Analyzing count data related to football using multilevel modeling

Abstract

Traditional multiple regression techniques treat the units of analysis as independent observations. A consequence for failing to recognise existing hierarchical structures is that standard errors of regression coefficients will be underestimated, leading to an overstatement of statistical significance. Standard errors for the coefficients of higher-level explanatory variables will be the most affected by ignoring grouping. Multilevel models overcome the limitations of traditional regression methods and are used to analyse hierarchical structured data where observations are nested within higher levels of classification. In these models, processes that occur at a higher level of analysis influence the characteristics and processes occurring at a lower level. One of the merits of using multilevel modeling is that this technique can separately estimate the predictive effects of an individual explanatory variable and its group-level mean. Moreover, in a multilevel model the groups in the sample are treated as a random sample selected from a population. The multilevel models considered in this dissertation are linear mixed models with three levels of nesting, which involve a mix of fixed and random effects. The dataset used provides information about the number of goals scored by footballers who played with 17 teams that were in the English premier league in seasons 2022-2023 and 2023-2024. Only teams that were in the premier league in both seasons were considered. The number of goals scored by each player per season is the dependent variable, which is related to a number of explanatory variables, including playing position (attacker, midfielder, defender), average playtime per game (in minutes), number of substitutions, number of fouls, number of offsides, number of yellow cards, number of assists, and the number of shots at goal made by the footballer per season. Since the goal frequency distribution is discrete and right skewed, Poisson three-level models were fitted, where the footballers (level-1 units) are nested in football teams (level 2 units), which in turn are nested in two football seasons (level-3 units).