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Related Concept Videos

Goodness-of-Fit Test01:16

Goodness-of-Fit Test

The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion.

David C Wheeler1, Demarc A Hickson, Lance A Waller

  • 1National Cancer Institute, 6120 Executive Boulevard, Bethesda, MD 20892.

Computational Statistics & Data Analysis
|January 19, 2011
PubMed
Summary

This study introduces a spatial local Deviance Information Criterion (DIC) for evaluating linear regression models. This method enhances model selection and understanding by visualizing local fit and parameter impacts.

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Area of Science:

  • Statistics
  • Spatial Analysis
  • Biostatistics

Background:

  • Assessing linear regression model adequacy is crucial for reliable analysis.
  • Existing methods like AIC and global DIC offer overall fit but lack local detail.
  • Visual assessment is vital for understanding model performance.

Purpose of the Study:

  • To introduce and evaluate a spatial local Deviance Information Criterion (DIC) for model selection and goodness-of-fit.
  • To develop visualization techniques for local model fit and influence.
  • To enhance understanding of Bayesian regression models in spatial contexts.

Main Methods:

  • Partitioning the DIC into local DIC, leverage, and deviance residuals.
  • Applying visualization techniques to local DIC and differences between models.
  • Utilizing a Bayesian framework for spatial analysis.

Main Results:

  • The local DIC effectively assesses local model fit and observation influence.
  • Visualizations of local DIC aid in refined model selection.
  • The approach clarifies the global and local impacts of covariates and parameters.

Conclusions:

  • Spatial local DIC provides a powerful tool for detailed model evaluation.
  • Visualization of local DIC improves understanding of complex spatial models.
  • This method offers enhanced diagnostic capabilities for regression analysis.