with 4 degrees of freedom, namely, χ1 comparing the multivariate single-pollutant model with the base model ( = 0). In stage 2, we repeated the same analysis using stage 2 samples, but only for pollutants with |χ1| > (pre-defined significance threshold), and calculated the same likelihood ratio test statistic χ 2. We also used equation (2) (replace z with χ) to calculate χjoint which was compared with a significance threshold . Again, thresholds and were selected to control the false positive rate and we set them to be 13.3 and 18.4, respectively (corresponding to a significance level of 0.01 for the chi-squared test with 4 degrees of freedom in each stage).
