bcPower Transformations to Multinormality

Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd

AQI −0.1534 0.0 -0.7781 0.4714

PM2.5 −0.2468 0.0 -0.6046 0.1109

PM10 0.9526 1.0 0.4643 1.4409

NO2 0.1247 1.0 −1.0050 1.2543

SO2 −0.3271 −0.5 −0.6019 −0.0523

CO −0.6059 −1.0 −1.1548 −0.0570

O3 1.0138 1.0 0.5136 1.5140

Likelihood ratio test that transformation parameters are equal to 0

(all log transformations)

LRT df pval

LR test, lambda = (0 0 0 0 0 0 0) 49.203387 2.07e-08

Likelihood ratio test that no transformations are needed

LRT df pval

LR test, lambda = (1 1 1 1 1 1 1) 133.52787 < 2.22e−16