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William R Shadish1, Alain F Zuur2, Kristynn J Sullivan1

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Summary
This summary is machine-generated.

Generalized additive models (GAMs) and generalized additive mixed models (GAMMs) offer advanced analysis for single-case design data. These methods effectively detect trends and assess treatment effectiveness, variability, and phase consistency.

Keywords:
Generalized additive modelMixed modelNonlinearitySingle-case designTrend

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Area of Science:

  • Behavioral Science
  • Statistical Modeling
  • Research Methodology

Background:

  • Single-case designs are crucial for evaluating interventions in various fields.
  • Traditional analysis methods may not fully capture the complexity of single-case data, such as trend and variability.
  • Generalized additive models (GAMs) and generalized additive mixed models (GAMMs) offer flexible approaches to analyze such data.

Purpose of the Study:

  • To demonstrate the application of GAMs and GAMMs for analyzing single-case design data.
  • To highlight the capability of these models in assessing key single-case research elements: level, trend, variability, overlap, immediacy, and phase consistency.
  • To provide guidance on testing treatment effectiveness, case differences, and variations in treatment effects and trends across cases.

Main Methods:

  • Application of generalized additive models (GAMs) and generalized additive mixed models (GAMMs).
  • Analysis of single-case design data, focusing on trend detection (linear and nonlinear).
  • Implementation using the R programming language, including syntax for quasibinomial models for overdispersed data and estimation of autoregressive and random effects.

Main Results:

  • GAMs and GAMMs effectively detect the functional form and shape of trends in single-case data.
  • These models can analyze treatment effectiveness, individual case differences, and variations in effects and trends.
  • Diagnostic statistics, graphs, and methods for handling overdispersion (e.g., quasibinomial models) are illustrated.

Conclusions:

  • GAMs and GAMMs provide a robust framework for analyzing complex single-case design data.
  • These statistical models enhance the interpretation of functional relations by considering multiple data characteristics.
  • The provided R syntax facilitates the practical implementation of these advanced analytical techniques in research.