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.

Examination of Homalometron elongatum Manter, 1947 and Description of a New Congener from Eucinostomus currani Zahuranec, 1980 in the Pacific Ocean off Costa Rica

Homalometron elongatum is reexamined using heat-killed material that was not subjected to pressure during fixation from Gerres cinereus collected from San Juan Harbor, Puerto Rico, U.S.A. The new material is compared with some paratype specimens and differs by having a much less variable forebody length, and a median rather than submedian genital pore. Tegumental spines reportedly cover the anterior end of the body but we observed tegumental spines covering the entire body surface in both the paratype and new material. Homalometron lesliorum n. sp. is described from Eucinostomus currani from the Pacific coasts of Costa Rica and Nicaragua. The new species has three pairs of oral papillae surrounding the mouth and thus resembles three other congeners: H. elongatum, Homalometron carapevae, and Homalometron papilliferum. Homalometron lesliorum n. sp. is distinguished from the three species by having the anterior extent of the vitelline follicles at or above the base of the ventral sucker, compared with posterior to the ventral sucker at the level of the seminal vesicle (H. elongatum) or further posterior at the posterior margin of the ovary (H. carapevae and H. papilliferum). The four species are further differentiated from one another by sucker width ratio, tegumental spine size and distribution, egg size, host preference, and biogeography. Comparison of nuclear ribosomal DNA (3' end of 18S, internal transcribed spacer [ITS]1, ITS2, and 5' end of 28S) between H. elongatum and H. lesliorum n. sp. revealed one variable base (n = 162) at the 3' end of 18S, 12 variable bases (n = 476) at ITS1, 10 variable bases (n = 310) at ITS2, and 11 variable bases (n = 1,325) at the 5' end fragment of 28S. Nuclear ribosomal DNA from Homalometron pallidum and Homalometron armatum are included for further comparison with H. elongatum and H. lesliorum n. sp.