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Assuming independence in spatial latent variable models: Consequences and implications of misspecification.
Francis K C Hui1, Nicole A Hill2, A H Welsh1
1Research School of Finance, Actuarial Studies & Statistics, Australian National University, Acton, Australia.
Biometrics
|December 19, 2020
Summary
Misspecifying the correlation structure in spatial generalized linear latent variable models (GLLVMs) can affect regression coefficient estimates. However, this misspecification consistently impacts latent variable estimation and prediction in spatial GLLVMs.
Area of Science:
- Ecology
- Statistics
- Environmental Science
Background:
- Multivariate spatial data are common in ecology and environmental science.
- Spatial generalized linear latent variable models (GLLVMs) are used to model this data.
- The impact of misspecifying the latent variable correlation structure in GLLVMs is not well understood.
Purpose of the Study:
- To investigate the effects of misspecifying the latent variable correlation structure in spatial GLLVMs.
- To assess the impact on parameter estimation and inference.
Main Methods:
- Theoretical analysis.
- Numerical simulations.
- Investigated spatial generalized linear latent variable models (GLLVMs).
Main Results:
- Maximum likelihood estimation and inference for regression coefficients are sensitive to misspecification, depending on response type, coefficient magnitude, loadings, and covariate spatial correlation.
- Estimation and inference of nonzero loadings are not robust to misspecification.
- Prediction of latent variables is also not robust to misspecification.
Conclusions:
- Misspecifying the latent variable correlation structure in spatial GLLVMs can lead to biased inference for regression coefficients.
- Latent variable estimation, inference, and prediction are consistently unreliable when the correlation structure is misspecified.
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