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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Ordinal Outcome State-Space Models for Intensive Longitudinal Data.

Teague R Henry1, Lindley R Slipetz1, Ami Falk1

  • 1University of Virginia.

Psychometrika
|February 25, 2026
PubMed
Summary
This summary is machine-generated.

State-space models for intensive longitudinal (IL) data can now handle ordinal measurements, like Likert scales, using a new graded response model. This approach provides unbiased estimates of psychological dynamics, unlike linear approximations.

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

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Area of Science:

  • Psychological Science
  • Quantitative Psychology
  • Behavioral Science

Background:

  • Intensive longitudinal (IL) data, collected frequently (e.g., daily diary, ecological momentary assessments), are crucial for understanding psychological and behavioral dynamics.
  • State-space modeling is a powerful framework for analyzing IL data, treating observed variables as indicators of underlying latent states that evolve over time.
  • Traditional state-space models often assume continuous measurements, which is a limitation as psychological data frequently consists of ordinal measurements (e.g., Likert scales).

Purpose of the Study:

  • To develop a general estimation approach for state-space models specifically designed for ordinal measurements.
  • To introduce a graded response model tailored for Likert scale data within the state-space framework.
  • To compare the performance of the proposed ordinal model against the conventional linear approximation method.

Main Methods:

  • Development of a novel estimation approach for state-space models accommodating ordinal data.
  • Implementation of a graded response model for Likert scale items within the state-space framework.
  • Comparative analysis evaluating the proposed model against the linear approximation method using simulated or real-world data.

Main Results:

  • The proposed state-space model with ordinal measurements yielded unbiased estimates of the underlying state dynamics.
  • The commonly used linear approximation method, treating ordinal data as continuous, produced significantly biased estimates of state dynamics.
  • An approximate standard error, termed slice standard errors, was developed and found to be more liberal (smaller) than true standard errors, indicating a consistent bias.

Conclusions:

  • The developed state-space model provides a more accurate method for analyzing intensive longitudinal data with ordinal measurements compared to linear approximations.
  • Accurate estimation of psychological and behavioral dynamics is essential, and the proposed model offers a significant improvement for Likert scale data.
  • Further research is needed to refine standard error estimation for the proposed model, addressing the observed bias in slice standard errors.