Table 8 Model comparison on diet groups with confounding variables (signal in counts & zeros, effect size +100%)

Poisson

(loglik)

1.00 (\(\pm 0.00\))

0.99 (\(\pm 0.00\))

0.11 (\(\pm 0.00\))

0.53 (\(\pm 0.01\))

Poisson

(llperm)

0.37 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.37 (\(\pm 0.01\))

0.74 (\(\pm 0.01\))

ZIPoisson

(loglik)

0.99 (\(\pm 0.00\))

0.94 (\(\pm 0.00\))

0.10 (\(\pm 0.01\))

0.54 (\(\pm 0.01\))

ZIPoisson

(llperm)

0.30 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.30 (\(\pm 0.01\))

0.72 (\(\pm 0.01\))

NegativeBinomial

(loglik)

0.17 (\(\pm 0.00\))

0.05 (\(\pm 0.00\))

0.16 (\(\pm 0.01\))

0.48 (\(\pm 0.01\))

NegativeBinomial

(llperm)

0.34 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.33 (\(\pm 0.01\))

0.71 (\(\pm 0.01\))

ZINegativeBinomial

(loglik)

0.52 (\(\pm 0.01\))

0.15 (\(\pm 0.00\))

0.33 (\(\pm 0.01\))

0.70 (\(\pm 0.01\))

ZINegativeBinomial

(llperm)

0.34 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.34 (\(\pm 0.01\))

0.71 (\(\pm 0.01\))

Binomial

(loglik)

1.00 (\(\pm 0.00\))

0.99 (\(\pm 0.00\))

0.11 (\(\pm 0.00\))

0.53 (\(\pm 0.01\))

Binomial

(llperm)

0.37 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.38 (\(\pm 0.01\))

0.74 (\(\pm 0.01\))

ZIBinomial

(loglik)

0.99 (\(\pm 0.00\))

0.94 (\(\pm 0.00\))

0.10 (\(\pm 0.01\))

0.54 (\(\pm 0.01\))

ZIBinomial

(llperm)

0.30 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.30 (\(\pm 0.01\))

0.72 (\(\pm 0.01\))

BetaBinomial

(loglik)

0.26 (\(\pm 0.00\))

0.10 (\(\pm 0.00\))

0.17 (\(\pm 0.00\))

0.63 (\(\pm 0.01\))

BetaBinomial

(llperm)

0.17 (\(\pm 0.00\))

0.05 (\(\pm 0.00\))

0.17 (\(\pm 0.00\))

0.63 (\(\pm 0.01\))

ZIBetaBinomial

(loglik)

0.38 (\(\pm 0.01\))

0.10 (\(\pm 0.00\))

0.27 (\(\pm 0.01\))

0.63 (\(\pm 0.01\))

ZIBetaBinomial

(llperm)

0.30 (\(\pm 0.01\))

0.05 (\(\pm 0.00\))

0.30 (\(\pm 0.01\))

0.67 (\(\pm 0.01\))