Abstract:
Estimation of total county crop yields is of interest to both federal and state governments. This article focuses on estimation of corn production in the counties of Ohio; Our primary goal is producing accurate estimates of corn yield per acre stratified by county and by size of farm. These estimates can be used in conjunction with census data to produce the desired total county corn yield estimates. Our data is responses of 3,842 farms to a voluntary survey. A Bayesian hierarchical random effects model is proposed. The key idea in this formulation involves the input of prior information based on anticipated spatial dependence of corn production between neighboring counties. The model suggested is sufficiently complex to prohibit simple computations. Hence, we employ Gibbs Sampling. The resulting estimates of yield per acre show a strong spatial trend. Lower productivity in the Appalachian foothills gradually increases to higher productivity in the central-northwest region. The geography of Ohio suggests this effect is reasonable. We also estimate the posterior covariance structure of the random effects, including the spatial county effect. This is a large covariance matrix and, thus, difficult to examine carefully. Our approach to investigation of this matrix is graphical examination of one row or "slice" at a time. The "slices" examined display a desirable spatial property; Neighboring counties are generally more correlated than distant counties. Our methodology is easily adaptable to other crops and states.
Keywords:
Bayesian analysis; Gibbs sampling; Markov random field.
tr10.pdf