Statistical Modelling 20 (3) (2020), 225–248

Exploring the randomness of mentally generated head–tail sequences

S Baena-Mirabete,
Department of Economics and Economic History,
Faculty of Economics and Business Studies,
Universitat Autónoma de Barcelona,
Barcelona,
Spain
e-mail: sergio.baena@uab.cat

and

Department of Mathematics,
Faculty of Sciences,
Universitat Autónoma de Barcelona,
Barcelona,
Spain


Anna Espinal,
Servei d'Estadística Aplicada,
Universitat Autónoma de Barcelona,
Barcelona,
Spain


Pedro Puig
Department of Mathematics,
Faculty of Sciences,
Universitat Autónoma de Barcelona,
Barcelona,
Spain


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.

Keywords:

longitudinal data; Higher-order Markov chains; latent Markov models; mixture of Markov chains.

Downloads:

Example data, code and supplementary material in zipped archive.
back