Title: Spatial Lag Model Trees
Date: 2019-04-06
Version: 1.0-1
Description: Model-based linear model trees adjusting for spatial correlation using a simultaneous autoregressive spatial lag, Wagner and Zeileis (2019) <doi:10.1111/geer.12146>.
Depends: R (≥ 3.3.0), partykit, spatialreg
Imports: Formula (≥ 1.2-1)
License: GPL-2 | GPL-3
NeedsCompilation: no
Packaged: 2019-04-06 20:03:40 UTC; zeileis
Author: Martin Wagner [aut], Achim Zeileis ORCID iD [aut, cre], Roger Bivand ORCID iD [ctb]
Maintainer: Achim Zeileis <Achim.Zeileis@R-project.org>
Repository: CRAN
Date/Publication: 2019-04-08 08:36:49 UTC

Determinants of Regional Economic Growth

Description

Growth regression data for NUTS2 regions in the European Union.

Usage

data("GrowthNUTS2")

Format

A data frame containing 255 observations on 58 variables.

ggdpcap

numeric. Average annual growth rate of real GDP per capita over the period 1995-2005.

accessair

numeric. Measure for potential accessability by air.

accessrail

numeric. Measure for potential accessability by rail.

accessroad

numeric. Measure for potential accessability by road.

airportdens

numeric. Airport density (number of airports per sqkm).

airports

factor. Number of airports.

arh0

numeric. Initial activity rate, highly educated.

arl0

numeric. Initial activity rate, low educated.

arm0

numeric. Initial activity rate, medium educated.

art0

numeric. Initial activity rate, total.

capital

factor. Does the region host country capital city?

connectair

numeric. Connectivity to comm. airports by car of the capital or centroid of region.

connectsea

numeric. Connectivity to comm. seaports by car of the capital or centroid of region.

distcap

numeric. Distance to capital city of respective country.

distde71

numeric. Distance to Frankfurt.

empdens0

numeric. Initial employment density.

ereh0

numeric. Initial employment rate, highly educated.

erel0

numeric. Initial employment rate, low educated.

erem0

numeric. Initial employment rate, medium educated.

eret0

numeric. Initial employment rate, total.

gdpcap0

numeric. Real GDP per capita in logs in 1995.

gpop

numeric. Growth rate of population.

hazard

numeric. Sum of all weighted hazard values.

hrstcore

numeric. Human resources in science and technology (core).

intf

numeric. Proportion of firms with own website regression.

outdens0

numeric. Initial output density.

popdens0

numeric. Initial population density.

raildens

numeric. Rail density (length of railroad network in km per sqkm).

regboarder

factor. Border region?

regcoast

factor. Coastal region?

regobj1

factor. Is the region within an Objective 1 region?

regpent27

factor. Pentagon EU 27 region? (London, Paris, Munich, Milan, Hamburg.)

roaddens

numeric. Road density (length of road network in km per sqkm).

seaports

factor. Does the region have a seaport?

settl

factor. Settlement structure.

shab0

numeric. Initial share of NACE A and B (Agriculture) in GVA.

shce0

numeric. Initial share of NACE C to E (Mining, Manufacturing and Energy) in GVA.

shgfcf

numeric. Share of gross fixed capital formation in gross value added.

shjk0

numeric. Initial share of NACE J to K (Business services) in GVA.

shsh

numeric. Share of highly educated in working age population.

shsl

numeric. Share of low educated in working age population.

shlll

numeric. Life long learning.

shsm

numeric. Share of medium educated in working age population.

telf

factor. A typology of estimated levels of business telecommunications access and uptake.

temp

numeric. Extreme temperatures.

urh0

numeric. Initial unemployment rate, highly educated.

url0

numeric. Initial unemployment rate, low educated.

urm0

numeric. Initial unemployment rate, medium educated.

urt0

numeric. Initial unemployment rate, total.

country

factor. Country within which the region is located.

cee

factor. Is the region within a Central and Eastearn European country?

piigs

factor. Is the region within a PIIGS country? (Portugal, Ireland, Italy, Greece, Spain.)

de

factor. Is the region within Germany?

es

factor. Is the region within Spain?

fr

factor. Is the region within France?

it

factor. Is the region within Italy?

pl

factor. Is the region within Poland?

uk

factor. Is the region within the United Kingdom?

References

Schneider U, Wagner M (2012). Catching Growth Determinants with the Adaptive Lasso. German Economic Review, 13(1), 71-85. doi: 10.1111/j.1468-0475.2011.00541.x

Examples

data("GrowthNUTS2")
summary(GrowthNUTS2)

Spatial Weights for European Union NUTS2 Regions

Description

Spatial weight matrices for NUTS2 regions in the European Union.

Usage

data("WeightsNUTS2")

Format

A list containing 40 listw weight matrices.

Source

Journal of Applied Econometrics Data Archive.

http://qed.econ.queensu.ca/jae/2013-v28.4/cuaresma-feldkircher/

References

Crespo Cuaresma J, Feldkircher M (2013). Spatial Filtering, Model Uncertainty and the Speed of Income Convergence in Europe. Journal of Applied Econometrics, 28(4), 720-741. doi: 10.1002/jae.2277

Spatial Lag Model Trees

Description

Model-based recursive partitioning based on linear regression adjusting for a (global) spatial simultaneous autoregressive lag.

Usage

lagsarlmtree(formula, data, listw = NULL, method = "eigen",
  zero.policy = NULL, interval = NULL, control = list(),
  rhowystart = NULL, abstol = 0.001, maxit = 100, 
  dfsplit = TRUE, verbose = FALSE, plot = FALSE, ...)

Arguments

formula

formula specifying the response variable and regressors and partitioning variables, respectively. For details see below.

data

data.frame to be used for estimating the model tree.

listw

a weights object for the spatial lag part of the model.

method

"eigen" (default) - the Jacobian is computed as the product of (1 - rho*eigenvalue) using eigenw, and "spam" or "Matrix_J" for strictly symmetric weights lists of styles "B" and "C", or made symmetric by similarity (Ord, 1975, Appendix C) if possible for styles "W" and "S", using code from the spam or Matrix packages to calculate the determinant; “Matrix” and “spam_update” provide updating Cholesky decomposition methods; "LU" provides an alternative sparse matrix decomposition approach. In addition, there are "Chebyshev" and Monte Carlo "MC" approximate log-determinant methods; the Smirnov/Anselin (2009) trace approximation is available as "moments". Three methods: "SE_classic", "SE_whichMin", and "SE_interp" are provided experimentally, the first to attempt to emulate the behaviour of Spatial Econometrics toolbox ML fitting functions. All use grids of log determinant values, and the latter two attempt to ameliorate some features of "SE_classic".

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE (default) assign NA - causing lagsarlm() to terminate with an error

interval

default is NULL, search interval for autoregressive parameter

control

list of extra control arguments - see lagsarlm

rhowystart

numeric. A vector of length nrow(data), to be used as an offset in estimation of the first tree. NULL by default, which results in an initialization with the root model (without partitioning).

abstol

numeric. The convergence criterion used for estimation of the model. When the difference in log-likelihoods of the model from two consecutive iterations is smaller than abstol, estimation of the model tree has converged.

maxit

numeric. The maximum number of iterations to be performed in estimation of the model tree.

dfsplit

logical or numeric. as.integer(dfsplit) is the degrees of freedom per selected split employed when extracting the log-likelihood.

verbose

Should the log-likelihood value of the estimated model be printed for every iteration of the estimation?

plot

Should the tree be plotted at every iteration of the estimation? Note that selecting this option slows down execution of the function.

...

Additional arguments to be passed to lmtree(). See mob_control documentation for details.

Details

Spatial lag trees learn a tree where each terminal node is associated with different regression coefficients while adjusting for a (global) spatial simultaneous autoregressive lag. This allows for detection of subgroup-specific coefficients with respect to selected covariates, while adjusting for spatial correlations in the data. The estimation algorithm iterates between (1) estimation of the tree given an offset of the spatial lag effect, and (2) estimation of the spatial lag model given the tree structure.

The code is still under development and might change in future versions.

Value

The function returns a list with the following objects:

formula

The formula as specified with the formula argument.

call

the matched call.

tree

The final lmtree.

lagsarlm

The final lagsarlm model.

data

The dataset specified with the data argument including added auxiliary variables .rhowy and .tree from the last iteration.

nobs

Number of observations.

loglik

The log-likelihood value of the last iteration.

df

Degrees of freedom.

dfsplit

degrees of freedom per selected split as specified with the dfsplit argument.

iterations

The number of iterations used to estimate the lagsarlmtree.

maxit

The maximum number of iterations specified with the maxit argument.

rhowystart

Offset in estimation of the first tree as specified in the rhowystart argument.

abstol

The prespecified value for the change in log-likelihood to evaluate convergence, as specified with the abstol argument.

listw

The listw object used.

mob.control

A list containing control parameters passed to lmtree(), as specified with ....

References

Wagner M, Zeileis A (2019). Heterogeneity and Spatial Dependence of Regional Growth in the EU: A Recursive Partitioning Approach. German Economic Review, 20(1), 67–82. doi: 10.1111/geer.12146 https://eeecon.uibk.ac.at/~zeileis/papers/Wagner+Zeileis-2019.pdf

See Also

lm, lagsarlm, lmtree

Examples

## data and spatial weights
data("GrowthNUTS2", package = "lagsarlmtree")
data("WeightsNUTS2", package = "lagsarlmtree")

## spatial lag model tree
system.time(tr <- lagsarlmtree(ggdpcap ~ gdpcap0 + shgfcf + shsh + shsm |
    gdpcap0 + accessrail + accessroad + capital + regboarder + regcoast + regobj1 + cee + piigs,
  data = GrowthNUTS2, listw = WeightsNUTS2$invw,
  minsize = 12, alpha = 0.05))
print(tr)
plot(tr, tp_args = list(which = 1))

## query coefficients
coef(tr, model = "tree")
coef(tr, model = "rho")
coef(tr, model = "all")
system.time({
ev <- eigenw(WeightsNUTS2$invw)
tr1 <- lagsarlmtree(ggdpcap ~ gdpcap0 + shgfcf + shsh + shsm |
    gdpcap0 + accessrail + accessroad + capital + regboarder + regcoast + regobj1 + cee + piigs,
  data = GrowthNUTS2, listw = WeightsNUTS2$invw, method = "eigen",
  control = list(pre_eig = ev), minsize = 12, alpha = 0.05)
})
coef(tr1, model = "rho")