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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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Interpretation of Confidence Intervals01:19

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Abstract: Inference and Interval Estimation for Indirect Effects With Latent Variable Models.

Carl F Falk1, Jeremy C Biesanz1

  • 1a University of British Columbia.

Multivariate Behavioral Research
|January 7, 2016
PubMed
Summary
This summary is machine-generated.

For latent variable indirect effects, the percentile bootstrap and likelihood-based confidence intervals offer reliable statistical inference. Bias-corrected bootstrap methods showed inflated Type I error rates in this simulation study.

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Area of Science:

  • Social sciences
  • Psychometrics
  • Statistical modeling

Background:

  • Structural equation modeling (SEM) and indirect effect (mediation) models are widely used in social sciences.
  • Limited research exists comparing methods for latent variable indirect effects and their precise effectiveness.

Purpose of the Study:

  • To extensively compare methods for constructing confidence intervals and making inferences about indirect effects with latent variables.
  • To evaluate the performance of various statistical techniques under different simulation conditions.

Main Methods:

  • A simulation study comparing percentile (PC) bootstrap, bias-corrected (BC) bootstrap, bias-corrected accelerated (BC a ) bootstrap, likelihood-based confidence intervals, partial posterior predictive, and joint significance tests.
  • Models included three reflective latent variables (independent, dependent, mediating).
  • Crossed conditions included sample size (100-500), indicators per variable (3 vs. 5), reliability (.7 vs. .9), and path coefficients (16 combinations).

Main Results:

  • Bias-corrected (BC) and bias-corrected accelerated (BC a ) bootstrap methods demonstrated inflated Type I error rates.
  • Likelihood-based confidence intervals and the PC bootstrap method exhibited adequate Type I error control and good coverage rates.
  • Simulation results were based on 1,000 replications per condition and 2,000 resamples per bootstrap method.

Conclusions:

  • The percentile bootstrap and likelihood-based confidence intervals are recommended for robust inference on indirect effects in latent variable models.
  • Researchers should exercise caution when using BC and BC a bootstrap methods due to potential Type I error inflation.
  • This study provides valuable empirical evidence for selecting appropriate statistical methods in mediation analysis with latent variables.