions, can be of length one, or a vector of activation functions for each layer. Currently supported: tanh, relu, leakyrelu, selu, or sigmoid

bias

whether use biases in the layers, can be of length one, or a vector (number of hidden layers including (last layer) but not first layer (intercept in first layer is specified by formula)) of logicals for each layer.

lambda

lambda penalty, strength of regularization: \(\lambda * (lasso + ridge)\)

alpha

weighting between lasso and ridge: \((1 - \alpha) * |weights| + \alpha ||weights||^2\)

dropout

probability of dropout rate

See Also

linear, sjSDM

Examples

if (FALSE) {
  
# Basic workflow:
## simulate community:
com = simulate_SDM(env = 3L, species = 7L, sites = 100L)

## fit model:
model = sjSDM(Y = com$response,env = com$env_weights, iter = 50L,
              verbose = FALSE) 
# increase iter for your own data 

# Default distribution is binomial("probit"). Alternatively, you can use
# binomial(logit), poisson("log"), "nbinom" (with log, still somewhat 
# experimental) and gaussian("identity")

coef(model)
summary(model)
getCov(model)

## plot results
species=c("sp1","sp2","sp3","sp4","sp5","sp6","sp7")
group=c("mammal","bird","fish","fish","mammal","amphibian","amphibian")
group = data.frame(species=species,group=group)
plot(model,group=group)

## calculate post-hoc p-values:
p = getSe(model)
summary(p)

## or turn on the option in the sjSDM function:
model = sjSDM(Y = com$response, env = com$env_weights, se = TRUE, 
              family = binomial("probit"), 
              iter = 2L,
              verbose = FALSE)
summary(model)

## fit model with interactions:
model = sjSDM(Y = com$response,
              env = linear(data = com$env_weights, formula = ~X1:X2 + X3), 
              se = TRUE,
              iter = 2L,
              verbose = FALSE) # increase iter for your own data 
summary(model)

## without intercept:
model = update(model, env_formula = ~0+X1:X2 + X3,
               verbose = FALSE)

summary(model)

## predict with model:
preds = predict(model, newdata = com$env_weights)

## calculate R-squared:
R2 = Rsquared(model)
print(R2)

# With spatial terms:
## linear spatial model
XY = matrix(rnorm(200), 100, 2)
model = sjSDM(Y = com$response, env = linear(com$env_weights), 
              spatial = linear(XY, ~0+X1:X2),
              iter = 50L,
              verbose = FALSE) # increase iter for your own data 
summary(model)
predict(model, newdata = com$env_weights, SP = XY)
R2 = Rsquared(model)
print(R2)

## Using spatial eigenvectors as predictors to account 
## for spatial autocorrelation is a common approach:
SPV = generateSpatialEV(XY)
model = sjSDM(Y = com$response, env = linear(com$env_weights), 
              spatial = linear(SPV, ~0+., lambda = 0.1),
              iter = 50L,
              verbose = FALSE) # increase iter for your own data 
summary(model)
predict(model, newdata = com$env_weights, SP = SPV)

## Visualize internal meta-community structure
an = anova(model,
           verbose = FALSE)

internal = internalStructure(an)
plot(internal)

## Visualize community assemlby effects 

plotAssemblyEffects(internal)

### see ?anova.sjSDM for mroe details


## non-linear(deep neural network) model
model = sjSDM(Y = com$response, env = linear(com$env_weights), 
              spatial = DNN(SPV,hidden = c(5L, 5L), ~0+.),
              iter = 2L,# increase iter for your own data 
              verbose = FALSE) 
summary(model)
predict(model, newdata = com$env_weights, SP = SPV)


# Regularization
## lambda is the regularization strength
## alpha weights the lasso or ridge penalty:
## - alpha = 0 --> pure lasso
## - alpha = 1.0 --> pure ridge
model = sjSDM(Y = com$response, 
              # mix of lasso and ridge
              env = linear(com$env_weights, lambda = 0.01, alpha = 0.5), 
              # we can do the same for the species-species associations
              biotic = bioticStruct(lambda = 0.01, alpha = 0.5),
              iter = 2L,# increase iter for your own data 
              verbose = FALSE) 
summary(model)
coef(model)
getCov(model)



# Anova 
com = simulate_SDM(env = 3L, species = 15L, sites = 200L, correlation = TRUE)

XY = matrix(rnorm(400), 200, 2)
SPV = generateSpatialEV(XY)
model = sjSDM(Y = com$response, env = linear(com$env_weights), 
              spatial = linear(SPV, ~0+.), 
              verbose = FALSE,
              iter = 50L) # increase iter for your own data 
result = anova(model, verbose = FALSE)
print(result)
plot(result)

## visualize internal meta-community structure
internal = internalStructure(an)
plot(internal)



# Deep neural networks
## we can fit also a deep neural network instead of a linear model:
model = sjSDM(Y = com$response,
              env = DNN(com$env_weights, hidden = c(10L, 10L, 10L)),
              verbose = FALSE,
              iter = 2L) # increase iter for your own data 
summary(model)
getCov(model)
pred = predict(model, newdata = com$env_weights)

## extract weights
weights = getWeights(model)

## we can also assign weights:
setWeights(model, weights)

## with regularization:
model = sjSDM(Y = com$response, 
              # mix of lasso and ridge
              env = DNN(com$env_weights, lambda = 0.01, alpha = 0.5), 
              # we can do the same for the species-species associations
              biotic = bioticStruct(lambda = 0.01, alpha = 0.5),
              verbose = FALSE,
              iter = 2L) # increase iter for your own data 
getCov(model)
getWeights(model)
}