spMarkov: Spatial Markov Matrices

In spdyn: Exploratory Space-Time Data Analysis

Spatial Markov Matrices

Description

A function to calculate Spatial Markov Matrices as proposed by Rey (2001).

Usage

spMarkov(data, listw, stateVars, n.states,
stateNames, style = "quantile", breaks,
breaks.lag, pool = TRUE, std = TRUE)

spInitState(data,listw,stateVars,n.states,
stateNames=NULL,style='quantile',
breaks,breaks.lag,pool=TRUE,std=TRUE)

Arguments

data	A data frame arranged in such a way that there is one row per observation, and one column recording the state of each observation, with as many columns as time periods.
listw	A list of spatial weights, as given by the spdep package (see: mat2listw, nb2listw).
stateVars	The columns in the data frame which describe the temporal evolution of the variable of interest (one column per year).
n.states	The number of states to be assumed for the Markov process.
stateNames	The names to be given to the states of the Markov process.
style	The type of intervals or breaks to be computed. Currently, two options are allowed: 'quantile' breaks, or 'fixed' breaks. In the latter case, the breaks should be provided by the user.
breaks	If style='fixed', the breaks to be provided by the user to discretize the data.
breaks.lag	If style='fixed', user provided breaks for the spatial lag.
pool	If pool=TRUE, the data is pooled, so that a unique set of time-invariant breaks is determined. If pool=FALSE (the default), each variable is discretized using time-variant breaks (i.e. a different set of breaks for each time period). If pool=TRUE, it is recommended to set std=TRUE.
std	Should the data be standardized? If std=TRUE, the data is standardized by each period by the mean.

Details

A spatial Markov matrix is a slight modification of the traditional Markov matrix, that conditions a region's transition probabilities on the initial state of its spatial lag, namely, on the initial state of its neighbours.

Note that unlike the markov function, currently spMarkov does not admit already discretized data. This is because to determine the spatial lag, a continous variable is required.

The function 'spMarkov' returns a spatial markov matrix. The function 'spInitStates' retrieves the initial states of the spatial markov process.

Value

An object of class 'spMarkov' containing two arrays of dimensions k*k*k, where k=n.states.

t	An array of transition counts
p	An array of transition probabilities

Note that each array can be interpreted as an object containing k matrices of dimensions k*k.

Author(s)

Osmar Leandro Loaiza Quintero

References

Rey, Sergio (2001). 'Spatial Empirics for Economic Growth and Convergence', Geographical Analysis, Vol.33, No.3.

See Also

steadyState, mfpt, nb2listw, poly2nb

Examples

data(usinc)
stateVars<-names(usinc[,7:87])
stateNames<-c('Poor','Lower','Middle','Upper','Rich')

#Create a list of spatial weights
require(spdep)
lw<-nb2listw(poly2nb(usinc,queen=TRUE),style='W')

M<-spMarkov(usinc, lw, stateVars=stateVars,n.states=5,stateNames=stateNames,pool=TRUE,std=TRUE)
M$t;M$p

spdyn documentation built on Oct. 28, 2024, 3 p.m.