A Bayesian model for online customer reviews data in tourism research: a robust analysis

Figures & data

Figure 1. Histograms of the rating data sets: Gstaad Palace Hotel (left figure) and Bellevire Gstaad Hotel (right figure).

Table 1. Customer score distribution for the two data sets considered.

	Data set #1 (Gstaad palace hotel)	Dataset #2 (Bellevire Gstaad hotel)
Score	Frequency	Frequency
[1,3)	2	14
[3,5)	2	14
[5,7)	4	63
[7,9)	14	244
[9,10]	98	136
Total	120	471
Descriptive summaries
Average score	9.40	8.01
Standard Deviation	1.52	1.80
Index of Dispersion	0.25	0.40

Table 2. Maximum likelihood estimate $\widehat{\mathrm{\theta }},$ standard error (SE) of $\widehat{\mathrm{\theta }}$ and AIC value for the both data sets and sampling distributions considered.

	Dataset #1			Dataset #2
Fitted distribution	$\widehat{\mathrm{\theta }}$	SE	AIC	$\widehat{\mathrm{\theta }}$	SE	AIC
Poisson	9.4	0.280	528.472	8.013	0.130	2063.190
Rescaled shifted binomial	9.4	0.106	399.256	8.013	0.057	1934.050

Figure 2. Top to down: Empirical and fitted frequencies of the two models considered (Poisson and rescaled shifted binomial distributions) of customers’ review data. Dataset #1 left and dataset #2 right.

Table 3. Elicitation of prior distributions: expert’s judgements, corresponding hyperparameters values and posterior quantities.

Poisson-gamma
	Expert judgement		Elicited prior parameters		Sample data		Posterior quantities
Hotel	Mean	Mode	$\mathrm{\alpha }$	$\mathrm{\beta }$	$n$	$x^{+}$	${\alpha }^{\mathrm{*}}$	${\beta }^{\mathrm{*}}$	${\rho }^{{\pi }_0}\left(\tilde{x}\right)$
Gstaad	9	9	180	20	5	46	226	25	9.04
					10	82	262	30	8.74
Bellevire G.	8	8	62.7	7.84	5	44	106.70	12.84	8.31
					10	96	158.70	17.84	8.89
Rescaled shifted binomial-shifted beta
	Expert Judgement		Elicited prior parameters		Sample data		Posterior quantities
Hotel	Mean	Mode	$\mathrm{\alpha }$	$\mathrm{\beta }$	$n$	$x^{+}$	${\alpha }^{\mathrm{*}}$	${\beta }^{\mathrm{*}}$	${\rho }^{{\pi }_0}\left(\tilde{x}\right)$
Gstaad	9	9	15	2	5	46	56	6	9.13
					10	82	87	20	8.32
Bellevire G.	8	8	10	3	5	44	49	9	8.60
					10	96	96	7	9.39

Figure 3. Range of the posterior mean (left) and RS factor (right) for the Gstaad Hotel case, observed data $n=5$ and $x^{+}=46$. Poisson-gamma model (top panel) and rescaled shifted binomial-shifted beta model (bottom panel).

Figure 4. Range of the posterior mean (left) and RS factor (right) for the Gstaad Hotel case, observed data $n=10$ and $x^{+}=82$. Poisson-gamma model (top panel) and rescaled shifted binomial-shifted beta model (bottom panel).

Figure 5. Range of the posterior mean (left) and RS factor (right) for the Bellevire Gstaad Hotel case, observed data $n=5$ and $x^{+}=46$. Poisson-gamma model (top panel) and rescaled shifted binomial-shifted beta model (bottom panel).

Figure 6. Range of the posterior mean (left) and RS factor (right) for the Bellevire Gstaad Hotel case, observed data $n=10$ and $x^{+}=82$. Poisson-gamma model (top panel) and rescaled shifted binomial-shifted beta model (bottom panel).