Chapter Motivation of basketball players: a random-effects logit model for the probability of winning

In the sport psychology, the theories of motivation, such as the McClelland's need achievement theory and the Nicholls' achievement goal theory, play an important role in the team sports in motivating and encouraging team members. The practical implementation of these theories relies on detecting the variables that significantly affect the probability of winning so as to identify the key elements for the team motivation, the role assignment, and the decision-making process. As the relevant variables change in accordance with the type of sport, in this contribution we focus on the basketball. In detail, we consider the traditional box score of the U.S. National Basket Association (NBA) regular season games played in the seasons 2016-17, 2017-18, 2018-19 and 2020-21. Each season comprises of 82 games played by each of the 30 teams, which cumulates to 4920 games. Hence, data have a multilevel structure, with multiple observations for each team. To properly address the data structure, the probability of winning is modelled through a random-intercept logit model, where teams are the upper-level units and games are the lower-level units. Among the independent variables, we take into account several possible determinants of winning, such as number of assists, number of offensive rebounds, number of defensive rebounds, number of turnovers, number of stolen balls, percentage of free throws made, number of fouls made. Moreover, we devote a special attention to the effect of two more independent variables: the number of key-players that are missing or injured and a dummy if the team plays without a day of rest between consecutive games. The study provides insights in the determinants of success of the basketball games: these results can be used by the team decision makers to assign roles that favor motivation and performance of players and of team as a whole

A bivariate finite mixture growth model with selection

AbstractA model is proposed to analyze longitudinal data where two response variables are available, one of which is a binary indicator of selection and the other is continuous and observed only if the first is equal to 1. The model also accounts for individual covariates and may be considered as a bivariate finite mixture growth model as it is based on three submodels: (i) a probit model for the selection variable; (ii) a linear model for the continuous variable; and (iii) a multinomial logit model for the class membership. To suitably address endogeneity, the first two components rely on correlated errors as in a standard selection model. The proposed approach is applied to the analysis of the dynamics of household portfolio choices based on an unbalanced panel dataset of Italian households over the 1998–2014 period. For this dataset, we identify three latent classes of households with specific investment behaviors and we assess the effect of individual characteristics on households' portfolio choices. Our empirical findings also confirm the need to jointly model risky asset market participation and the conditional portfolio share to properly analyze investment behaviors over the life-cycle

A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses

We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed approach, the random vector used to represent the latent traits is assumed to have a discrete distribution with support points corresponding to different latent classes in the population. We also allow for different parameterizations for the conditional distribution of the response variables given the latent traits - such as those adopted in the Graded Response model, in the Partial Credit model, and in the Rating Scale model - depending on both the type of link function and the constraints imposed on the item parameters. For the proposed models we outline how to perform maximum likelihood estimation via the Expectation-Maximization algorithm. Moreover, we suggest a strategy for model selection which is based on a series of steps consisting of selecting specific features, such as the number of latent dimensions, the number of latent classes, and the specific parametrization. In order to illustrate the proposed approach, we analyze data deriving from a study on anxiety and depression as perceived by oncological patients.Comment: 25 pages; 10 table

Preterm Birth: analysis of longitudinal Data on siblings Based on random-effects logit Models

INTRODUCTION: The literature about the determinants of a preterm birth is still controversial. We approach the analysis of these determinants distinguishing between woman’s observable characteristics, which may change over time, and unobservable woman’s characteristics, which are time invariant and explain the dependence between the typology (normal or preterm) of consecutive births. METHODS: We rely on a longitudinal dataset about 28,603 women who delivered for the first time in the period 2005–2013 in the Umbria Region (Italy). We consider singleton physiological pregnancies originating from natural conceptions with birthweight of at least 500 g and gestational age between 24 and 42 weeks; the overall number of deliveries is 34,224. The dataset is based on the Standard Certificates of Life Birth collected in the region in the same period. We estimate two types of logit model for the event that the birth is preterm. The first model is pooled and accounts for the information about possible previous preterm deliveries, including the lagged response among the covariates. The second model takes explicitly into account the longitudinal structure of data through the introduction of a random effect that summarizes all the (time invariant) unobservable characteristics of a woman affecting the probability of a preterm birth. RESULTS: The estimated models provide evidence that the probability of a preterm birth depends on certain woman’s demographic and socioeconomic characteristics, other than on the previous history in terms of miscarriages and the baby’s gender. Besides, as the random-effects model fits significantly better than the pooled model with lagged response, we conclude for a spurious state dependence between repeated preterm deliveries. CONCLUSION: The proposed analysis represents a useful tool to detect profiles of women with a high risk of preterm delivery. Such profiles are detected taking into account observable woman’s demographic and socioeconomic characteristics as well as unobservable and time-constant characteristics, possibly related to the woman’s genetic makeup. TRIAL REGISTRATION: Not applicable