Exploring the randomness of mentally generated head–tail sequences. (June 2020)

• Record Type: Journal Article
• Authors: Baena-Mirabete, S; Espinal, Anna; Puig, Pedro
• Is Part Of: Statistical modelling. Volume 20:Number 3(2020)
• Page Start: 225
• Page End: 248
• Publication Date: 2020-06
• Subjects: longitudinal data -- Higher-order Markov chains -- latent Markov models -- mixture of Markov chains; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18816410
• Languages: English
• ISSNs: 1471-082X

Abstract

It is well known that people deviate from randomness as they attempt to mentally generate head–tail sequences as randomly as possible. This deviation from randomness is quantified by an excess of repetitions or alternations between successive responses more than would be expected by chance. We conducted an experiment in which a sample of students was asked to mentally simulate a sequence as if it is produced by a fair coin. We propose several models based on Markov chains for analysing the dynamic of head–tail outcomes in these sequences. First, we explore observed Markov chains and suggest some practical solutions to reduce the number of parameters. However, there is a need for more sophisticated models, and in this case, we propose latent Markov models and mixture of Markov chains to analyse these head–tail sequences. A generalization of the so-called mixture transition distribution (MTD) model is also considered.