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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Ordinal Outcome State-Space Models for Intensive Longitudinal Data.

Teague R Henry1, Lindley R Slipetz2, Ami Falk2

  • 1Department of Psychology and School of Data Science, University of Virginia, Charlottesville, USA. ycp6wm@virginia.edu.

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|June 11, 2024
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Summary
This summary is machine-generated.

New state-space models accurately analyze ordinal intensive longitudinal (IL) data, unlike linear approximations. This improves understanding of psychological dynamics captured through daily diary and ecological momentary assessments.

Keywords:
ecological momentary assessmentintensive longitudinal dataitem response theoryordinal measurementsparticle filteringstate-space modeling

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Area of Science:

  • Psychological Science
  • Quantitative Psychology
  • Psychometrics

Background:

  • Intensive longitudinal (IL) data, collected frequently (e.g., daily diary, ecological momentary assessments), are vital for understanding psychological dynamics.
  • State-space modeling is a powerful framework for analyzing IL data, but traditionally requires continuous measurements.
  • Psychological research often involves ordinal data (e.g., Likert scales), posing a challenge for existing state-space models.

Purpose of the Study:

  • To develop a general estimation approach for state-space models accommodating ordinal measurements.
  • To specifically address Likert scale data using a graded response model within state-space analysis.
  • To compare the performance of the new ordinal model against the traditional linear approximation method.

Main Methods:

  • Developed a novel state-space modeling approach for ordinal data, incorporating a graded response model.
  • Employed simulation studies to evaluate the accuracy and bias of the proposed model.
  • Compared the proposed model's parameter estimates and state dynamics against a linear approximation approach.

Main Results:

  • The proposed state-space model with ordinal measurements yielded unbiased estimates of state dynamics.
  • The conventional linear approximation method, treating ordinal data as continuous, produced significantly biased estimates.
  • Introduced 'slice standard errors' for approximate confidence intervals, noting they tend to be more liberal (smaller) than true standard errors.

Conclusions:

  • The developed state-space model provides accurate estimation for intensive longitudinal data with ordinal measurements.
  • Treating ordinal data as continuous in state-space models can lead to substantial biases in psychological research.
  • The new methodology enhances the analysis of complex psychological processes using readily available ordinal data formats.