. Author manuscript; available in PMC: 2018 Oct 1.

Published in final edited form as: Foodborne Pathog Dis. 2017 Jul 18;14(10):587–592. doi: 10.1089/fpd.2017.2308

Table 1.

Goodness of fit and statistics comparison by model

Model 1^*
Model 2		Hurdle NB	NB	Hurdle NB Full	ZINB	NB.Plus
M0^†	LR		^***			^***
	V (BIC)	79.0, ^***	79.9, ^***	91.5, ^***	89.5, ^***	89.5, ^***

Hurdle	LR			^***
NB	V (BIC)		9.2, ^***	37.6, ^***	40.4, ^***	40.5, ^***

NB	LR					^***
NB	V (BIC)	(−9.2), ^***		29.6, ^***	33.4, ^***	33.5, ^***

Hurdle	LR	^***
NB full	V (BIC)	(−37.6), ^***	(−29.6), ^***		3.7, 0.0001	3.9, 5.1e-5

ZINB	LR
	V (BIC)	(−40.4), ^***	(−33.4), ^***	(−3.7), 0.0001		174.2, ^***

NB.Plus	LR		^***
NB.Plus	V (BIC)	(−40.5), ^***	(−33.5), ^***	(−3.9), 5.1e-5	(−174.2), ^***

−2 × log likelihood		−115539	−114403	−109482	−109525	−109525
^‡		25	17	47	25	24
AIC		115589	114437	109576	109575	109573
BIC		115825	114597	110019	109811	109799
MAE		0.3963	0.4046	0.3809	0.3798	0.3798
Predicted no. zeros		72918	73540	72918	73403	73403

Models are listed from left to right and top to bottom as their fits improve;

Hurdle NB = Hurdle negative binomial with covariates in the count component only, NB = Negative binomial without demographic covariates, Hurdle NB Full = hurdle negative binomial with covariates in both zero and count components, ZINB = Zero-inflated negative binomial with covariates in the count component only, NB.Plus = Negative binomial with demographic covariates;

^†

Null model; LR= Likelihood ratio test; V (BIC) = Vuong BIC corrected Non-Nested Hypothesis Test-Statistic;

^***

= p-value less than 2.2e-16 when testing model 1 versus model2 with alpha < 0.05;

^‡

Number of parameters estimated; AIC = Akaike information criterion; BIC = Bayesian information criterion; MAE = Mean absolute error