Lab 2: Introduction to Geographically Weighted Regression

In this lab, I used the statistical methods of ordinary least squares regression (OLS) and geographically weighted regression (GWR) to explore at the relationship between kindergarten language test scores and the makeup of their neighbourhood with a set of socio-economic factors in Vancouver, British Columbia. OLS and GWR are both statistical process that link a set of independent variables with one dependent variable to determine the strength and estimate the characteristics of the relationship between each variable. The differences between the two regressions are that OLS provides a global average, while GWR accounts for local geography.

The dependent variable here was kindergarten language test scores. The data came from the Early Development Instrument (EDI), which is an international questionnaire measuring a child’s ability to meet age-appropriate development expectations and is given kindergarten teachers to complete about their students. The set of independent variables came from census surveys and included relative income, percentage of recent immigrants in a neighbourhood, percentage of single-parent households, if the child is ESL (0 = No, 1 = Yes), and their social skills (a value from 0-100).  These independent variables were determined to be the factors with the highest variability or AdjR2 value and lowest AICc through the preliminary exploratory regression, meaning they have the greatest geographically impact on language skills, and thus, are the most important factors.

To exhibit the significance of geography, the table below shows a comparison of the GWR parameter range with the OLS parameters.

The greater the GWR parameter range for each factor, the less the OLS parameters actually matter, and thusly, the more geography actually matters. So, for example, ESL has the highest OLS parameter at 5.45 and its GWR parameter range is between -2.18 and 10.99, yet the next largest OLS parameter is Soc_sc at 0.62 but its GWR range is 0.44 to 0.88, which is the lowest range of all the variables measured. In this case, the OLS parameter matters much less for ESL than it does for Soc_sc. Exploring this, one might think that ESL would have a large effect on language skills no matter where you are, but this analysis actually shows that if a child grows up in a neighbourhood where there are a lot of ESL children, they are not necessarily forced to learn English as fast a child who is one of few ESL children and requires English to communicate.

After the exploratory regression, I ran a grouping analysis, which divided Vancouver into 5 neighbourhood groupings based on similar characteristics from the enumeration areas census data. The results of this can be seen in the map below. Here, it is evident that childhood language scores are more dependent on local geography in East Vancouver than any other neighbourhood, which makes sense because it is a lower income area. Granville Island was a designated grouping here, but it does not matter to this analysis since not many people live here and there are no language scores in this area.

To help interpret the GWR analysis results, I also created used the Spatially Constrained Multivariate Clustering tool to create a raster for each of the independent variables to show their influence on specific local areas. The results for single parent households and social skills are shown below.

 

One of the most interesting revelations from this is that there seems to be a strong positive correlation to single-parent households and language skills around the western part Kingsway. Nothing can said about any individual in such a large scale analysis, and obviously there would never be policies put into place to create more single-parent households, but this could likely mean that there is strong school policies for supporting single-parent households that have a large positive impact on early childhood language skills. This suggests that schools play a very crucial role and is supported by the many people who are willing to pay thousands more to live in near identical houses so that their children can go to better schools.

Spam prevention powered by Akismet