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As is usual practice, we carefully ensured the quality of the fit (value of R-squared, significance of coefficients, over-fitting).
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R-squared 0.36 0.22 Significance levels: *** = significant at the 1% level, ** = significant at the 5% level, *= significant at the 10% level .
Visibility, together with humidity, was found appropriate in predicting PM2.5 (R-squared: 0.64) and PM10 (R-squared: 0.62).
However dropping one of these items had no effect on the direction of associations and only minimal effect on the pseudo R-squared value or the significance and magnitude of the regression coefficient, hence the full set of items were retained in the analysis.
Models revealed 95% significance of confidence level with difference less than 0.2 between Pred R-Squared value of 0.9515 and Adj R-Squared.
A compiled gene list was created using a more stringent R-squared cutoff (> 0.5) from significance analysis.
A P-value of 0.05 is taken as the significance level, and higher R-squared indicated a better model fit.
All the model specifications fit well to the data set as indicated by the likelihood ratio test that the coefficient parameters are statistically significantly different from 0 at 1% significance level and the pseudo R-squared value is quite high.
Use of the spatial error and spatial lag regression improved the fit of the models in all measures; improving the significance of independent variables, increasing R-squared (a pseudo- R in spatial regression) and the log-likelihood, and decreasing the Akaike info criterion (AIC) and Schwarz criterion relative to the OLS regression.
Significance of the more complex model was assessed by its improvement of adjusted R-squared and by likelihood ratio test.
The ranges of adjusted R-squared values were 0.733 0.995 (all ps < 0.238, the linear fits for five participants failed to reach significance), 0.84 0.992 (all ps < 0.002), and 0.923 0.993 (all ps < 0.001) for target prevalence of 5, 15, and 25, respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com