Analysis of tips received in restaurants using a GAMLSS approach

Abstract

The main aim of this paper is to analyse the amount of tips obtained by a waiter in a restaurant, in dollars, while taking into account other collected variables within the establishment. In total, 244 observations were analysed, and six extra covariates were obtained in addition to the received tips (target variable), one numerical covariate (total bill in dollars) and five factors: payer gender (two levels: male; female), smoking status (two levels: yes; no), day of the week (four levels: Thursday; Friday; Saturday; Sunday), meal type (two levels: lunch; dinner), and number of people at the table (three levels: 1 or 2; 3; 4 or more). The generalised additive models for location, scale, and shape (GAMLSS) were considered due to its high flexibility. Given the asymmetric nature of the tip variable, three distributions were considered to explain the response: gamma, inverse Gaussian, and Box-Cox Cole and Green (BCCG). A stepwise-based procedure was utilised in the covariate selection process for each of the distribution parameters, and the best models for each distribution were compared using the Akaike information criterion (AIC). The model based on the BCCG distribution returned the lowest AIC and based on a residual analysis, it was found to be suitable for explaining the dataset under study.