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Related Concept Videos

Expected Frequencies in Goodness-of-Fit Tests01:19

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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).
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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
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Bootstrap-adjusted quasi-likelihood information criteria for mixed model selection.

Wentao Ge1, Junfeng Shang2

  • 1RevSpring, Newark, OH, USA.

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We introduce two new bootstrap-based model selection criteria, QAICb1 and QAICb2, for linear mixed models. These criteria offer improved accuracy in estimating model discrepancies, outperforming existing methods in simulations and real-world data analysis.

Keywords:
Compound symmetric structureKullback–Leibler discrepancyasymptotically unbiased estimatorautoregressive correlation structurenonparametric bootstrapsemiparametric bootstrap

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Model selection is crucial for accurate statistical inference.
  • Linear mixed models are widely used for complex data structures.
  • Existing criteria may have limitations in bias estimation.

Purpose of the Study:

  • To propose novel bootstrap-based model selection criteria (QAICb1, QAICb2) for linear mixed models.
  • To establish the asymptotic unbiasedness of these criteria as estimators of Kullback-Leibler discrepancy.
  • To demonstrate the superiority of the proposed criteria over existing methods.

Main Methods:

  • Development of two quasi-likelihood-based bootstrap criteria (QAICb1, QAICb2).
  • Theoretical proof of asymptotic unbiasedness and equivalence.
  • Monte Carlo simulations across diverse mixed model settings.
  • Utilizing generalized estimating equations (GEE) for criterion calculation.

Main Results:

  • QAICb1 and QAICb2 are asymptotically unbiased estimators of Kullback-Leibler discrepancy.
  • Proposed criteria demonstrated superior performance in selecting the true model compared to existing methods in simulations.
  • Effectiveness validated using Parkinson's Progression Markers Initiative (PPMI) data.

Conclusions:

  • The proposed QAICb1 and QAICb2 criteria provide a robust approach to model selection in linear mixed models.
  • Bootstrap methodology enhances bias estimation, leading to improved model selection accuracy.
  • These criteria offer a valuable tool for researchers analyzing complex longitudinal or clustered data.