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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

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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.
A...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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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.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Profile-likelihood Confidence Intervals in Item Response Theory Models.

R Philip Chalmers1, Jolynn Pek2, Yang Liu3

  • 1a Department of Educational Psychology , The University of Georgia.

Multivariate Behavioral Research
|June 9, 2017
PubMed
Summary

Profile-likelihood confidence intervals (PL CIs) offer a superior alternative to traditional Wald-type confidence intervals (CIs) in item response theory. Simulations show PL CIs provide more reliable estimates for both direct and transformed parameters.

Keywords:
Item response theoryWald confidence intervalslarge-sample confidence intervalslikelihood inferenceprofile-likelihood confidence intervals

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Area of Science:

  • Statistics
  • Psychometrics
  • Educational Measurement

Background:

  • Confidence intervals (CIs) are crucial for quantifying parameter estimate variability in inferential statistics.
  • Traditional CIs in item response theory (IRT) often rely on large-sample approximations (Wald-type) using maximum likelihood estimation.
  • These methods can be limited by sample size and parameter characteristics.

Purpose of the Study:

  • Introduce and evaluate profile-likelihood confidence intervals (PL CIs) as an alternative to Wald-type CIs in IRT models.
  • Compare the performance of PL CIs against classical Wald-type CIs.
  • Assess CI performance for both directly estimated and post-estimated transformed parameters.

Main Methods:

  • Developed and applied profile-likelihood confidence intervals (PL CIs) for IRT parameters.
  • Conducted Monte Carlo simulations to compare PL CIs with Wald-type CIs.
  • Evaluated CIs for both non-transformed and transformed IRT parameters.

Main Results:

  • Profile-likelihood confidence intervals (PL CIs) demonstrated consistently superior performance compared to Wald-type confidence intervals.
  • This improved performance was observed for both directly estimated parameters and transformed parameters.
  • PL CIs offer a more robust method for quantifying uncertainty in IRT parameter estimates.

Conclusions:

  • Profile-likelihood confidence intervals (PL CIs) are recommended for constructing confidence intervals in item response theory.
  • PL CIs provide more accurate and reliable interval estimates than traditional Wald-type methods, especially for transformed parameters.
  • This advancement enhances the precision of inferential statistics in IRT applications.