103 research outputs found
Don't Tie Yourself to an Onion: Don’t Tie Yourself to Assumptions of Normality
A structural measurement model (Adams, Wilson, & Wu, 1997) consists of an item response theory model for responses conditional on ability and a structural model that describes the distribution of ability in the population. As a rule, ability is assumed to be normally distributed in the population. However, there are situations where there is reason to assume that the distribution of ability is nonnormal. In this paper, we show that nonnormal ability distributions are easily modeled in a Bayesian framewor
A Tutorial on Fisher Information
In many statistical applications that concern mathematical psychologists, the
concept of Fisher information plays an important role. In this tutorial we
clarify the concept of Fisher information as it manifests itself across three
different statistical paradigms. First, in the frequentist paradigm, Fisher
information is used to construct hypothesis tests and confidence intervals
using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher
information is used to define a default prior; lastly, in the minimum
description length paradigm, Fisher information is used to measure model
complexity
Logistic regression and Ising networks: prediction and estimation when violating lasso assumptions
The Ising model was originally developed to model magnetisation of solids in
statistical physics. As a network of binary variables with the probability of
becoming 'active' depending only on direct neighbours, the Ising model appears
appropriate for many other processes. For instance, it was recently applied in
psychology to model co-occurrences of mental disorders. It has been shown that
the connections between the variables (nodes) in the Ising network can be
estimated with a series of logistic regressions. This naturally leads to
questions of how well such a model predicts new observations and how well
parameters of the Ising model can be estimated using logistic regressions. Here
we focus on the high-dimensional setting with more parameters than observations
and consider violations of assumptions of the lasso. In particular, we
determine the consequences for both prediction and estimation when the sparsity
and restricted eigenvalue assumptions are not satisfied. We explain by using
the idea of connected copies (extreme multicollinearity) the fact that
prediction becomes better when either sparsity or multicollinearity is not
satisfied. We illustrate these results with simulations.Comment: to appear, Behaviormetrika, 201
Bayesian inference for low-rank Ising networks
Estimating the structure of Ising networks is a notoriously difficult problem. We demonstrate that using a latent variable representation of the Ising network, we can employ a full-data-information approach to uncover the network structure. Thereby, only ignoring information encoded in the prior distribution (of the latent variables). The full-data-information approach avoids having to compute the partition function and is thus computationally feasible, even for networks with many nodes. We illustrate the full-data-information approach with the estimation of dense network
Interpreting the Ising Model: The Input Matters
The Ising model is a model for pairwise interactions between binary variables
that has become popular in the psychological sciences. It has been first
introduced as a theoretical model for the alignment between positive (+1) and
negative (-1) atom spins. In many psychological applications, however, the
Ising model is defined on the domain instead of the classical domain
. While it is possible to transform the parameters of a given Ising
model in one domain to obtain a statistically equivalent model in the other
domain, the parameters in the two versions of the Ising model lend themselves
to different interpretations and imply different dynamics, when studying the
Ising model as a dynamical system. In this tutorial paper, we provide an
accessible discussion of the interpretation of threshold and interaction
parameters in the two domains and show how the dynamics of the Ising model
depends on the choice of domain. Finally, we provide a transformation that
allows to transform the parameters in an Ising model in one domain into a
statistically equivalent Ising model in the other domain
- …