Use of the generalized linear model for forecasting the number of visits to museums in Mexico: comparison between ordinary linear and Poisson regression

Abstract

It is of great interest for establishments that offer a product or service, for example museums, to know the number of possible visits as a function of other variables that customers will make in a specific period. This to evaluate the degree of demand that exists and at the same time, evaluate if the dissemination strategies are working or otherwise, make more appropriate decisions to improve the quality of attention and satisfaction with visitors. To implement the generalized linear model to estimate the number of annual visits to museums in Mexican territory as a function of predictive variables, a database of 110 museums taken from the Instituto Nacional de Estadística y Geografía (INEGI) for the years 2017 and 2018 was used. The models used were regression ordinary linear (RLO) and Poisson regression (RP) and these were applied to all the principal components of eleven predictor variables (web page, reception and service capacity, main theme, permanent collection, ownership, entry, adult fee, discounts, type of visits, open days of the year and temporary exhibitions) to counteract multicollinearity. Besides, the coefficient of determination ( ) was measured between the observed and estimated data to determine the method with the best fit. The functions were used to estimate the number of visits for the years 2019 and 2020. With the model that best fit, an analysis of estimation errors was performed. Comparing the observed data for the years 2017 and 2018 with the results estimated with the characteristic functions of each model, the determination coefficients were  0.61 for the RLO and 0.86 for the PR, respectively. For the years 2019 and 2020, the coefficients of determination obtained were 0.68 and 0.31 for the RLO, and 0.87 and 0.84 for the RP, respectively. The maximum error of estimation registered was between 10 001 and 20 000 annual visits. It is shown that the most suitable model to forecast future annual visits to any museum in Mexico is the Poisson regression. It is believed that the high adjustment to the data observed with the PR method is because these did not have an excess of zeros and fulfilled the assumption of equidispersion. Finally, with the proposed characteristic function, the number of annual visits can be estimated with a maximum error of around 10 %, which is low compared to the maximum number of annual visits that a museum receives.