Choice modelling with Gaussian processes in the social sciences: A case study of neighbourhood choice in Stockholm.

We present a non-parametric extension of the conditional logit model, using Gaussian process priors. The conditional logit model is used in quantitative social science for inferring interaction effects between personal features and choice characteristics from observations of individual multinomial decisions, such as where to live, which car to buy or which school to choose. The classic, parametric model presupposes a latent utility function that is a linear combination of choice characteristics and their interactions with personal features. This imposes strong and unrealistic constraints on the form of individuals' preferences. Extensions using non-linear basis functions derived from the original features can ameliorate this problem but at the cost of high model complexity and increased reliance on the user in model specification. In this paper we develop a non-parametric conditional logit model based on Gaussian process logit models. We demonstrate its application on housing choice data from over 50,000 moving households from the Stockholm area over a two year period to reveal complex homophilic patterns in income, ethnicity and parental status.

Using Bayesian dynamical systems, model averaging and neural networks to determine interactions between socio-economic indicators.

Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the 'best' explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the 'best' model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.

Modelling optimal allocation of resources in the context of an incurable disease.

Nodding syndrome has affected and led to the deaths of children between the ages of 5 and 15 in Northern Uganda since 2009. There is no reliable explanation of the disease, and currently the only treatment is through a nutritional programme of vitamins, combined with medication to prevent symptoms. In the absence of a proper medical treatment, we develop a dynamic compartmental model to plan the management of the syndrome and to curb its effects. We use incidence data from 2012 and 2013 from Pader, Lamwo and Kitgum regions of Uganda to parameterize the model. The model is then used to look at how to best plan the nutritional programme in terms of first getting children on to the programme through outreach, and then making sure they remain on the programme, through follow-up. For the current outbreak of nodding disease, we estimate that about half of available resources should be put into outreach. We show how to optimize the balance between outreach and follow-up in this particular example, and provide a general methodology for allocating resources in similar situations. Given the uncertainty of parameter estimates in such situations, we perform a robustness analysis to identify the best investment strategy. Our analysis offers a way of using available data to determine the best investment strategy of controlling nodding syndrome.

The dynamics of democracy, development and cultural values.

Over the past decades many countries have experienced rapid changes in their economies, their democratic institutions and the values of their citizens. Comprehensive data measuring these changes across very different countries has recently become openly available. Between country similarities suggest common underlying dynamics in how countries develop in terms of economy, democracy and cultural values. We apply a novel Bayesian dynamical systems approach to identify the model which best captures the complex, mainly non-linear dynamics that underlie these changes. We show that the level of Human Development Index (HDI) in a country drives first democracy and then higher emancipation of citizens. This change occurs once the countries pass a certain threshold in HDI. The data also suggests that there is a limit to the growth of wealth, set by higher emancipation. Having reached a high level of democracy and emancipation, societies tend towards equilibrium that does not support further economic growth. Our findings give strong empirical evidence against a popular political science theory, known as the Human Development Sequence. Contrary to this theory, we find that implementation of human-rights and democratisation precede increases in emancipative values.

Initiators, leaders, and recruitment mechanisms in the collective movements of damselfish.

Explaining how individual behavior and social interactions give rise to group-level outcomes and affect issues such as leadership is fundamental to the understanding of collective behavior. Here we examined individual and collective behavioral dynamics in groups of humbug damselfish both before and during a collective movement. During the predeparture phase, group activity increased until the collective movement occurred. Although such movements were precipitated by one individual, the success or failure of any attempt to instigate a collective movement was not solely dependent on this initiator's behavior but on the behavior of the group as a whole. Specifically, groups were more active and less cohesive before a successful initiation attempt than before a failed attempt. Individuals who made the most attempts to initiate a collective movement during each trial were ultimately most likely to lead the collective movement. Leadership was not related to dominance but was consistent between trials. The probability of fish recruiting to a group movement initiative was an approximately linear function of the number of fish already recruited. Overall, these results are consistent with nonselective local mimetism, with the decision to leave based on a group's, rather than any particular individual's, readiness to leave.

The dynamics, causes and possible prevention of Hepatitis E outbreaks.

Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that R0 is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least 16% and 17% respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of R0 for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.

Collective irrationality and positive feedback.

Recent experiments on ants and slime moulds have assessed the degree to which they make rational decisions when presented with a number of alternative food sources or shelter. Ants and slime moulds are just two examples of a wide range of species and biological processes that use positive feedback mechanisms to reach decisions. Here we use a generic, experimentally validated model of positive feedback between group members to show that the probability of taking the best of options depends crucially on the strength of feedback. We show how the probability of choosing the best option can be maximized by applying an optimal feedback strength. Importantly, this optimal value depends on the number of options, so that when we change the number of options the preference of the group changes, producing apparent "irrationalities". We thus reinterpret the idea that collectives show "rational" or "irrational" preferences as being a necessary consequence of the use of positive feedback. We argue that positive feedback is a heuristic which often produces fast and accurate group decision-making, but is always susceptible to apparent irrationality when studied under particular experimental conditions.