1. Stata in Space:
An example for the econometric analysis of spatially explicit raster data
--- Daniel Müller ---
Institute of Agricultural Economics
and Social Sciences
Humboldt University Berlin
Berlin -- August, 12th, 2003

2. Outline Introduction Spatial data analysis Data preparation
The empirical example
Econometric estimation
Export of results and geovisualization

3. Introduction
Socioeconomic data usually exist for (discrete) social entities, rarely explicitly linked to location (georeferenced)
‘Natural’ data: often continuous (rainfall, slope, elevation) and georeferenced
Integration of both data sources can provide additional insights
Allows to understand spatial patterns & processes
Knowing the where can help us infer the why
necessary?

4. Spatial data analysis
Spatial analysis is the analysis of data linked to location (spatial data)
Why analysis of spatial data ?
Variables of interest vary in space
Location matters!
Spatial analysis can provide important insights:
geographical targeting of investments
diffusion of technologies
causes and consequences of land-use change

5. What’s special about spatial data ?
Spatial data analysis
What’s special about spatial data ?
=> Location matters !!!
=> Tobler’s 1st law of geography (1979):
“Everything is related to everything else, but near things are more related than distant things.”
=> Spatial effects:
- spatial autocorrelation
- spatial heterogeneity
1. Location matters: absolute and relative; physical measurement often, economic data seldom an explicit spatial sample
2. Dependence = spatial structure

6. Peculiarities in space: Spatial effects
Spatial data analysis
Peculiarities in space: Spatial effects
1. Spatial autocorrelation
Coincidence of value similarity with locational similarity
Second dimension adds mathematical complexity (multiple directions)
2. Spatial heterogeneity
Each location is unique
Units of observations not homogeneous across space
Structural instability over space, e.g. heteroskedasticity
non-constant error variances due to, e.g. unequal population densities or varying technological development

7. Peculiarities in space: spatial effects [2]
Spatial data analysis
Peculiarities in space: spatial effects [2]
Spatial effects due to:
interactions among neighboring agents
data from different sources
different sample designs
varying aggregation rules
“Spatial relationships among observations can result in unreliable estimates and misguided statistical inference of the parameters.” (Anselin 1988).
=> Corrections necessary
non-constant error variances

8. Geographic Information Systems (GIS):
Spatial data analysis
Geographic Information Systems (GIS):
Compile, store, manipulate, analyse, visualize spatial data
Consist of hardware, software, data and procedures
Data models: vector & raster

9. Spatial data analysis Raster data model:
Arrangement of regularly shaped, contiguous cells
Continuous data layers; fit together edge-to-edge
Typically consist of square cells
Each cell represents a location in a raster GIS
Cells are arranged in layers
Values of a cell indicate characteristics of that location
Data is composed of many layers covering the same geographical area

10. Raster data model --- file structure:
Spatial data analysis
Raster data model --- file structure:
Header:
Contains spatial information! 1 2 3 4 5 6

11. Raster data model --- land use map:
Spatial data analysis
Raster data model --- land use map:

12. From data layers to resulting map
Spatial data analysis
From data layers to resulting map
data layers
overlays
analyses
output

13. Importing grids into Stata
Data preparation
Importing grids into Stata
ras2dta , files(filelist) [ idcell(varname) nodata(#) dropmiss xcoord(#) ycoord(#) genxcoor(varname) genycoor(varname) header(filename) saving(filelist) replace clear ]
infile-s grids (filelist) into Stata:
-generate-s IDcode for each cell (=observation)
reads the information from the header (if present)
“ sets missing values to a specified number
“ drop-s unnecessary empty cells
“ generate-s X and Y coordinates
“ save-s the header information in a file

14. Integration of data layers
Data preparation
Integration of data layers
Import of raster grids (-ras2dta-)
Combination of raster layers in Stata (-joinby-, -merge-) based on spatial identifier (ID-code of cells)
Socioeconomic (survey, census) data can be joined to grids based on, e.g., administrative boundaries

15. Corrections of spatial effects
Data preparation
Corrections of spatial effects
Spatial lag variables with index values for latitude (Y) and longitude (X)
Spatially lagged variables
Regular sampling from a grid
=> 1. can be done with -ras2dta-
=> 2. we ignore here
=> 3. is easy in Stata, e.g. with : -spatsam-
non-constant error variances

16. Data preparation
spatsam , gap(#) xcoord(varname) ycoord(varname) [ saving(filename) norestore noseed replace ]
Basically that‘s:
keep if (xcoord / gap) == int (xcoord / gap) & (ycoord / gap) == int (ycoord / gap)
Therefore, only every #-th observation in X and Y direction is kept in the sample.
non-constant error variances

17. Land use change in Vietnam
The empirical example
Land use change in Vietnam
Land use as an inherently spatial process
Returns to land use are (spatially) affected by:
market accessibility (von Thünen)
land rent (Ricardo)
Possible factors to consider:
soil quality, topography, climate, market locations, population density, technology
Limited dependent variable problem (-mlogit-)

18. The empirical example Data Satellite image interpretation:
- land cover => land use (change)
GIS, maps, point measurements:
- geophysical indicators => topography, soil, climate
Socioeconomic & policy variables:
- village survey, secondary statistics
=> technology, population, education, market access
Data integration based on spatial identifier and (approximated) village areas

19. Econometric estimation
Observations: 964,000 pixels (50 x 50 m)
Spatial sample: every 5. cell in X & Y direction
Estimation: 35,000 observations
=> Dependent: five land cover classes (1, 2, .., 5)
=> Independent: a) geophysical
b) socioeconomic
c) policy
d) spatial effects
non-constant error variances

20. Econometric estimation
1. Estimation of the influence of hypothesized determinants on land use.
2. What is the probability that a certain pixel falls into one of the five land-use categories?
=> -mlogit- (reduced form, clustered for villages)
=> -mlogtest, iia-, -fitstat- (Long & Freese)
Then we take the highest predicted probability as predicted land use.
observations within villages likely not independent -> SE underestimated -> robust SE clustered for villages

21. Outputting results from Stata
Export of results
Outputting results from Stata
dta2ras [varlist], xcoord(#) ycoord(#) cellsize(#) [ header(filename) idcell(varname) nodata(#) xllcorner(#) yllcorner(#) saving(varlist) replace ]
writes header in front of file with the information from xcoord(#) ycoord(#) cellsize(#) or header(); (optionally) nodata(#) xllcorner(#) yllcorner(#)
then the results can be mapped in the GIS

22. Geovisualization of results
Prediction map

23. Geovisualization of results
Maximum predicted probabilities

24. Thank you. Questions, comments and critique welcome
Thank you ! Questions, comments and critique welcome ! ____________________________ © Daniel Müller Institute of Agricultural Economics and Social Sciences Humboldt University Berlin Stata ados available for download at: