Managing score heterogeneity between online consumer review websites

Figures & data

Table 1. Descriptive quantities of the sample distribution for the three OCR websites

OCR website	Mean	Standard deviation	Sample size (number of reviews)
Booking.com	$9.14$	$1.65$	$n_1=419$
TripAdvisor.com	$9.31$	$2.35$	$n_2=206$
Hoteles.com	$9.37$	$1.42$	$n_3=102$

Figure 1. Feedback histograms for the three OCR websites for hotel Santa Catalina.

Table 2. Posterior probabilities of the partitions in the case study

Models	Configurations	Parameter relationship	Posterior probability
	Homogeneity
$M_1$	$(123)$	${\lambda }_1={\lambda }_2={\lambda }_3$	0.22
	Intermediate Heterogeneity
$M_2$	$(1|23)$	${\lambda }_1\ne {\lambda }_2={\lambda }_3$	0.57
$M_3$	$(2|13)$	${\lambda }_2\ne {\lambda }_1={\lambda }_3$	0.05
$M_4$	$(3|12)$	${\lambda }_3\ne {\lambda }_1={\lambda }_2$	0.09
	Heterogeneity
$M_5$	$(1|2|3)$	${\lambda }_1\ne {\lambda }_2\ne {\lambda }_3$	0.07

Figure 2. Posterior distributions (left panel) and boxplot (right panel) of ${\lambda }_i$, $i=1,2,3.$.

Table 3. Posterior summaries of ${\lambda }_i,i=1,2,3$

Parameter	Post. mean	Post. median	$95\mathrm{\%}$ HPD interval
${\lambda }_1$	$9.14$	$9.14$	$(9.05,9.23)$
${\lambda }_2$	$9.31$	$9.31$	$(9.19,9.42)$
${\lambda }_3$	$9.37$	$9.37$	$(9.21,9.52)$

Table 4. Posterior summaries of $\lambda$ under each model $M_i,i=1,\dots ,5$ and the proposed BMA

Model	Post. mean	Post. median	$95\mathrm{\%}$ Credibility interval
$M_1$	$8.60$	$8.75$	$(6.44,9.84)$
$M_2$	$8.71$	$8.78$	$(7.29,9.68)$
$M_3$	$8.72$	$8.80$	$(7.30,9.70)$
$M_4$	$8.76$	$8.84$	$(7.36,9.71)$
$M_5$	$8.78$	$8.83$	$(7.66,9.60)$
BMA	$8.69$	$8.78$	$(7.07,9.72)$

Figure 3. Posterior distribution of $\lambda$ for each heterogeneity configuration (models $M_i,i=1,\dots ,5,$ in dashed grey lines) and the corresponding posterior BMA distribution (continuous black line).