Deer-Vehicle Crash Patterns Across Ecoregions in Michigan

Deer-vehicle collisions (DVCs) impact the economic and social well being of humans. We examined large-scale patterns behind DVCs across 3 ecoregions: Southern Lower Peninsula (SLP), Northern Lower Peninsula (NLP), and Upper Peninsula (UP) in Michigan. A 3 component conceptual model of DVCs with drivers, deer, and a landscape was the framework of analysis. The conceptual model was parameterized into a parsimonious mathematical model. The dependent variable was DVCs by county by ecoregion and the independent variables were percent forest cover, percent crop cover, mean annual vehicle miles traveled (VMT), and mean deer density index (DDI) by county. A discriminant function analysis of the 4 independent variables by counties by ecoregion indicated low misclassification, and provided support to the groupings by ecoregions. The global model and all sub-models were run for the 3 ecoregions and evaluated using information-theoretic approaches. Adjusted R2 values for the global model increased substantially from the SLP (0.21) to the NLP (0.54) to the UP (0.72). VMT and DDI were important variables across all 3 ecoregions. Percent crop cover played an important role in DVCs in the SLP and UP. The scale at which causal factors of DVCs operate appear to be finer in southern Michigan than in northern Michigan. Reduction of DVCs will likely occur only through a reduction in deer density, a reduction in traffic volume, or in modification of sitespecific factors, such as driver behavior, sight distance, highway features, or speed limits.

Improved Regression Estimation of a Multivariate Relationship with Population Data on the Bivariate Relationship

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from population-level data. We show here that such population- level data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariate-specific associations (partial effects) of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being ‘‘directly constrained.’’ Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus ‘‘indirectly constrained’’ by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women’s rates of marital fertility, available from population-level data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.