3,502 research outputs found
Estimation of latent variable models for ordinal data via fully exponential Laplace approximation
Latent variable models for ordinal data represent a useful tool in different
fields of research in which the constructs of interest are not directly
observable. In such models, problems related to the integration of the
likelihood function can arise since analytical solutions do not exist.
Numerical approximations, like the widely used Gauss Hermite (GH) quadrature,
are generally applied to solve these problems. However, GH becomes unfeasible
as the number of latent variables increases. Thus, alternative solutions have
to be found. In this paper, we propose an extended version of the Laplace
method for approximating the integrals, known as fully exponential Laplace
approximation. It is computational feasible also in presence of many latent
variables, and it is more accurate than the classical Laplace method
Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data
Much of the trading activity in Equity markets is directed to brokerage
houses. In exchange they provide so-called "soft dollars," which basically are
amounts spent in "research" for identifying profitable trading opportunities.
Soft dollars represent about USD 1 out of every USD 10 paid in commissions.
Obviously they are costly, and it is interesting for an institutional investor
to determine whether soft dollar inputs are worth being used (and indirectly
paid for) or not, from a statistical point of view. To address this question,
we develop association measures between what broker--dealers predict and what
markets realize. Our data are ordinal predictions by two broker--dealers and
realized values on several markets, on the same ordinal scale. We develop a
structural equation model with latent variables in an ordinal setting which
allows us to test broker--dealer predictive ability of financial market
movements. We use a multivariate logit model in a latent factor framework,
develop a tractable estimator based on a Laplace approximation, and show its
consistency and asymptotic normality. Monte Carlo experiments reveal that both
the estimation method and the testing procedure perform well in small samples.
The method is then used to analyze our dataset.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS213 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Hyper-g Priors for Generalized Linear Models
We develop an extension of the classical Zellner's g-prior to generalized
linear models. The prior on the hyperparameter g is handled in a flexible way,
so that any continuous proper hyperprior f(g) can be used, giving rise to a
large class of hyper-g priors. Connections with the literature are described in
detail. A fast and accurate integrated Laplace approximation of the marginal
likelihood makes inference in large model spaces feasible. For posterior
parameter estimation we propose an efficient and tuning-free
Metropolis-Hastings sampler. The methodology is illustrated with variable
selection and automatic covariate transformation in the Pima Indians diabetes
data set.Comment: 30 pages, 12 figures, poster contribution at ISBA 201
Asymptotic properties of adaptive maximum likelihood estimators in latent variable models
Latent variable models have been widely applied in different fields of
research in which the constructs of interest are not directly observable, so
that one or more latent variables are required to reduce the complexity of the
data. In these cases, problems related to the integration of the likelihood
function of the model arise since analytical solutions do not exist. In the
recent literature, a numerical technique that has been extensively applied to
estimate latent variable models is the adaptive Gauss-Hermite quadrature. It
provides a good approximation of the integral, and it is more feasible than
classical numerical techniques in presence of many latent variables and/or
random effects. In this paper, we formally investigate the properties of
maximum likelihood estimators based on adaptive quadratures used to perform
inference in generalized linear latent variable models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ531 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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