lagsarlmtree: Spatial Lag Model Trees

In lagsarlmtree: 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")

Example output

Loading required package: partykit
Loading required package: grid
Loading required package: libcoin
Loading required package: mvtnorm
Loading required package: spatialreg
Loading required package: spData
To access larger datasets in this package, install the spDataLarge
package with: `install.packages('spDataLarge',
repos='https://nowosad.github.io/drat/', type='source')`
Loading required package: Matrix
Registered S3 methods overwritten by 'spatialreg':
  method                   from 
  residuals.stsls          spdep
  deviance.stsls           spdep
  coef.stsls               spdep
  print.stsls              spdep
  summary.stsls            spdep
  print.summary.stsls      spdep
  residuals.gmsar          spdep
  deviance.gmsar           spdep
  coef.gmsar               spdep
  fitted.gmsar             spdep
  print.gmsar              spdep
  summary.gmsar            spdep
  print.summary.gmsar      spdep
  print.lagmess            spdep
  summary.lagmess          spdep
  print.summary.lagmess    spdep
  residuals.lagmess        spdep
  deviance.lagmess         spdep
  coef.lagmess             spdep
  fitted.lagmess           spdep
  logLik.lagmess           spdep
  fitted.SFResult          spdep
  print.SFResult           spdep
  fitted.ME_res            spdep
  print.ME_res             spdep
  print.lagImpact          spdep
  plot.lagImpact           spdep
  summary.lagImpact        spdep
  HPDinterval.lagImpact    spdep
  print.summary.lagImpact  spdep
  print.sarlm              spdep
  summary.sarlm            spdep
  residuals.sarlm          spdep
  deviance.sarlm           spdep
  coef.sarlm               spdep
  vcov.sarlm               spdep
  fitted.sarlm             spdep
  logLik.sarlm             spdep
  anova.sarlm              spdep
  predict.sarlm            spdep
  print.summary.sarlm      spdep
  print.sarlm.pred         spdep
  as.data.frame.sarlm.pred spdep
  residuals.spautolm       spdep
  deviance.spautolm        spdep
  coef.spautolm            spdep
  fitted.spautolm          spdep
  print.spautolm           spdep
  summary.spautolm         spdep
  logLik.spautolm          spdep
  print.summary.spautolm   spdep
  print.WXImpact           spdep
  summary.WXImpact         spdep
  print.summary.WXImpact   spdep
  predict.SLX              spdep
   user  system elapsed 
  1.868   0.012   1.926 
Spatial lag model tree

Model formula:
ggdpcap ~ gdpcap0 + shgfcf + shsh + shsm | gdpcap0 + accessrail + 
    accessroad + capital + regboarder + regcoast + regobj1 + 
    cee + piigs

Fitted party:
[1] root
|   [2] capital in no
|   |   [3] piigs in no: n = 176
|   |        (Intercept)      gdpcap0       shgfcf         shsh         shsm 
|   |        0.110545460 -0.011707661  0.002077862  0.021946900  0.001792086 
|   |   [4] piigs in yes
|   |   |   [5] regcoast in no: n = 13
|   |   |       (Intercept)     gdpcap0      shgfcf        shsh        shsm 
|   |   |        0.16061625 -0.01589749 -0.04688569  0.07885805 -0.02344598 
|   |   |   [6] regcoast in yes: n = 39
|   |   |        (Intercept)      gdpcap0       shgfcf         shsh         shsm 
|   |   |        0.073481036 -0.011064754  0.091556636  0.116680209  0.009419106 
|   [7] capital in yes: n = 27
|        (Intercept)      gdpcap0       shgfcf         shsh         shsm 
|        0.205608579 -0.022342977 -0.007502503  0.041083421  0.052843323 

Number of inner nodes:    3
Number of terminal nodes: 4
Number of parameters per node: 5
Objective function (residual sum of squares): 0.01553945

Rho (from lagsarlm model):
      rho 
0.8373894 
  (Intercept)     gdpcap0       shgfcf       shsh         shsm
3  0.11054546 -0.01170766  0.002077862 0.02194690  0.001792086
5  0.16061625 -0.01589749 -0.046885688 0.07885805 -0.023445980
6  0.07348104 -0.01106475  0.091556636 0.11668021  0.009419106
7  0.20560858 -0.02234298 -0.007502503 0.04108342  0.052843323
      rho 
0.8373894 
           rho         .tree3         .tree5         .tree6         .tree7 
   0.837389353    0.110545460    0.160616252    0.073481036    0.205608579 
.tree3:gdpcap0 .tree5:gdpcap0 .tree6:gdpcap0 .tree7:gdpcap0  .tree3:shgfcf 
  -0.011707661   -0.015897486   -0.011064754   -0.022342977    0.002077862 
 .tree5:shgfcf  .tree6:shgfcf  .tree7:shgfcf    .tree3:shsh    .tree5:shsh 
  -0.046885688    0.091556636   -0.007502503    0.021946900    0.078858046 
   .tree6:shsh    .tree7:shsh    .tree3:shsm    .tree5:shsm    .tree6:shsm 
   0.116680209    0.041083421    0.001792086   -0.023445980    0.009419106 
   .tree7:shsm 
   0.052843323 
   user  system elapsed 
  1.829   0.020   1.902 
      rho 
0.8373894 

lagsarlmtree documentation built on May 1, 2019, 7:05 p.m.