Score-Based Approaches to Heterogeneity in Psychological Models

Statistische Modelle menschlicher Kognition und Verhaltens stützen sich häufig auf aggregierte Daten und vernachlässigen dadurch oft Heterogenität in Form von Unterschieden zwischen Personen oder Gruppen. Die Nichtberücksichtigung vorliegender Heterogenität kann zu verzerrten Parameterschätzungen und zu falsch positiven oder falsch negativen Tests führen. Häufig kann Heterogenität mithilfe von Kovariaten erkannt und vorhergesagt werden. Allerdings erweist sich die Identifizierung von Prädiktoren von Heterogenität oft als schwierige Aufgabe. Zur Lösung dieses Problems schlage ich zwei neue Ansätze vor, um individuelle und gruppenspezifische Unterschiede mithilfe von Kovariaten vorherzusagen. Die vorliegende kumulative Dissertation setzt sich aus drei Projekten zusammen. Projekt 1 widmet sich dem Verfahren IPC-Regression (Individual Parameter Contribution), welches die Exploration von Parameterheterogenität in Strukturgleichungsmodellen (SEM) mittels Kovariaten erlaubt. Unter anderem evaluiere ich IPC-Regression für dynamische Panel-Modelle, schlage eine alternative Schätzmethode vor und leite IPCs für allgemeine Maximum-Likelihood-Schätzer her. Projekt 2 veranschaulicht, wie IPC-Regression in der Praxis eingesetzt werden kann. Dazu führe ich schrittweise in die Implementierung von IPC-Regression im ipcr-Paket für die statistische Programmiersprache R ein. Schließlich werden in Projekt 3 SEM-Trees weiterentwickelt. SEM-Trees sind eine modellbasierte rekursive Partitionierungsmethode zur Identifizierung von Kovariaten, die Gruppenunterschiede in SEM-Parametern vorhersagen. Die bisher verwendeten SEM-Trees sind sehr rechenaufwendig. In Projekt 3 kombiniere ich SEM-Trees mit unterschiedlichen Score-basierten Tests. Die daraus resultierenden Score-Guided-SEM-Tees lassen sich deutlich schneller als herkömmlichen SEM-Trees berechnen und zeigen bessere statistische Eigenschaften.Statistical models of human cognition and behavior often rely on aggregated data and may fail to consider heterogeneity, that is, differences across individuals or groups. If overlooked, heterogeneity can bias parameter estimates and may lead to false-positive or false-negative findings. Often, heterogeneity can be detected and predicted with the help of covariates. However, identifying predictors of heterogeneity can be a challenging task. To solve this issue, I propose two novel approaches for detecting and predicting individual and group differences with covariates. This cumulative dissertation is composed of three projects. Project 1 advances the individual parameter contribution (IPC) regression framework, which allows studying heterogeneity in structural equation model (SEM) parameters by means of covariates. I evaluate the use of IPC regression for dynamic panel models, propose an alternative estimation technique, and derive IPCs for general maximum likelihood estimators. Project 2 illustrates how IPC regression can be used in practice. To this end, I provide a step-by-step introduction to the IPC regression implementation in the ipcr package for the R system for statistical computing. Finally, Project 3 progresses the SEM tree framework. SEM trees are a model-based recursive partitioning method for finding covariates that predict group differences in SEM parameters. Unfortunately, the original SEM tree implementation is computationally demanding. As a solution to this problem, I combine SEM trees with a family of score-based tests. The resulting score-guided SEM trees compute quickly, solving the runtime issues of the original SEM trees, and show favorable statistical properties

Predicting Differences in Model Parameters with Individual Parameter Contribution Regression Using the R Package ipcr

Unmodeled differences between individuals or groups can bias parameter estimates and may lead to false-positive or false-negative findings. Such instances of heterogeneity can often be detected and predicted with additional covariates. However, predicting differences with covariates can be challenging or even infeasible, depending on the modeling framework and type of parameter. Here, we demonstrate how the individual parameter contribution (IPC) regression framework, as implemented in the R package ipcr, can be leveraged to predict differences in any parameter across a wide range of parametric models. First and foremost, IPC regression is an exploratory analysis technique to determine if and how the parameters of a fitted model vary as a linear function of covariates. After introducing the theoretical foundation of IPC regression, we use an empirical data set to demonstrate how parameter differences in a structural equation model can be predicted with the ipcr package. Then, we analyze the performance of IPC regression in comparison to alternative methods for modeling parameter heterogeneity in a Monte Carlo simulation.Peer Reviewe

Thermalization vs. Isotropization & Azimuthal Fluctuations

Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage.Comment: 12 pages, presented at `Correlations and Fluctuations in Relativistic Nuclear Collisions', MIT, April 05, minor correction

Isotropization by QCD Plasma Instabilities

Numerical solutions of the Wong-Yang-Mills equations with anisotropic particle momentum distributions are presented. Their isotropization by collective effects due to the classical Yang-Mills field is shown.Comment: 4 pages, 4 figures, contribution to the Quark Matter 2005 proceeding

La demande d'assurance dépendance dans un cadre trivarié.

Private insurance for long-term care is underdeveloped in European countries and in the US. This paper tries to understand why the market is underdevelopped by using a theoretical approach and putting the emphasis on insurance demand. It shows that demand for long term care insurance can be low because current and expected health condition of individuals have a strong effect on wealth utility and thus insurance demand. Individual preferences may lead some persons not to seek insure. The underdevelopped market of long-term care insurance might not be only due to insurance supply, market failures, family impacts or institutional design. It is analyzed as a direct consequence of individual preferences.dépendance; assurance dépendance; demande d'assurance;

Shear viscosity of a superfluid Fermi gas in the unitarity limit

We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature T limit the shear viscosity scales as xi^5/T^5, where the universal parameter 'xi' relates the chemical potential and the Fermi energy, mu=xi E_F. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature T_c. A naive extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of ~ 5 of the proposed lower bound hbar/(4\pi k_B).Comment: 9 pages, 7 figures, LaTeX2

Modeling dynamic personality theories in a continuous‐time framework: An illustration

Objective Personality psychology has traditionally focused on stable between-person differences. Yet, recent theoretical developments and empirical insights have led to a new conceptualization of personality as a dynamic system (e.g., Cybernetic Big Five Theory). Such dynamic systems comprise several components that need to be conceptually distinguished and mapped to a statistical model for estimation. Method In the current work, we illustrate how common components from these new dynamic personality theories may be implemented in a continuous time-modeling framework. Results As an empirical example, we reanalyze experience sampling data with N = 180 persons (with on average T = 40 [SD = 8] measurement occasions) to investigate four different effects between momentary happiness, momentary extraverted behavior, and the perception of a situation as social: (1) between-person effects, (2) contemporaneous effects, (3) autoregressive effects, and (4) cross-lagged effects. Conclusion We highlight that these four effects must not necessarily point in the same direction, which is in line with assumptions from dynamic personality theories.Peer Reviewe

Local equilibrium of the quark-gluon plasma

Within kinetic theory, we look for local equilibrium configurations of the quark-gluon plasma by maximizing the local entropy. We use the well-established transport equations in the Vlasov limit, supplemented with the Waldmann-Snider collision terms. Two different classes of local equilibrium solutions are found. The first one corresponds to the configurations that comply with the so-called collisional invariants. The second one is given by the distribution functions that cancel the collision terms, representing the most probable binary interactions with soft gluon exchange in the t-channel. The two sets of solutions agree with each other if we go beyond these dominant processes and take into account subleading quark-antiquark annihilation/creation and gluon number non-conserving processes. The local equilibrium state appears to be colorful, as the color charges are not locally neutralized. Properties of such an equilibrium state are analyzed. In particular, the related hydrodynamic equations of a colorful fluid are derived. Possible neutralization processes are also briefly discussed.Comment: 20 pages; minor changes, to be published in Phys. Rev.

Fluctuations from dissipation in a hot non-Abelian plasma

We consider a transport equation of the Boltzmann-Langevin type for non-Abelian plasmas close to equilibrium to derive the spectral functions of the underlying microscopic fluctuations from the entropy. The correlator of the stochastic source is obtained from the dissipative processes in the plasma. This approach, based on classical transport theory, exploits the well-known link between a linearized collision integral, the entropy and the spectral functions. Applied to the ultra-soft modes of a hot non-Abelian (classical or quantum) plasma, the resulting spectral functions agree with earlier findings obtained from the microscopic theory. As a by-product, it follows that B\"odeker's effective theory is consistent with the fluctuation-dissipation theorem.Comment: 9 pages, revtex, no figures, identical to published versio