Much research in network analysis of adolescent friendships assumes that friendships represent liking and social interaction, friendships are directed, and friendships are equivalent to one another. This study investigates the meaning of friendship for eight diverse cohorts of sixth graders. Analysis of focus group and survey data suggests that these adolescents construe friendship as a multidimensional role relation composed primarily of relational norms, expectations for mutual behavior. Their friendship definitions may also include mutual liking and interaction, and other structural expectations such as reciprocity, homophily, and transitivity. Lastly, boys and girls weight these dimensions differently in defining friendship. 相似文献
ABSTRACT In the stepwise procedure of selection of a fixed or a random explanatory variable in a mixed quantitative linear model with errors following a Gaussian stationary autocorrelated process, we have studied the efficiency of five estimators relative to Generalized Least Squares (GLS): Ordinary Least Squares (OLS), Maximum Likelihood (ML), Restricted Maximum Likelihood (REML), First Differences (FD), and First-Difference Ratios (FDR). We have also studied the validity and power of seven derived testing procedures, to assess the significance of the slope of the candidate explanatory variable x2 to enter the model in which there is already one regressor x1. In addition to five testing procedures of the literature, we considered the FDR t-test with n ? 3 df and the modified t-test with n? ? 3 df for partial correlations, where n? is Dutilleul's effective sample size. Efficiency, validity, and power were analyzed by Monte Carlo simulations, as functions of the nature, fixed vs. random (purely random or autocorrelated), of x1 and x2, the sample size and the autocorrelation of random terms in the regression model. We report extensive results for the autocorrelation structure of first-order autoregressive [AR(1)] type, and discuss results we obtained for other autocorrelation structures, such as spherical semivariogram, first-order moving average [MA(1)] and ARMA(1,1), but we could not present because of space constraints. Overall, we found that:
the efficiency of slope estimators and the validity of testing procedures depend primarily on the nature of x2, but not on that of x1;
FDR is the most inefficient slope estimator, regardless of the nature of x1 and x2;
REML is the most efficient of the slope estimators compared relative to GLS, provided the specified autocorrelation structure is correct and the sample size is large enough to ensure the convergence of its optimization algorithm;
the FDR t-test, the modified t-test and the REML t-test are the most valid of the testing procedures compared, despite the inefficiency of the FDR and OLS slope estimators for the former two;
the FDR t-test, however, suffers from a lack of power that varies with the nature of x1 and x2; and
the modified t-test for partial correlations, which does not require the specification of an autocorrelation structure, can be recommended when x1 is fixed or random and x2 is random, whether purely random or autocorrelated. Our results are illustrated by the environmental data that motivated our work.
Within the context of choice experimental designs, most authors have proposed designs for the multinomial logit model under the assumption that only the main effects matter. Very little attention has been paid to designs for attribute interaction models. In this article, three types of Bayesian D-optimal designs for the multinomial logit model are studied: main-effects designs, interaction-effects designs, and composite designs. Simulation studies are used to show that in situations where a researcher is not sure whether or not attribute interaction effects are present, it is best to take into account interactions in the design stage. In particular, it is shown that a composite design constructed by including an interaction-effects model and a main-effects model in the design criterion is most robust against misspecification of the underlying model when it comes to making precise predictions. 相似文献
For the balanced two-way layout of a count response variable Y classified by fixed or random factors A and B, we address the problems of (i) testing for individual and interactive effects on Y of two fixed factors, and (ii) testing for the effect of a fixed factor in the presence of a random factor and conversely. In case (i), we assume independent Poisson responses with µij= E(Y| A=i,B=j) = αiβjγij corresponding respectively to the multiplicative interactive and non-interactive cases. For case (ii) with factor A random, we derive a multivariate gamma-Poisson model by mixing on the random variable associated with each level of A. In each case Neyman C(α) score tests are derived. We present simulation results,and apply the interaction test to a data set, to evaluate and compare the size and power of the score test for interaction between two fixed factors, the competing Poisson-based likelihood ratio test, and the F-tests based on the assumptions that √Y+1 or log(Y+1) are approximately normal. Our results provide strong evidence that the normal-theory based F-tests typically are very far from nominal size, and that the likelihood ratio test is somewhat more liberal than the score test. 相似文献