. Author manuscript; available in PMC: 2009 Jul 6.

Published in final edited form as: Atmos Environ (1994). 2008 Jun 1;42(18):4047–4062. doi: 10.1016/j.atmosenv.2008.01.044

Table 4.

Predictive performance of the final model and alternative models

Model description				Cross-validation results
Model description	Number of spatial terms^a	Covariates included	Model fit R^2,^b	Intercept^c	Slope^c	Cross-validation R^2,^d
Final model	180 monthly^e	All	0.74	2.4 +/− 0.9	0.92 +/− 0.003	0.62
Seasonal spatial terms	4 seasonal^e	All	0.59	2.1 +/− 0.1	0.94 +/− 0.004	0.54
GAM spatial smoothing only	180 monthly	None	0.76	3.7 +/− 0.1	0.87 +/− 0.004	0.51
Inverse distance weighted interpolation	NA	None	NA	8.3 +/− 0.1	0.65 +/− 0.005	0.29
Nearest neighbor interpolation	NA	None	NA	15.5 +/− 0.2	0.42 +/− 0.006	0.22^f

Corresponds to the extent of control for space-time interaction in the model.

Derived from fitting the model to all data from sets 1 through 9, including data from states adjacent to the study region.

Presented as (parameter estimate +/− standard error) from linear regression of observations on predictions.

Derived from cross-validation on sets 1 through 9, with each set held out in turn (one site in Pennsylvania was removed as an outlier); 43 345 observations total.

Refers to number of time-varying spatial terms fit in the first stage of the model in addition to one spatial term fit in the second stage.

Because the nearest monitor was not always within the 50 km neighborhood, only 20 189 pairs of observations are available rather than the full set of 43 345 observations.