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.

Portraits of Protestant Teens: A Report on Teenagers in Major U.S. Denominations

This report examines the religious beliefs and practices of American Protestant teenagers using new, nationally representative survey data from the National Study of Youth and Religion (NSYR). The NSYR is a major study of the religious and spiritual lives of contemporary American teens, which recently produced a book on its major findings entitled, Soul Searching: the Religious and Spiritual Lives of American Teenagers (by Christian Smith with Melinda Lundquist Denton, Oxford University Press, 2005). In addition to broadly describing the religious outlook of Protestant teenagers today — and as a more detailed, descriptive follow-up to that book — this report highlights several positive and negative experiences and evaluations of teenagers in different Protestant denominations and groupings of denominations. In brief, this report presents the following findings in these areas of interest: ♦ Religious Participation: Protestant teenagers are relatively active in religious organizations and activities, both within and beyond their churches. About one-half of all Protestant teens attend church weekly, participate in Sunday school or in a religious youth group, pray and attend a religious summer camp or retreat, though less than one-third read the Bible each week. This also means, however, that substantial numbers of Protestant teens are not actively participating in their religious traditions. Teens from conservative denominations such as Southern Baptist Convention and Assemblies of God are especially likely to regularly attend church and participate in other religious activities. ♦ Theological Beliefs: Protestant teenagers are likely to hold many traditional Christian religious beliefs. The majority of Protestant teens say they believe in God, the afterlife, angels, demons, miracles, judgment day and they view God as a personal being involved in the lives of people today. Sizable numbers of Protestant teens, on the other hand, do not hold these traditional Christian religious beliefs. Teens from conservative and black Protestant denominations are more likely than mainline Protestant teens to hold these religious beliefs. ♦ Importance of Faith: The majority of Protestant teenagers report that their religious faith is very important in their lives. Most of them also say that their families talk about religion together, that they have shared their faith with someone not of their faith and that they have had a powerful worship experience. A large minority of all Protestant teenagers, and in the case of some denominations a majority of teenagers, do not report that religious faith is very important in their lives. Teens from conservative and black Protestant denominations are particularly likely to report that faith is important in their lives. ♦ Evaluations of Churches: The majority of Protestant teenagers express relatively positive views of their churches and fellow church members. They typically report that they would continue to attend church if it were totally up to them, that they would attend a similar church if given the choice and that their current church is generally warm and welcoming. Protestant adolescents, however, do have some reservations about and problems with their churches and fellow church attendees, as spelled out in the following pages, particularly with other teenage attendees.

Harbor Porpoise (Phocoena phocoena) Abundance in Alaska: Bristol Bay to Southeast Alaska, 1991-1993

Between 1991 and 1993, Alaska harbor porpoise (Phocoena phocoena) abundance was investigated during aerial surveys throughout much of the coastal and offshore waters from Bristol Bay in the eastern Bering Sea to Dixon Entrance in Southeast Alaska. Line-transect methodology was used, and only those observations made during optimal conditions were analyzed. Survey data indicated densities of 4.48 groups/100 km2, or approximately 3,531 harbor porpoises (95% C.I. 2,206-5,651) in Bristol Bay and 0.54 groups/100 km2, or 136 harbor porpoises (95% C.I. 11-1,645) for Cook Inlet. Efforts off Kodiak Island resulted in densities of 1.85 groups/100 km2, or an abundance estimate of 740 (95% C.I. 259-2,115). Surveys off the south side of the Alaska Peninsula found densities of 2.03 groups/100 km2 and an abundance estimate of 551 (95% C.I. 423-719). Surveys of offshore waters from Prince William Sound to Dixon Entrance yielded densities of 4.02 groups/100 km’ and an abundance estimate of 3,982 (95% C.I. 2,567-6,177). Combining all years and areas yielded an uncorrected density estimate of 3.82 porpoises per 100 km2, resulting in an abundance estimate of 8,940 porpoises (CV = 13.8%) with a 95% confidence interval of 6,746-11,848. Using correction factors from other studies to adjust for animals missed by observers, the total number of Alaska harbor porpoises is probably three times this number.