1,721,029 research outputs found
Selection Tests for possibly misspecified hierarchical multinomial marginal models
No full textHierarchical marginal models have been proposed for categorical data to overcome some limitations of the log-linear approach in modeling marginal distributions. These models can easily satisfy marginal conditional independence conditions and describe with great flexibility the dependence of marginal distributions on covariates. As the richness of the family of hierarchical marginal models leads to comparing models that do not satisfy a nesting relationship, statistical tests for model selection from non-nested, possibly mis- specified marginal models are introduced
Maximum likelihood inference for log-linear models subject to constraints of double monotone dependence
No full textTo model an hypothesis of double monotone dependence between two ordinal categorical variables and usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined respectively on the conditional distributions of given and on the conditional distributions of given are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model
Hierarchical Multinomial Marginal Models
No full textQuesto lavoro descrive i modelli marginali gerarchici per tabelle di contingenza multidimensionali basati su una parametrizzazione delle probabilità congiunte proposta da Bartolucci et al. (2007). Questa classe di modelli include come casi particolari molti modelli per tabelle di contingenza, introdotti come alternative ai modelli log-lineari per ovviare alle ben note limitazioni di questi ultimi nel parametrizzare distribuzioni marginali e nel trattare in modo appropriato le variabili ordinali. L’utilità dei modelli presentati è illustrata nel contesto della parametrizzazione di modelli ricorsivi a blocchi specificati dalle proprietà markoviane di Andersson, Madigan e Perlman
Modelling different behaviours in disclosing risk perception
No full textIn many fields, people are requested to express their level of awareness about some risk (mainly associated with health, environment, energy, etc.) by selecting a category in an ordered scale.We propose a model for such ordinal data by taking into account that the observed response does not necessarily reflect the respondent’s true opinion since the final answer can be inaccurate or completely random. The proposed model hypothesizes three behaviors in the process of answering: accurate interviewees express their risk perception exactly, uncertain ones randomly select the response according to the uniform distribution, and inaccurate interviewees make evaluation errors but with high probability they choose a rating close to the true one. Statistical inference for the proposed models is addressed without assuming that the model, to be fitted, is correctly specified. Two real case studies on the awareness of geo-hydrological risk and work-related stress risk are considered using the proposed methodology
A class of smooth models satisfying marginal and context specific conditional independencies
No full textWe study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional independence models which are known to be non-smooth belong to this class. We introduce a new marginal log-linear parameterization and show that smoothness may be restored by restricting one or more independence statements to hold conditionally to a restricted subset of the configurations of the conditioning variables. Our results are based on a specific reconstruction algorithm from log-linear parameters to probabilities and fixed point theory. Several examples are examined and a general rule for determining the implied conditional independence restrictions is outlined
Multiple hidden Markov models for categorical time series
No full textWe introduce multiple hidden Markov models (MHMMs) where a multivariate categorical time series depends on a latent multivariate Markov chain. MHMMs provide an elegant framework for specifying various independence relationships between multiple discrete time processes. These independencies are interpreted as Markov properties of a mixed graph and a chain graph associated respectively to the latent and observation components of the MHMM. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of observable variables given the latent states
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