# Specify Network Smoother in Formulae

### Description

This function specifies all of the information required to smooth parameters over the segments of a stream network using an adjacency matrix, and a vector of flow weights.

### Usage

1 |

### Arguments

`adjacency` |
A sparse adjacency matrix of class " |

`weight` |
A character string indicating the column name of a numeric vector of flow weights contained in the |

`fixed.df` |
Positive scalar indicating a fixed number of degrees of freedom to allocate to the stream network component, overriding the criterion minimisation for this component. Under the default setting, NULL, the degrees of freedom are chosen automatically. |

### Value

A list combining the processed input components above. For internal use within `smnet`

.

`adjacency` |
Sparse adjacency matrix |

`weight` |
Numeric vector of flow weights |

`netID` |
Integer identifying network of interest |

### Author(s)

Alastair Rushworth

### See Also

smnet, get_adjacency, show_weights

### Examples

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# Set up an SSN object - this part taken
# from the SSN:::SimulateOnSSN help file
example_network<- createSSN(
n = 50,
obsDesign = binomialDesign(200),
predDesign = binomialDesign(50),
importToR = TRUE,
path = paste(tempdir(),"/example_network",sep = ""),
treeFunction = iterativeTreeLayout
)
# plot the simulated network structure with prediction locations
# plot(example_network, bty = "n", xlab = "x-coord", ylab = "y-coord")
## create distance matrices, including between predicted and observed
createDistMat(example_network, "preds", o.write=TRUE, amongpred = TRUE)
## extract the observed and predicted data frames
observed_data <- getSSNdata.frame(example_network, "Obs")
prediction_data <- getSSNdata.frame(example_network, "preds")
## associate continuous covariates with the observation locations
# data generated from a normal distribution
obs <- rnorm(200)
observed_data[,"X"] <- obs
observed_data[,"X2"] <- obs^2
## associate continuous covariates with the prediction locations
# data generated from a normal distribution
pred <- rnorm(50)
prediction_data[,"X"] <- pred
prediction_data[,"X2"] <- pred^2
## simulate some Gaussian data that follows a 'tail-up' spatial process
sims <- SimulateOnSSN(
ssn.object = example_network,
ObsSimDF = observed_data,
PredSimDF = prediction_data,
PredID = "preds",
formula = ~ 1 + X,
coefficients = c(1, 10),
CorModels = c("Exponential.tailup"),
use.nugget = TRUE,
CorParms = c(10, 5, 0.1),
addfunccol = "addfunccol")$ssn.object
## extract the observed and predicted data frames, now with simulated values
sim1DFpred <- getSSNdata.frame(sims, "preds")
sim1preds <- sim1DFpred[,"Sim_Values"]
sim1DFpred[,"Sim_Values"] <- NA
sims <- putSSNdata.frame(sim1DFpred, sims, "preds")
# create the adjacency matrix for use with smnet
adjacency <- get_adjacency(
paste(tempdir(), "/example_network", sep = ""),
net = 1
)
# not run - plot the adjacency matrix
# display(adjacency[[1]])
# sometimes it is useful to see which varaibles are valid network weights
# in the data contained within the SSN object
show_weights(sims, adjacency)
# fit a penalised spatial model to the stream network data
# Sim_Values are quadratic in the X covariate. To highlight
# the fitting of smooth terms, this is treated as non-linear
# and unknown using m().
mod_smn <- smnet(formula = Sim_Values ~ m(X) + m(X2) +
network(adjacency = adjacency, weight = "shreve"),
data.object = sims, netID = 1)
# not run - plot different summaries of the model
plot(mod_smn, type = "covariates")
plot(mod_smn, type = "segments", weight = 4, shadow = 2)
plot(mod_smn, type = "full", weight = 4, shadow = 2)
# obtain predictions at the prediction locations and plot
# against true values
preds <- predict(mod_smn, newdata = getSSNdata.frame(sims, "preds"))
plot(preds$predictions, sim1preds)
# obtain summary of the fitted model
summary(mod_smn)
``` |