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Joint analysis of dispersed count-time data using a bivariate latent factor model.

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This study introduces a new statistical model for joint count and time data, enhancing accuracy and speed measurements. The Beta-binomial model improves fit for complex data, with bootstrap methods offering reliable standard error estimation.

Keywords:
Beta‐binomial distributionaccuracy count dataitem response theoryoral reading fluencyoverdispersionpsychometric calibrationresponse time analysis

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Data Analysis

Background:

  • Accurate measurement of accuracy and speed is crucial in various fields.
  • Existing models may not fully capture the complexities of joint count-time data.
  • Over-dispersion in count data is common and requires specialized distributions.

Purpose of the Study:

  • To develop and evaluate a joint count-time data model with a two-factor latent trait structure.
  • To implement parameter estimation using method-of-moments (MOM) and maximum likelihood estimation (MLE) via Monte Carlo Expectation-Maximization (MCEM).
  • To assess the performance of standard error estimation methods, particularly bootstrap resampling.

Main Methods:

  • Utilized a Beta-binomial distribution for count variables and a log-normal distribution for time variables.
  • Derived marginal moments for method-of-moments (MOM) estimators.
  • Employed Monte Carlo Expectation-Maximization (MCEM) for maximum likelihood estimation (MLE).
  • Estimated standard errors using the observed information matrix and bootstrap resampling.

Main Results:

  • Simulation studies demonstrated the accuracy and computational efficiency of the proposed estimators.
  • Bootstrap resampling showed superior performance for standard error estimation, especially for dispersion parameters.
  • Analysis of oral reading fluency (ORF) data revealed significant item-level dispersion variations.
  • The Beta-binomial model provided an improved fit compared to standard models, confirmed by SRMSR values.

Conclusions:

  • The developed joint count-time model effectively captures latent traits related to accuracy and speed.
  • The Beta-binomial distribution is advantageous for modeling over-dispersed count data in this context.
  • Bootstrap resampling is a robust method for estimating standard errors in complex models.
  • The methodology offers a valuable tool for analyzing complex measurement data, as shown with ORF data.