On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood

Karabatsos, George

doi:10.1007/s11336-017-9581-x

Cited by 14 publications

(15 citation statements)

References 19 publications

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“…However, we go further than analyzing simple "toy" models such as the dosage example above and consider models defined by arbitrarily complex linear constraints on multinomial parameters. Analyzing this class of model is known to be computationally challenging, especially for highly complex linear constraints as those defined by random preference models (Smeulders et al, 2018) and the axioms of additive conjoint measurement (Karabatsos, 2018). In the following, Section 1.1 highlights the relevance of inequality-constrained multinomial models for testing psychological theories.…”

Section: Introductionmentioning

confidence: 99%

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Heck

Davis‐Stober

2019

Journal of Mathematical Psychology

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Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices).For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq, which provides an easily-accessible interface to a computationally efficient implementation of these techniques.

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Section: Introductionmentioning

confidence: 99%

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Heck

Davis‐Stober

2019

Journal of Mathematical Psychology

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“…The abstract measurement theory (Krantz et al, 1971) can be viewed as a formal development of the theory of scale types by Stevens (1946). More recent literature provides ideas on how to apply abstract measurement theory to probabilistic models (Karabatsos, 2001;Karabatsos & Ullrich, 2002;Luce & Steingrimsson, 2011;Karabatsos, 2018;Šimkovic & Träuble, 2019). Historically, it has been the dominant theoretical framework to discuss the impact of the qualitative assumptions about measurement on the validity of statistical inferences (Anderson, 1961;Gaito, 1980;Stine, 1989).…”

Section: Implications Of Measurement Theory For the Analysis Of Looking Timesmentioning

confidence: 99%

Additive and multiplicative probabilistic models of infant looking times

Šimkovic¹,

Träuble²

2021

PeerJ

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Additive and multiplicative regression models of habituation were compared regarding the fit to looking times from a habituation experiment with infants aged between 3 and 11 months. In contrast to earlier studies, the current study considered multiple probability distributions, namely Weibull, gamma, lognormal and normal distribution. In the habituation experiment the type of contrast between the habituation and the test trial was varied (luminance, color or orientation contrast), crossed with the number of habituation trials (1, 3, 5, or 7 habituation trials) and crossed with three age cohorts (4, 7, 10 months). The initial mean LT to dark stimuli (around 3.7 s) was considerably shorter than the mean LT to green and gray stimuli (around 5 s). Infants showed the strongest dishabituation to changes from dark to bright (luminance contrast) and weak-to-no dishabituation to a 90-degrees rotation of the gray stimuli (orientation contrast). The dishabituation was stronger after five and seven habituation trials, but the result was not statistically robust. The gamma distribution showed the best fit in terms of log-likelihood and mean absolute error and the best predictive performance. Furthermore, the gamma distribution showed small correlations between parameters relative to other models. The normal additive model showed an inferior fit and medium correlations between the parameters. In particular, the positive correlation between the initial looking time (LT) and the habituation rate was likely responsible for a different interpretation relative to the multiplicative models of the main effect of age on the habituation rate. Otherwise, the additive and multiplicative models provided similar statistical conclusions. The performance of the model versions without pooling and with partial pooling across participants (also called random-effects, multi-level or hierarchical models) were compared. The latter type of models showed worse data fit but more precise predictions and reduced correlations between the parameters. The performance of model variants with auto-regressive time structures were explored but showed considerably worse fit. The performance of quadratic models that allowed non-monotonic changes in LTs were investigated as well. However, when fitted with LT data, these models did not produce non-monotonic change in LTs. The study underscores the utility of partial-pooling models in terms of providing more accurate predictions. Further, it agrees with previous research in that a multiplicative LT model is preferable. Nevertheless, the current results suggest that the impact of the choice of an additive model on the statistical inference is less dramatic then previously assumed.

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“…We can sample or simulate data from this kind of models but their likelihood function is typically too costly to evaluate. The models are called implicit (Diggle and Gratton, 1984) or simulator-based models (Gutmann and Corander, 2016) and are widely used in scientific domains including ecology (Wood, 2010), epidemiology (Corander et al, 2017), psychology (Karabatsos, 2017) and cosmology (Weyant et al, 2013). For example, the demographic evolution of two species can be simulated by a set of stochastic differential equations controlled by birth/predation rates but computation of the likelihood is intractable.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Gaussian Copula ABC

Chen,

Gutmann

2019

Preprint

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Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the combination of two classical ABC approaches -regression ABC and sequential ABC. The key idea is that rather than learning the posterior directly, we first target another auxiliary distribution that can be learned accurately by existing methods, through which we then subsequently learn the desired posterior with the help of a Gaussian copula. During this process, the complexity of the model changes adaptively according to the data at hand. Experiments on a synthetic dataset as well as three real-world inference tasks demonstrates that the proposed method is fast, accurate, and easy to use.

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On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood

Cited by 14 publications

References 19 publications

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Additive and multiplicative probabilistic models of infant looking times

Adaptive Gaussian Copula ABC

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