An Example of the Use of Geographically
Weighted Regression Using Data From Haiti
For the geographically weighted regression example here a simple bivariate model is specified. The two
variables used are:
1.
2.
Dependent variable - Weight = Residual between age-standardised weight curve and actial weight variable used: wtaNCHS / 1000.0
Predictor variable - Wealth = prosperity indicator - variable used: wealthscore * 1000.0
The weight variable is based on the National Centre for Health Statistics reference data for the age/weight
standardisation. The wealth variable is based on the DHS (Demographic and Health Surveys) prosperity
indicator.
Unlike a standard regression model (for example based on ordinary least squares) this approach allows the
regression coefficients to vary over geographical space. In this way it is possible to measure variability in the
relationship between the two variables across different geographical locations - and to visualise this change in
relationship as a map.
The following map shows the intercept as a geographically varying entity. This can be thought of as a base level
weight in a locality - if the wealth index were zero, this is the expected weight. Note that since weight is defined
here as relative to a standardised age/weight curve, values are negative - suggesting that with very little wealth,
children would be expecxted to be under weight for their age. This varies spatially, being particularly low around
Port au Prince and on the western coast.
In this map the regression coefficient linking the weight variable to the wealth indicator is shown. This can be
understood as a weight/wealth 'gradient' - for a unit increase in the wealth index, it provides the associated
change in weight. Since all values are positive, in this example it always indicates an increase in weight. One
notable pattern is a very high value of this coefficient around Port au Prince - suggesting that an increase in
wealth would have a more notable increase in body weight around the capital. Also a similar value is observed in
rural regions in the north. Also of note is the fact that the patterns do not always follow the administrative
boundaries - this suggests that there may be difficulties in using techniques such as multi level modelling, which
consider within country variability, but do so by organising the data into a prescribed set of areas, such as
adminstrative regions.