95,034 research outputs found
Generating Correlated Ordinal Random Values
Ordinal variables appear in many field of statistical research. Since working with simulated data is an accepted technique to improve models or test results there is a need for providing correlated ordinal random values with certain properties like marginal distribution and correlation structure. The present paper describes two methods for generating such values: binary conversion and a mean mapping approach. The algorithms of the two methods are described and some examples of the outcomes are shown
Bayesian Estimation Under Informative Sampling
Bayesian analysis is increasingly popular for use in social science and other
application areas where the data are observations from an informative sample.
An informative sampling design leads to inclusion probabilities that are
correlated with the response variable of interest. Model inference performed on
the observed sample taken from the population will be biased for the population
generative model under informative sampling since the balance of information in
the sample data is different from that for the population. Typical approaches
to account for an informative sampling design under Bayesian estimation are
often difficult to implement because they require re-parameterization of the
hypothesized generating model, or focus on design, rather than model-based,
inference. We propose to construct a pseudo-posterior distribution that
utilizes sampling weights based on the marginal inclusion probabilities to
exponentiate the likelihood contribution of each sampled unit, which weights
the information in the sample back to the population. Our approach provides a
nearly automated estimation procedure applicable to any model specified by the
data analyst for the population and retains the population model
parameterization and posterior sampling geometry. We construct conditions on
known marginal and pairwise inclusion probabilities that define a class of
sampling designs where consistency of the pseudo posterior is
guaranteed. We demonstrate our method on an application concerning the Bureau
of Labor Statistics Job Openings and Labor Turnover Survey.Comment: 24 pages, 3 figure
Selection Bias Correction and Effect Size Estimation under Dependence
We consider large-scale studies in which it is of interest to test a very
large number of hypotheses, and then to estimate the effect sizes corresponding
to the rejected hypotheses. For instance, this setting arises in the analysis
of gene expression or DNA sequencing data. However, naive estimates of the
effect sizes suffer from selection bias, i.e., some of the largest naive
estimates are large due to chance alone. Many authors have proposed methods to
reduce the effects of selection bias under the assumption that the naive
estimates of the effect sizes are independent. Unfortunately, when the effect
size estimates are dependent, these existing techniques can have very poor
performance, and in practice there will often be dependence. We propose an
estimator that adjusts for selection bias under a recently-proposed frequentist
framework, without the independence assumption. We study some properties of the
proposed estimator, and illustrate that it outperforms past proposals in a
simulation study and on two gene expression data sets.Comment: 21 pages, 2 figure
- ā¦