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Prediction with measurement errors in finite populations.
Julio M Singer1, Edward J Stanek, Viviana B Lencina
1Departamento de Estatística, Universidade de São Paulo, Brazil.
Statistics & Probability Letters
|December 14, 2011
Summary
We explored best linear unbiased prediction (BLUP) for subjects with varying measurement errors. Finite population mixed models adjust shrinkage constants differently based on error sources, impacting predictor bias and mean squared error.
Area of Science:
- Statistics
- Biostatistics
- Quantitative Methods
Background:
- Best linear unbiased prediction (BLUP) is crucial for estimating latent values in the presence of measurement error.
- Heteroskedastic measurement errors, where variability differs across observations, complicate standard BLUP.
- Understanding the impact of different error structures on BLUP is essential for accurate statistical inference.
Purpose of the Study:
- To compare the standard mixed model BLUP with a finite population mixed model (FPMM) BLUP for latent values with heteroskedastic measurement errors.
- To investigate how subject-specific versus measurement condition-specific heteroskedasticity affects BLUP shrinkage constants.
- To analyze the bias and mean squared error of these predictors under different error assumptions.
Main Methods:
- Comparison of standard mixed model BLUP and FPMM BLUP using a simple example.
- Framing a mixed model within a finite population context with two sources of variability: simple random sampling and heteroskedastic measurement errors.
- Analysis of BLUP shrinkage constants and predictor performance (bias, mean squared error) under subject-specific and measurement condition-specific error structures.
Main Results:
- When measurement errors are subject-specific, FPMM BLUP uses pooled variance for shrinkage constants, differing from the individual variances in standard BLUP.
- When errors are measurement condition-specific, FPMM BLUP yields different shrinkage constants.
- Subject-specific errors lead to a biased standard mixed model predictor with smaller mean squared error than the FPMM BLUP.
Conclusions:
- The interpretation of BLUPs can be complex when measurement errors are heteroskedastic and subject-specific.
- FPMM offers an alternative framework for BLUP with heteroskedastic errors, yielding different shrinkage properties.
- The choice of model and assumptions about error structure significantly influence the properties of estimated latent values.
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