Predictor

β

Measure

BMA^{1}

LASSO^{2}

PLSR^{3}

SPCA^{4}


X
_{
1
}

0.30

Estimate (ESE)

0.26 (0.18)

0.27 (0.05)

0.24 (0.07)

0.0013 (0.0070)

Percent included

88.5%

100%

N/A

5.6%

X
_{
3
}

0.30

Estimate (ESE)

0.28 (0.15)

0.27 (0.04)

0.23 (0.06)

0.0005 (0.0036)

Percent included

95.8%

100%

N/A

3.8%

X
_{
1
}*X
_{
3
}

0.10

Estimate (ESE)

0.11 (0.06)

0.11 (0.01)

0.10 (0.02)

0.19 (0.04)

Percent included

97.7%

100%

N/A

100%


Average model size

4.5

5.4

10

1.3

 Average estimated effects, empirical standard errors, percentages of correct identification of nonzero coefficients, and average model size corresponding to four statistical methods in a timeseries study with count response and 4 air pollutants. Sample size for each replicate was N=400. The true model size was 3 with intercept not counted, and the possible maximum model size was 10. ESE, empirical standard error of the estimate. Results are based on 1000 replicates.
 Estimate of the nonzero predictor is calculated as the mean of the products that estimated regression coefficient of this predictor multiplies the indicator function that this predictor is correctly identified during each replication. The percentage of the nonzero predictor quantifies the proportion of correct identification of this predictor over 1000 replicates in each method. ^{1}In BMA, predictors with their posterior probabilities greater than 10% are regarded as identified. ^{2}Predictors with their estimated LASSO regression coefficients not equal to zero are considered identified. ^{3}No variable selection has been applied in PLSR because it uses all predictors. ^{4}In SPCA, predictors are identified if their Wald’s statistics from univariate models are larger than a threshold value.