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Related Concept Videos

State Space Representation01:27

State Space Representation

319
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.
Consider an RLC circuit, a...
319
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

134
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Experimental Designs01:16

Experimental Designs

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An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are three widely used types of experimental design - pre-experimental design, true experimental design, and quasi-experimental design. In pre-experimental design, the researcher compares the data before and after some interventions or treatments. The true-experimental design has more than one purposefully created group, a commonly measured...
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

95
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...
95
State Space to Transfer Function01:21

State Space to Transfer Function

339
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
339
Transfer Function to State Space01:23

Transfer Function to State Space

441
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
441

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Related Experiment Video

Updated: Oct 1, 2025

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
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Estimating and Testing Causal Mediation Effects in Single-Case Experimental Designs Using State-Space Modeling.

Benedikt Langenberg1, Ingrid C Wurpts2, Gemma G M Geuke3

  • 19167Bielefeld University, Bielefeld, Germany.

Evaluation & the Health Professions
|March 5, 2022
PubMed
Summary

This study introduces single-case causal mediation analysis, a new method for understanding change mechanisms in individuals. It uses state-space modeling to analyze direct and indirect treatment effects in single-case experiments.

Keywords:
experimental designsmediator variablespermutation testsperson-centered approachtime series

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Area of Science:

  • Psychology
  • Statistics
  • Behavioral Science

Background:

  • Single-case experimental designs (SCEDs) are valuable for studying individual change.
  • Causal mediation analysis is crucial for understanding mechanisms of change.
  • Integrating these approaches offers a powerful tool for researchers.

Purpose of the Study:

  • To present single-case causal mediation analysis (SCCMA).
  • To propose a novel time-discrete state-space modeling method for SCCMA.
  • To demonstrate SCCMA's application in analyzing treatment effects and mechanisms in individual data.

Main Methods:

  • Developed a time-discrete state-space modeling approach for SCCMA.
  • Applied the method to a single-case experiment on stress and craving in an alcohol consumer.
  • Conducted a simulation study to evaluate the estimation and testing of standardized indirect effects.

Main Results:

  • The proposed state-space model accurately estimated direct and indirect treatment effects.
  • Simulation results showed acceptable precision in parameter recovery.
  • Maximum likelihood and permutation procedures effectively calculated p-values and standard errors.

Conclusions:

  • Single-case causal mediation analysis, using state-space modeling, is a promising method for SCEDs.
  • The approach facilitates the investigation of mechanisms of change at the individual level.
  • Further research should address limitations concerning causal inference and time lag selection.