Bayesian Tests and Model Diagnostics in Conditionally Independent Hierarchical Models

Albert, Jim; Chib, Siddhartha

doi:10.2307/2965555

Cited by 32 publications

(28 citation statements)

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“…Although rare today in cognitive modeling, random effects modeling of the variability in data is common within biostatistics and psychometrics, including the use of a number of statistically sophisticated methods. We believe that a researcher may be able to use the parameter distributions estimated from one of these augmented models to better understand the nature of the underlying participant or item variability (e.g., Albert, 1999;Albert & Chib, 1997). In turn, this exploratory knowledge may point the way to how best to incorporate random effect assumptions into a particular cognitive model.…”

Section: Modeling Inhomogeneities In the Data The Case Of Heterogeneimentioning

confidence: 99%

Assessing individual differences in categorical data

Smith

Batchelder

2008

Psychonomic Bulletin & Review

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This article develops statistical methods to detect individual differences in cognitive data in the form of categorical observations from a set of participants, each of whom responds to the same set of item events-for example, memory items, item serial positions, or repeated choice trials. The purpose of these methods is to determine whether there is heterogeneity in either participants or item events that might make it inappropriate to aggregate the data, respectively, over participants or item events. These determinations are especially important in the case where the data will be analyzed with a cognitive model. If heterogeneity in participants or item events is detected, several recent developments in computational statistics make it feasible to augment a parametric model with a hierarchical level that models random effects on the parameters. On the other hand, a model that includes random effects assumptions on the parameters is clearly more complex (e.g., Myung & Pitt, 1997) and capable of accounting for more data than the same model is, assuming that all effects are equal; so the decision of whether or not to include random effects in a model analysis is a crucial one. Our methods for informing this decision, because they are based on the sampling assumptions of the basic data structure itself, are completely agnostic as to the appropriate cognitive model underlying the data. Before developing the methods, it is useful to review the way that most cognitive models have been employed in the past and how researchers have tried to deal with parametric heterogeneity.Parametric stochastic models of cognition are usually assessed with data taken from one or more experimental conditions consisting of a group of participants, each of whom provides responses to the same set of item events (hereafter, items). Within a given experimental condition, subsets of these observations are usually pooled (aggregated) and treated as if they are a sample from the cognitive model. In the terminology of mathematical statistics, the assumption that a sequence of observations constitutes a sample from a parametric model means that the observations arise from a sequence of independent and identically distributed (i.i.d.) random variables, whose common distribution is determined through the model equations by some fixed but unknown set of model parameters (e.g., Hogg, McKean, & Craig, 2005;Lehmann & Romano, 2005). One particular form of this assumption is when data on a particular item are aggregated over participants and analyzed on the assumption of no individual differences-that is, the assumption of participant homogeneity. Another form of the assumption is when the data from each particular participant are treated as a sample over items. It is not uncommon in list-memory experiments (e.g., the middle items of free recall, old or new items in recognition memory) to aggregate the data over both participants and items, thereby treating all the observations in some experimental condition as a sample from the model.Most examples in ...

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Section: Modeling Inhomogeneities In the Data The Case Of Heterogeneimentioning

confidence: 99%

Assessing individual differences in categorical data

Smith

Batchelder

2008

Psychonomic Bulletin & Review

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“…There are a number of model selection approaches, such as P-value based, Akaike Information Criterion [Akaike 1973], the Bayesian information criterion [Albert and Chib 1997] or Principal Component Analysis (PCA) [Wold et al 1987]. DETect uses Least Absolute Shrinkage and Selection Operation (LASSO) [Tibshirani 1996], which provides the best trade-off between accuracy, efficiency and complexity.…”

Section: Modelling Unitmentioning

confidence: 99%

Decentralised Detection of Emergence in Complex Adaptive Systems

O'Toole

Nallur

Clarke

2017

ACM Trans. Auton. Adapt. Syst.

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This paper describes Decentralised Emergence Detection (DETect), a novel distributed algorithm that enables agents to collaboratively detect emergent events in Complex Adaptive Systems (CAS). Nondeterministic interactions between agents in CAS can give rise to emergent behaviour or properties at the system level. The nature, timing and consequence of emergence is unpredictable and may be harmful to the system or individual agents. DETect relies on the feedback that occurs from the system level (macro) to the agent level (micro) when emergence occurs. This feedback constrains agents at the micro-level, and results in changes occurring in the relationship between an agent and its environment. DETect uses statistical methods to automatically select the properties of the agent and environment to monitor, and tracks the relationship between these properties over time. When a significant change is detected, the algorithm uses distributed consensus to determine if a sufficient number of agents have simultaneously experienced a similar change. On agreement of emergence, DETect raises an event, which its agent or other interested observers can use to act appropriately. The approach is evaluated using a multi-agent case study.

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“…Let ( | 1 ) and ( | 2 ) denote the marginal density of data under 1 and 2 , respectively. A popular choice for selecting models is achieved via Bayes factor (BF) (e.g., [37][38][39]). However, in view of the fact that computing BF involves the high-dimensional density which is hard to estimate well, we prefer comparing the following logarithm of pseudomarginal likelihood (LPML) [40,41]:…”

Section: Model Selection Model Selection Is An Important Issue Inmentioning

confidence: 99%

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

Xia

Gou

2016

Journal of Applied Mathematics

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Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology.

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Bayesian Tests and Model Diagnostics in Conditionally Independent Hierarchical Models

Cited by 32 publications

References 0 publications

Assessing individual differences in categorical data

Assessing individual differences in categorical data

Decentralised Detection of Emergence in Complex Adaptive Systems

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

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