Three Ways of Implementing the EM Algorithm when Parameters are not Identifiable

We consider situations where the incomplete nature of the observed data causes identifiability problem. Rather than imposing identifiability constraints on the parameters and then implement the EM algorithm subject to these constraints, we argue that for certain problems, an easier option is to ignore the constraints during the M‐steps of the EM procedure. We also suggest a way of carrying out constrained maximization approximately by using Cox and Wermuth's (1990) method for approximating the constrained maximizers from the unconstrained ones at each M‐step. The simplicity and validity of the unconstrained EM procedure are demonstrated using three examples involving bivariate probit regression, multivariate normal order statistics model and the multinominal distribution. Potential applications to more complicated models are also outlined.     

On the Numerical Availability of Multiple Comparison Procedures

In the past many multiple comparison procedure were difficult to perform. Usually, such procedures can be traced back to studentized multiple contrast tests. Numerical difficulties restricted the use of the exact procedures to simple, commonly balanced, designs. Conservative approximations or simulation based approaches have been used in the general cases. However, new efforts and results in the past few years have led to fast and efficient computations of the underlying multidimensional integrals. Inferences for any finite set of linear functions of normal means are now numerically feasible. These include all‐pairwise comparisons, comparisons with a control (including dose‐response contrasts), multiple comparison with the best, etc. The article applies the numerical progress on multiple comparisons procedures for common balanced and unbalanced designs within the general linear model.     

Estimation of a Joint Distribution Function with Multivariate Interval‐Censored Data when the Nonparametric MLE is not Unique

A nonparametric estimator of a joint distribution function F₀ of a d‐dimensional random vector with interval‐censored (IC) data is the generalized maximum likelihood estimator (GMLE), where d ≥ 2. The GMLE of F₀ with univariate IC data is uniquely defined at each follow‐up time. However, this is no longer true in general with multivariate IC data as demonstrated by a data set from an eye study. How to estimate the survival function and the covariance matrix of the estimator in such a case is a new practical issue in analyzing IC data. We propose a procedure in such a situation and apply it to the data set from the eye study. Our method always results in a GMLE with a nonsingular sample information matrix. We also give a theoretical justification for such a procedure. Extension of our procedure to Cox's regression model is also mentioned.     

Cluster Randomization Trials: A Simulation Study

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel‐Haenszel chi‐square statistic (χ²_MH), the adjusted Mantel‐Haenszel chi‐square statistics of Rao and Scott using both an unpooled design effect (χ²_RSN) and a pooled design effect (χ²_RSP), the adjusted Mantel‐Haenszel chi‐square statistic of Donald and Donner (χ²_DD), the chi‐square statistic using the GEE approach (χ²_GEE), the adjusted Mantel‐Haenszel chi‐square statistic of Begg (χ²_B), the Wald (χ²_W), the robust Wald (χ²_RW), the score (χ²_S), the robust score (χ²_RS), and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ²_RS and the adjusted Mantel‐Haenszel chi‐square statistics of Zhang and Boos (χ²_ZBP and χ²_ZBN) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intracluster correlation is zero or the cluster sizes are balanced. χ²_RS performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.     

长尾姬鼠分类地位的探讨

长期以来长尾姬鼠（Ａｐｏｄｅｍｕｓ ｏｒｅｓｔｅｓ）的分类地位一直不确定。基于在云南中部无量山区采集的大量姬鼠类标本,经单变量和多变量分析,长尾姬鼠明显区别于中华姬鼠（Ａ．ｄｒａｃｏ）。主要鉴别特征在于体长、尾长及尾长与本长的比例,且相关分析表明,该两种的尾长与体长具显著的相关性。而对无量山姬鼠的生态地理分布研究显示,长尾姬鼠与中华姬鼠具完全同域分布,因此认为长尾姬鼠是一有效种。无量山区现有姬鼠３     

Synthesis and structural characterization of enantiopure levodropropizine

Enantiopure levodropropizine can be synthesized in high yield by the direct nucleophilic addition of 1-phenylpiperazine to (R)-glycidol followed by recrystallization in absolute ethanol. A chiral HPLC method has been developed for the determination of its optical purity. The enantiomeric enrichment behavior of this compound in the recrystallization process is discussed according to its binary melting point phase diagram. Single crystal x-ray structural analysis shows the intermolecular hydrogen-bonding interactions between the hydroxyl and piperazinyl groups within the crystal lattice of levodropropizine. © 1996 Wiley-Liss, Inc.     

A mini binary vector series for plant transformation

A streamlined mini binary vector was constructed that is less than 1/2 the size of the pBIN19 backbone (3.5 kb). This was accomplished by eliminating over 5 kb of non-T-DNA sequences from the pBIN19 vector. The vector still retains all the essential elements required for a binary vector. These include a RK2 replication origin, the nptIII gene conferring kanamycin resistance in bacteria, both the right and left T-DNA borders, and a multiple cloning site (MCS) in between the T-DNA borders to facilitate cloning. Due to the reduced size, more unique restriction sites are available in the MCS, thus allowing more versatile cloning. Since the traF region was not included, it is not possible to mobilize this binary vector into Agrobacterium by triparental mating. This problem can be easily resolved by direct transformation. The mini binary vector has been demonstrated to successfully transform Arabidopsis plants. Based on this mini binary vector, a series of binary vectors were constructed for plant transformation.     

Estimates of heritability and correlations of morphometric traits in Clarkia (Onagraceae)

Summary Interspecific heritability values were estimated using parent-offspring regression analyses for 11 morphological traits differentiating Clarkia nitens and C. speciosa subsp. polyantha. Estimates ranged from near 0 for anther color and germination percentage, to 0.8 for calyx length and petal tip color. Phenotypic, genetic, and environmental correlation matrices were computed to determine the extent of interspecific correlations of traits. Cluster analyses of the genetic and environmental correlation matrices each resulted in three clusters of correlated traits; however, the clusters derived from the two matrices were different. The clusters produced by analysis of the environmental correlation matrix were similar to the factors obtained from principal component analysis of the phenotypic correlation matrix. Genetic correlations may result from strong linkage due to interspecific chromosomal differences.     

Lightning density and burning frequency in South African vegetation

This study investigates lightning density in relation to burning frequency in five South African biomes. Data from automatic lightning flash counters distributed throughout South Africa are used to estimate the range and mean values of annual lightning ground-strike density in each biome. The lowest average lightning frequencies were recorded in the karoo and fynbos biomes, while the highest values were obtained in the sour and inland mountain divisions of the grassland biome, with intermediate values computed for the savanna-woodland and forest biomes. These results were compared with published findings on the effects of different burning frequencies on plant communities in each biome. In general, plant communities occurring in areas experiencing the highest annual lightning densities (e.g., sour and mixed grassland, and moist savanna-woodland) tolerate and require more frequent burning than those typical of areas subject to lower lightning densities (e.g., fynbos, forest, sweet grassland, and arid savanna-woodland). These findings suggest that the constituent plant populations in each biome have adapted to burning frequency according to the local probability of ignition by lightning in the areas they inhabit, and that present day responses of plant communities to burning reflect their ancestral exposure to fire in the course of their evolutionary development under pre-existing, natural fire regimes.Research sponsered by the South African Council for Scientific and Industrial Research. We thank the Director, National Electrical Engineering Research Institute (NEERI), Pretoria, South Africa, and H. Kröninger, Lightning Research Division, NEERI, for providing data on lightning ground-strike densities and coordinates and elevations for counters in South Africa. We thank Drs J. H. Bock and M. T. Mentis for commenting on an early draft of this paper.