Hierarchical models in ecology: confidence intervals, hypothesis testing, and model selection using data cloning

Ecology ◽  
2009 ◽  
Vol 90 (2) ◽  
pp. 356-362 ◽  
Author(s):  
José Miguel Ponciano ◽  
Mark L. Taper ◽  
Brian Dennis ◽  
Subhash R. Lele
Keyword(s):  
Model Selection ◽  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Hierarchical Models ◽  
Data Cloning ◽  
Using Data

Confidence intervals for a difference between lognormal means in cluster randomization trials

2014 ◽  
Vol 26 (2) ◽  
pp. 598-614 ◽  
Author(s):  
Julia Poirier ◽  
GY Zou ◽  
John Koval
Keyword(s):  
Confidence Intervals ◽  
Community Acquired Pneumonia ◽  
Small Sample ◽  
Cluster Randomization ◽  
Critical Pathway ◽  
Arithmetic Means ◽  
Multiple Parameters ◽  
The Difference ◽  
Using Data ◽  
Small Sample Sizes

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

Uncertainty and Inference for Verification Measures

2007 ◽  
Vol 22 (3) ◽  
pp. 637-650 ◽  
Author(s):  
Ian T. Jolliffe
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Multiple Testing ◽  
Prediction Intervals ◽  
Hypothesis Tests ◽  
Statistical Inferences ◽  
The Difference ◽  
Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

Confidence Intervals and Hypothesis Testing

2013 ◽  
pp. 417-453
Author(s):  
Pierre Lafaye de Micheaux ◽  
Rémy Drouilhet ◽  
Benoit Liquet
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals
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