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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
Random and Systematic Errors01:20

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Updated: Jun 17, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Spatial Linear Mixed Models with Covariate Measurement Errors.

Yi Li1, Haicheng Tang, Xihong Lin

  • 1Department of Biostatistics and Computational Biology, Dana Farber Cancer Institute, 44 Binney St, Boston, MA 02115.

Statistica Sinica
|January 5, 2010
PubMed
Summary
This summary is machine-generated.

Ignoring measurement error in spatial data analysis biases results. This study introduces a new linear mixed model to accurately estimate spatial regression coefficients and variance components, correcting for these errors.

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Last Updated: Jun 17, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Spatial statistics
  • Biostatistics
  • Public health research

Background:

  • Covariate measurement errors are common in spatial public health data.
  • Existing methods primarily use Gibbs sampling for parameter estimation.
  • The theoretical impact of ignoring measurement error on spatial analysis is not well understood.

Purpose of the Study:

  • To propose a new class of linear mixed models for spatial data with covariate measurement errors.
  • To quantify the asymptotic biases in regression coefficients and variance components when measurement error is ignored.
  • To develop a structural modeling approach for maximum likelihood estimation (MLE) in spatial covariate measurement error models.

Main Methods:

  • Development of linear mixed models for spatial data incorporating covariate measurement errors.
  • Theoretical analysis of asymptotic biases in naive estimators.
  • Application of a structural modeling approach for MLE.
  • Utilizing an EM algorithm for inference.
  • Employing an increasing-domain asymptotic framework.

Main Results:

  • Naive estimators of regression coefficients are attenuated when measurement error is ignored.
  • Naive estimators of variance components are inflated when measurement error is ignored.
  • The proposed MLE method provides accurate estimation by accounting for measurement error.
  • Demonstrated importance of adjusting for covariate measurement errors through analysis of Scottish lip cancer data and simulation studies.

Conclusions:

  • Ignoring covariate measurement errors in spatial data analysis leads to significant biases.
  • The proposed linear mixed models and MLE approach effectively address these biases.
  • Accurate spatial data analysis in public health requires explicit adjustment for measurement errors.