Spatial Analysis of Census Mail Response Rates: 1990–2010 - Space-Time Integration in Geography and GIScience - page 142

Tabl e 9. 1 Summary of US county-level MRRs

Year n Mean Standard deviation Minimum Maximum

1990 2,431 66.7 8.23 18 87

2000 3,015 70.0 10.28 13 90

2010 3,042 70.4 11.12 20 95

essentially lack MRR data. The 1990 data were complied for only those counties
with substantial populations, resulting in and additional 611 missing values, and
hence a total of 636 missing values. The 2000 data contain an additional 25 missing
values, for a total of 50 missing values for that year. The 2010 data are complete for
3,042 counties. The data are reported as percentages, resulting in standardization
to a denominator of 100 vis-a-vis the geographic variation in population across the
US. Table 9.1 tabulates basic summary statistics for these percentages. Figure 9.1
portrays the three geographic distributions of MRRs.

9.2 A Conceptual Framework for the Data Analysis

Because MRRs are percentages, they constitute a binomial random variable.
Their proper analysis involves generalized linear model or logistic regression
techniques that account for both spatial and temporal dependencies, as well as
space-time interactions. This paper extends eigenvector spatial filtering principles
and conceptualizations to eigenvector space-time filtering of binomial random
variables through the employment of a random effects term, a novel methodological
development at the research frontiers of space-time geography and GIScience.

9.2.1 Eigenvector Spatial Filtering

Eigenvector spatial filtering (see Griffith and Chun 2012 ) uses a set of synthetic
proxy variables, which are extracted as eigenvectors from an n-by-n spatial weight
matrix C that ties geographic objects together in space, and then adds these vectors
as control variables to a model specification in order to account for spatial autocorre-
lation by filtering it out of the model residuals. These control variables identify and
isolate the stochastic spatial dependencies among the georeferenced observations,
thus allowing model building to proceed as if the observations are independent.
One popular implementation of eigenvector spatial filtering utilizes an eigenfunc-
tion decomposition of the matrix version of the numerator of the Moran Coefficient
index of spatial autocorrelation:
I 11 T =n C I 11 T =n ;

(9.1)