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.

Correlation of the middle Eocene Kellogg Shale of northern California

The Kellogg Shale of northern California has traditionally been considered to be late Eocene in age on the basis of benthic foraminifer, radiolarian, and diatom correlations. The 30-m-thick Kellogg section exposed west of Byron, California, however, contains middle Eocene planktonic foraminifers (Zone P12), coccoliths (Subzones CP13c and CP14a), silicoflagellates (Dictyocha hexacantha Zone), and diatoms. Quantitative studies of the silicoflagellates and diatoms show a general cooling trend through the section which is consistent with paleoclimatic trends for this part of the middle Eocene (ca. 42-45 Ma) from elsewhere in the world. Seven new silicoflagellate taxa (Corbisema angularis. C, exilis, C, hastate miranda, C. inermis ballantina, C. regina, Dictyocha byronalis, Naviculopsis Americana) and one new coccolithophorid species (Helicosphaera neolophota) are described.