Self modeling with flexible, random time transformations

Methods for modeling sets of complex curves where the curves must be aligned in time (or in another continuous predictor) fall into the general class of functional data analysis and include self-modeling regression and time-warping procedures. Self-modeling regression (SEMOR), also known as a shape invariant model (SIM), assumes the curves have a common shape, modeled nonparametrically, and curve-specific differences in amplitude and timing, traditionally modeled by linear transformations. When curves contain multiple features that need to be aligned in time, SEMOR may be inadequate since a linear time transformation generally cannot align more than one feature. Time warping procedures focus on timing variability and on finding flexible time warps to align multiple data features. We draw on these methods to develop a SIM that models the time transformations as random, flexible, monotone functions. The model is motivated by speech movement data from the University of Wisconsin X-ray microbeam speech production project and is applied to these data to test the effect of different speaking conditions on the shape and relative timing of movement profiles.     

Richards's equation and nonlinear mixed models applied to avian growth: why use them?

Postnatal growth is an important life‐history trait that varies widely across avian species, and several equations with a sigmoidal shape have been used to model it. Classical three‐parameter models have an inflection point fixed at a percentage of the upper asymptote which could be an unrealistic assumption generating biased fits. The Richards model emerged as an interesting alternative because it includes an extra parameter that determines the location of the inflection point which can move freely along the growth curve. Recently, nonlinear mixed models (NLMM) have been used in modeling avian growth because these models can deal with a lack of independence among data as typically occurs with multiple measurements on the same individual or on groups of related individuals. Here, we evaluated the usefulness of von Bertalanffy, Gompertz, logistic, U₄ and Richards's equations modeling chick growth in the imperial shag Phalacrocorax atriceps. We modelled growth in commonly used morphological traits, including body mass, bill length, head length and tarsus length, and compared the performance of models by using NLMM. Estimated adult size, age at maximum growth and maximum growth rates markedly differed across models. Overall, the most consistent performance in estimated adult size was obtained by the Richards model that showed deviations from mean adult size within 5%. Based on AICc values, the Richards equation was the best model for all traits analyzed. For tarsus length, both Richards and U₄ models provided indistinguishable fits because the relative inflection value estimated from the Richards model was very close to that assumed by the U₄ model. Our results highlight the bias incurred by three‐parameter models when the assumed inflection placement deviates from that derived from data. Thus, the application of the Richards equation using the NLMM framework represents a flexible and powerful tool for the analysis of avian growth.     

诱变后混合菌在锌矿中生长的研究

为了研究诱变后混合菌的生长情况,我们采用Leathen和9K培养基,培养保存2年的诱变菌群和连续传代的诱变菌群,做出它们的生长曲线。结果表明:连续传代的诱变菌群2天达到稳定期,而保存2年的诱变菌群生长达到稳定期,需要多生长2天;在培养基中,加入矿浆浓度(2%、4%、8%、16%、32%)的硫化锌矿,矿浆浓度在32%时E茵群生长量最高;矿浆浓度4%、8%、16%时B菌群生长量最高;矿浆浓度2%时D菌群生长量最高。实验结果说明:混合菌诱变可以大大提高菌群在锌矿中生长能力。     

EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy''s data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed.