Spatial Analysis of Census Mail Response Rates: 1990–2010 - Space-Time Integration in Geography and GIScience - page 149

The constructed ESTF yields a pseudo-R 2 value of 0.6868, and produces a
deviance statistic value of 1.6468. These results are superior to those for the two
model specifications presented in the preceding section of this paper. The individual
time components of this ESTF produce the following results:

Pseudo-R 2 Year

1990 0.6685

2000 0.7075

2010 0.6622

Estimating a random effects term with this ESTF specification renders a SURE
geographic variate, which should account solely for data heterogeneity, that is
constant through time; none of the eigenvectors from expression ( 9.1 ) should, or
do, covary with it. The estimated SURE has a mean of 0.00122, but deviates from
a normal frequency distribution. The addition of this variate increases the pseudo-
R 2 value to 0.8785, which is a substantial increase over the ESF and time-lagged
model specifications. The individual time components of this ESTF-plus-SURE
specification produce the following results:

Pseudo-R 2 Year

1990 0.7899

2000 0.9109

2010 0.8932

The affiliated deviance statistic is 0.64810, again raising the question of whether
or not the SURE term has only 2 degrees of freedom associated with it.
Figure 9.4 portrays the ESTF and the SURE. The cloud of highest values
shifts eastward through time, whereas the cloud of lowest values basically covers
Arizona, New Mexico and Texas. Keeping in mind that eigenvectors are unique
to a multiplicative factor of 1, these patterns resemble a mirror image of those
portrayed in Figs. 9.2 and 9.3 . The heart of Appalachia is visible in all of these maps.
The maps in Fig. 9.4 more closely resemble their MRR counterparts in Fig. 9.1 than
do these maps in Figs. 9.2 and 9.3 . The SURE looks like the random pattern that it
is. It looks more chaotic than the SURE patterns appearing in Figs. 9.2 and 9.3 .

9.6 Implications and Concluding Comments

This paper summarizes an analysis of census MRRs from the three US decennial
censuses conducted for 1990-2010 whose most successful descriptions employ a
random effects model framework. Especially, eigenvector spatial filtering combined
with a random effects model furnishes a flexible way to account for spatial as
well as non-spatial random effects simultaneously in a model specification. Further,
eigenvector spatial filtering has been extended to eigenvector space-time filtering