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Autoregressive growth curves and Kalman filtering
1Department of Epidemiology & Preventive Medicine, University of Maryland, School of Medicine, Baltimore 21201.
Statistics in Medicine
|January 1, 1988
Summary
This study uses a Kalman filter to estimate parameters for polynomial growth curves with autoregressive errors, introducing a novel disturbed highest derivative polynomial model for flexible analysis of individual and population growth, even with irregular data.
Area of Science:
- Statistics
- Biostatistics
- Time Series Analysis
Background:
- Estimating parameters in polynomial growth curves with autoregressive (AR) errors and irregularly-spaced data presents analytical challenges.
- Existing models may require equally spaced data or rely heavily on regression coefficients, limiting flexibility.
- A need exists for robust growth curve models adaptable to complex error structures and non-uniform sampling.
Purpose of the Study:
- To develop and apply a Kalman filter approach for maximum likelihood (ML) estimation of parameters in polynomial growth curves with AR-1 errors.
- To introduce the disturbed highest derivative polynomial (DHDP) as a novel, flexible model for growth curves.
- To extend the DHDP model for population-level analysis incorporating covariates.
Main Methods:
- Utilized a Kalman filter to compute ML estimates for autoregressive and polynomial parameters.
- Introduced the disturbed highest derivative polynomial (DHDP) model, independent of regression coefficients.
- Employed ML estimation via Kalman filter for disturbance and observation error variances, followed by optimal smoothing for the DHDP curve.
- Extended the individual DHDP analysis to population growth curves using multi-individual data with covariates.
Main Results:
- Successfully applied the Kalman filter for ML estimation in polynomial growth models with AR-1 errors and irregular data.
- Demonstrated the efficacy of the DHDP model, which does not rely on regression coefficients and allows for flexible growth curve representation.
- Showcased the ability to estimate error variances and obtain optimally smoothed growth curves.
- Validated the extension of the DHDP model for population growth analysis.
Conclusions:
- The Kalman filter provides an effective tool for estimating parameters in complex growth curve models.
- The disturbed highest derivative polynomial (DHDP) model offers a robust and flexible alternative for analyzing individual and population growth, accommodating irregular data and AR-1 errors.
- The developed methodology enhances the analysis of growth patterns in various scientific fields.