27,191 research outputs found
From patterned response dependency to structured covariate dependency: categorical-pattern-matching
Data generated from a system of interest typically consists of measurements
from an ensemble of subjects across multiple response and covariate features,
and is naturally represented by one response-matrix against one
covariate-matrix. Likely each of these two matrices simultaneously embraces
heterogeneous data types: continuous, discrete and categorical. Here a matrix
is used as a practical platform to ideally keep hidden dependency among/between
subjects and features intact on its lattice. Response and covariate dependency
is individually computed and expressed through mutliscale blocks via a newly
developed computing paradigm named Data Mechanics. We propose a categorical
pattern matching approach to establish causal linkages in a form of information
flows from patterned response dependency to structured covariate dependency.
The strength of an information flow is evaluated by applying the combinatorial
information theory. This unified platform for system knowledge discovery is
illustrated through five data sets. In each illustrative case, an information
flow is demonstrated as an organization of discovered knowledge loci via
emergent visible and readable heterogeneity. This unified approach
fundamentally resolves many long standing issues, including statistical
modeling, multiple response, renormalization and feature selections, in data
analysis, but without involving man-made structures and distribution
assumptions. The results reported here enhance the idea that linking patterns
of response dependency to structures of covariate dependency is the true
philosophical foundation underlying data-driven computing and learning in
sciences.Comment: 32 pages, 10 figures, 3 box picture
On a semiparametric survival model with flexible covariate effect.
A semiparametric hazard model with parametrized time but general covariate dependency is formulated and analyzed inside the framework of counting process theory. A profile likelihood principle is introduced for estimation of the parameters: the resulting estimator is n1/2-consistent, asymptotically normal and achieves the semiparametric efficiency bound. An estimation procedure for the nonparametric part is also given and its asymptotic properties are derived. We provide an application to mortality data.
The Estimation of Item Response Models with the lmer Function from the lme4 Package in R
In this paper we elaborate on the potential of the lmer function from the lme4 package in R for item response (IRT) modeling. In line with the package, an IRT framework is described based on generalized linear mixed modeling. The aspects of the framework refer to (a) the kind of covariates -- their mode (person, item, person-by-item), and their being external vs. internal to responses, and (b) the kind of effects the covariates have -- fixed vs. random, and if random, the mode across which the effects are random (persons, items). Based on this framework, three broad categories of models are described: Item covariate models, person covariate models, and person-by-item covariate models, and within each category three types of more specific models are discussed. The models in question are explained and the associated lmer code is given. Examples of models are the linear logistic test model with an error term, differential item functioning models, and local item dependency models. Because the lme4 package is for univariate generalized linear mixed models, neither the two-parameter, and three-parameter models, nor the item response models for polytomous response data, can be estimated with the lmer function.
Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS)
to regression with functional response. This allows us to simultaneously model
point-wise mean curves, variances and other distributional parameters of the
response in dependence of various scalar and functional covariate effects. In
addition, the scope of distributions is extended beyond exponential families.
The model is fitted via gradient boosting, which offers inherent model
selection and is shown to be suitable for both complex model structures and
highly auto-correlated response curves. This enables us to analyze bacterial
growth in \textit{Escherichia coli} in a complex interaction scenario,
fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
A unifying representation for a class of dependent random measures
We present a general construction for dependent random measures based on
thinning Poisson processes on an augmented space. The framework is not
restricted to dependent versions of a specific nonparametric model, but can be
applied to all models that can be represented using completely random measures.
Several existing dependent random measures can be seen as specific cases of
this framework. Interesting properties of the resulting measures are derived
and the efficacy of the framework is demonstrated by constructing a
covariate-dependent latent feature model and topic model that obtain superior
predictive performance
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An Overview of Models for Response Times and Processes in Cognitive Tests.
Response times (RTs) are a natural kind of data to investigate cognitive processes underlying cognitive test performance. We give an overview of modeling approaches and of findings obtained with these approaches. Four types of models are discussed: response time models (RT as the sole dependent variable), joint models (RT together with other variables as dependent variable), local dependency models (with remaining dependencies between RT and accuracy), and response time as covariate models (RT as independent variable). The evidence from these approaches is often not very informative about the specific kind of processes (other than problem solving, information accumulation, and rapid guessing), but the findings do suggest dual processing: automated processing (e.g., knowledge retrieval) vs. controlled processing (e.g., sequential reasoning steps), and alternative explanations for the same results exist. While it seems well-possible to differentiate rapid guessing from normal problem solving (which can be based on automated or controlled processing), further decompositions of response times are rarely made, although possible based on some of model approaches
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