Description Usage Arguments Value Author(s) References See Also Examples
Set up powerlaw or nonparametric weights for the neighbourhood
component of hhh4
models as proposed by Meyer and Held (2014).
Without normalization, powerlaw weights are
w_ji = o_ji^d, where o_ji
is the order of neighbourhood between regions i and j,
see nbOrder
, and d is to be estimated.
In the nonparametric formulation, maxlag1
orderspecific
logweights are to be estimated (the firstorder weight is always
fixed to 1 for identifiability).
1 2 3 4 5 
maxlag 
a single integer specifying a limiting order of
neighbourhood. If spatial dependence is not to be truncated at some
high order, 
to0 

normalize 
logical indicating if the weights should be normalized such that the rows of the weight matrix sum to 1 (default). Note that normalization does not work with islands, i.e., regions without neighbours. 
log 
logical indicating if the decay parameter d should be estimated on the logscale to ensure positivity. 
initial 
initial value of the parameter vector. 
a list which can be passed as a specification of parametric
neighbourhood weights in the control$ne$weights
argument of
hhh4
.
Sebastian Meyer
Meyer, S. and Held, L. (2014): Powerlaw models for infectious disease spread. The Annals of Applied Statistics, 8 (3), 16121639. doi: 10.1214/14AOAS743
nbOrder
to determine the matrix of neighbourhood orders
from a binary adjacency matrix.
siaf.powerlaw
, and siaf.step
for modelling
distance decay as power law or step function in
twinstim
spacetime point process models.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  data("measlesWeserEms")
## data contains neighbourhood orders as required for parametric weights
neighbourhood(measlesWeserEms)[1:6,1:6]
max(neighbourhood(measlesWeserEms)) # max order is 5
## fit a powerlaw decay of spatial interaction
## in a hhh4 model with seasonality and random intercepts in the endemic part
measlesModel < list(
ar = list(f = ~ 1),
ne = list(f = ~ 1, weights = W_powerlaw(maxlag=5, normalize=TRUE, log=FALSE)),
end = list(f = addSeason2formula(~1 + ri(), S=1, period=52),
offset = population(measlesWeserEms)),
family = "NegBin1")
## fit the model
set.seed(1) # random intercepts are initialized randomly
measlesFit < hhh4(measlesWeserEms, measlesModel)
summary(measlesFit) # "neweights.d" is the decay parameter d
## plot the spatiotemporal weights o_ji^d / sum_k o_jk^d
## as a function of neighbourhood order
plot(measlesFit, type="neweights")
## Due to normalization, same distance does not necessarily mean same weight.
## There is no evidence for a power law of spatial interaction in this
## small observation region with only 17 districts.
## A possible simpler model is firstorder dependence, i.e., using
## 'weights = neighbourhood(measlesWeserEms) == 1' in the 'ne' component.

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