Using limited dependent variable estimators for estimating percent decay

Abstract

The data used for the estimation of percent decay are bounded by zero and 100. Because a value of 100% indicates that the tree is completely decayed, this value is not observable in nature. However, a value of zero percent is often observed over a wide range of the independent variables. The distribution of percent decay is a combination of a truncated continuous distribution for percent decay greater than zero and a discrete component for the zero percents. The use of ordinary least squares with this type of data results in biased and inconsistent estimates of the coefficients of a percent decay equation. An alternative is the tobit estimator (a combined regression and probit estimator based on a maximum likelihood equation), which results in consistent estimates of the coefficients if the error terms of the model are independent and identically distributed as the truncated normal distribution. A Monte Carlo simulation using data for three species with different proportions of zero percents was performed to compare the ordinary least squares and tobit estimators. As expected, the tobit estimator resulted in quite different estimates of the coefficients of the equations than did ordinary least squares. An unexpected result was that the estimated expected percent decay was slightly more biased for the tobit estimator than for the ordinary least squares estimator, even with a large number of zero percents in the data set. Possible explanations for the Monte Carlo simulation results and recommendations for fitting percent decay equations are given in the paper.