This study explores the prediction of a continuous target variable that is primarily measured as an ordinal outcome. Interest in such prediction may occur given data from double- or two-phase sampling designs, where an auxiliary variable is measured at all sampling units and a target and predictor variable, X, at a subset of those units. This study focuses on the case where X is nonnegative, is conditional on a zero process, and is sampled using a cluster sampling design. We model the ordinal outcome using cumulative logistic regression and the conditional regressor X, following log transformation, in a Bayesian setting. Estimation of model parameters and prediction of missing X is generally accurate and precise, particularly with sufficiently large <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\text {Pr}(X>0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Pr</mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo>></mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and associated variances. This study is motivated by a need to accurately estimate the biomass of submersed aquatic vegetation on the Upper Mississippi River, where two types of measurements for biomass are available: inexpensive, ordinal biomass scores and expensive, continuous diver-harvested biomass data. Here, X represents plant biomass and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\text {Pr}(X>0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Pr</mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo>></mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is the usual species site occupancy measure. When fit using biomass data from the submerged aquatic vegetation species Vallisneria americana Michx, our model estimates parameters within the parameter space region where the model performed acceptably using synthetic data. We expect this model to appeal to investigators with ordered outcomes, cluster designs, and one or more continuous, positive predictors.

Estimating Submersed Aquatic Vegetation Biomass Using a Hierarchical Bayesian Model of Ordinal Measurements and Structural Zeros

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2026年8月4日

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J. Sherman,
K. St. Clair,
B. R. Gray,
D. Larson

摘要

This study explores the prediction of a continuous target variable that is primarily measured as an ordinal outcome. Interest in such prediction may occur given data from double- or two-phase sampling designs, where an auxiliary variable is measured at all sampling units and a target and predictor variable, X, at a subset of those units. This study focuses on the case where X is nonnegative, is conditional on a zero process, and is sampled using a cluster sampling design. We model the ordinal outcome using cumulative logistic regression and the conditional regressor X, following log transformation, in a Bayesian setting. Estimation of model parameters and prediction of missing X is generally accurate and precise, particularly with sufficiently large $\text {Pr}(X>0)$ $Pr (X > 0)$ and associated variances. This study is motivated by a need to accurately estimate the biomass of submersed aquatic vegetation on the Upper Mississippi River, where two types of measurements for biomass are available: inexpensive, ordinal biomass scores and expensive, continuous diver-harvested biomass data. Here, X represents plant biomass and $\text {Pr}(X>0)$ $Pr (X > 0)$ is the usual species site occupancy measure. When fit using biomass data from the submerged aquatic vegetation species Vallisneria americana Michx, our model estimates parameters within the parameter space region where the model performed acceptably using synthetic data. We expect this model to appeal to investigators with ordered outcomes, cluster designs, and one or more continuous, positive predictors.