Asymptotic bias in the linear mixed effects model under non-ignorable missing data mechanisms

Summary.  In longitudinal studies, missingness of data is often an unavoidable problem. Estimators from the linear mixed effects model assume that missing data are missing at random. However, estimators are biased when this assumption is not met. In the paper, theoretical results for the asymptotic bias are established under non-ignorable drop-out, drop-in and other missing data patterns. The asymptotic bias is large when the drop-out subjects have only one or no observation, especially for slope-related parameters of the linear mixed effects model. In the drop-in case, intercept-related parameter estimators show substantial asymptotic bias when subjects enter late in the study. Eight other missing data patterns are considered and these produce asymptotic biases of a variety of magnitudes.     

On the statistical computation of the sample multiple correlation moefficient

Based on the recursive formulas of Lee (1988) and Singh and Relyea (1992) for computing the noncentral F distribution, a numerical algorithm for evaluating the distributional values of the sample squared multiple correlation coefficient is proposed. The distributional function of this statistic is usually represented as an infinite weighted sum of the iterative form of incomplete beta integral. So an effective algorithm for the incomplete beta integral is crucial to the numerical evaluation of various distribution values. Let a and b denote two shape parameters shown in the incomplete beta integral and hence formed in the sampling distribution functionn be the sample size, and p be the number of random variates. Then both 2a = p - 1 and 2b = n - p are positive integers in sampling situations so that the proposed numerical procedures in this paper are greatly simplified by recursively formulating the incomplete beta integral. By doing this, it can jointly compute the distributional values of probability dens function (pdf) and cumulative distribution function (cdf) for which the distributional value of quantile can be more efficiently obtained by Newton's method. In addition, computer codes in C are developed for demonstration and performance evaluation. For the less precision required, the implemented method can achieve the exact value with respect to the jnite significant digit desired. In general, the numerical results are apparently better than those by various approximations and interpolations of Gurland and Asiribo (1991),Gurland and Milton (1970), and Lee (1971, 1972). When b = (1/2)(n -p) is an integer in particular, the finite series formulation of Gurland (1968) is used to evaluate the pdf/cdf values without truncation errors, which are served as the pivotal one. By setting the implemented codes with double precisions, the infinite series form of derived method can achieve the pivotal values for almost all cases under study. Related comparisons and illustrations are also presented     

Impact of a Homonegativity Awareness Workshop on Attitudes Toward Homosexuality

The current study evaluated the effects of a homonegativity awareness workshop on attitudes toward homosexuality and examined individual difference variables associated with attitude change. Participants included 71 female and 43 male students (approximate mean age?=?23). Compared to a control group of introductory psychology students, participants were less homonegative and erotophobic (F(1, 359)?=?62.47 and 15.92, ps?<?.001) after the workshop. Implications for contact with gay and lesbian persons through structured intervention programs on attitudes toward homosexuality are discussed in terms of both the practice and theory of reducing prejudice and discrimination.     

A Theory of Rational Choice under Ignorance

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons.     

不完全契约、质量监督与农业企业外包——基于中国农业上市公司的实证研究

农业企业的产品质量与组织分工形式密切相关。在契约不完全理论的基础上构建引入质量监督与企业外包决策的经济模型,提出质量监督成本的提高会促使农业企业选择纵向一体化生产模式的理论假说,并基于2012-2021年中国农业上市公司数据,采用动态面板系统GMM方法展开经验研究证实。结果表明,生产环节的难以监督和契约制度环境不完善产生的质量监督成本使农业上市公司外包水平显著下降,间接验证了农业企业为保证中间产品质量需增大对专业化经营主体的监督费用,从而影响其组织分工形式的理论假说。此外,企业的资产专用性、市场规模和资产规模都会对外包程度产生影响。进一步分组回归发现：与养殖类企业相比,质量监督成本对生产过程相对复杂的种植类企业外包水平的负向影响更为显著。     

Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

Notes on testing carry-over effects in continuous data under an incomplete block crossover design

We consider hypothesis testing and estimation of carry-over effects in continuous data under an incomplete block crossover design when comparing two experimental treatments with a placebo. We develop procedures for testing differential carry-over effects based on the weighted-least-squares (WLS) method. We apply Monte Carlo simulations to evaluate the performance of these test procedures in a variety of situations. We use the data regarding the forced expiratory volume in one second (FEV₁) readings taken from a double-blind crossover trial comparing two different doses of formoterol with a placebo to illustrate the use of test procedures proposed here.     

Ignorability conditions for frequentist non parametric analysis of conditional distributions with incomplete data

Rubin (1976 Rubin, D.B. (1976). Inference and missing data. Biometrika 63(3):581–592.[Crossref], [Web of Science ®] , [Google Scholar]) derived general conditions under which inferences that ignore missing data are valid. These conditions are sufficient but not generally necessary, and therefore may be relaxed in some special cases. We consider here the case of frequentist estimation of a conditional cdf subject to missing outcomes. We partition a set of data into outcome, conditioning, and latent variables, all of which potentially affect the probability of a missing response. We describe sufficient conditions under which a complete-case estimate of the conditional cdf of the outcome given the conditioning variable is unbiased. We use simulations on a renal transplant data set (Dienemann et al.) to illustrate the implications of these results.     

Outliers in incomplete multiresponse experiments

Identification of outlier vectors in block designs for incomplete multiresponse experiments has been considered. Design is composed of two sets of experimental units. Different numbers of response variables are observed from these two sets. Cook-statistic has been developed for identification of outliers. The developed statistic has been illustrated with a real-life data set. It has been shown that presence of outliers can distort the overall conclusion from an experiment.     

Order statistics from the linear-exponential distribution,part I: increasing hazard rate case

For the linear-exponential distribution with increasing hazard rate, exact and explicit expressions for means, product moments and percentage points of order statistics are obtained. Some recurrence relations for both single and product moments of order statistics are also derived. These recurrence relations would enable one to obtain all the higher order moments of order statistics for all sample sizes from those of the lower order