Generating random correlation matrices based on vines and extended onion method

Lewandowski, Daniel; Kurowicka, Dorota; Joe, Harry

doi:10.1016/j.jmva.2009.04.008

Cited by 838 publications

(694 citation statements)

References 6 publications

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“…As mentioned in Section 2, the LKJ-correlation prior with parameter ζ > 0 ( Lewandowski et al 2009) is used for this purpose. In brms, this prior is abbreviated as "lkj(zeta)" and correlation matrix parameters are named as cor_<group>, (e.g., cor_patient), so that set_prior("lkj(2)", class = "cor", group = "patient") is a valid statement.…”

Section: Prior: Prior Distributions Of Model Parametersmentioning

confidence: 99%

brms: An R Package for Bayesian Multilevel Models Using Stan

Bürkner¹

2017

J. Stat. Soft.

6,654

5,501

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The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit -among others -linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.

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Section: Prior: Prior Distributions Of Model Parametersmentioning

confidence: 99%

brms: An R Package for Bayesian Multilevel Models Using Stan

Bürkner¹

2017

J. Stat. Soft.

6,654

5,501

View full text Add to dashboard Cite

show abstract

“…We define priors on and : Each element in is specified to be drawn from the positive half-Cauchy distribution such that σ ∼ C + (0,2.5). A suitable prior for is the LKJ Cholesky distribution (Lewandowski et al, 2009), whose density is given by …”

Section: Appendix A: Monte Carlo Experimentsmentioning

confidence: 99%

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Vij

Krueger

2017

Transportation Research Part B: Methodological

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This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any arbitrary degree of accuracy. The grid with unequal intervals, in particular, offers greater flexibility than existing multivariate nonparametric specifications, while requiring the estimation of a small number of additional parameters. An expectation maximization algorithm is developed for the estimation of these models. Multiple synthetic datasets and a case study on travel mode choice behavior are used to demonstrate the value of the model framework and estimation algorithm. Compared to extant models that incorporate random taste heterogeneity through continuous mixture distributions, the proposed model provides better out-of-sample predictive ability. Findings reveal significant differences in willingness to pay measures between the proposed model and extant specifications. The case study further demonstrates the ability of the proposed model to endogenously recover patterns of attribute non-attendance and choice set formation.3

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“…As Lewandowski-Kurowicka-Joe [2009] point out, the speed of calculations is an important aspect in generating a set of random correlation matrices. In this paper, the elements of (symmetric) matrices are generated as uniformly distributed random variables that are between -1 and 1, and the positive semidefinite matrices are considered as simulated correlation matrices.…”

Section: Hungarian Statistical Review Special Number 21mentioning

confidence: 99%

Comparison of goodness measures for linear factor structures

Szüle¹

2017

Statisztikai szemle

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Linear factor structures often exist in empirical data, and they can be mapped by factor analysis. It is, however, not straightforward how to measure the goodness of a factor analysis solution since its results should correspond to various requirements. Instead of a unique indicator, several goodness measures can be defined that all contribute to the evaluation of the results.This paper aims to find an answer to the question whether factor analysis outputs can meet several goodness criteria at the same time. Data aggregability (measured by the determinant of the correlation matrix and the proportion of explained variance) and the extent of latency (defined by the determinant of the antiimage correlation matrix, the maximum partial correlation coefficient and the Kaiser-Meyer-Olkin measure of sampling adequacy) are studied. According to the theoretical and simulation results, it is not possible to meet simultaneously these two criteria when the correlation matrices are relatively small. For larger correlation matrices, however, there are linear factor structures that combine good data aggregability with a high extent of latency.

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Generating random correlation matrices based on vines and extended onion method

Cited by 838 publications

References 6 publications

brms: An R Package for Bayesian Multilevel Models Using Stan

brms: An R Package for Bayesian Multilevel Models Using Stan

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Comparison of goodness measures for linear factor structures

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