一类半参数可变系数广义线性模型及其拟合

Along the line of the classical generalized linear model,the classical generalized linear model is improved in this article by assuming the partial coefficients of the regressors to be arbitrary functions of the points in some metric space.This new type of regression model is called in this article semiparametric vary coefficient generalized linear model and the back fitting approach is suggested to fit the proposed model,and the smoothing parameter therein are studied.The proposed model not only have higher flexibility and adaptability,but also is suitable for analysis spatial data and therefore has extensive application backgrounds.

Diagnostics in generalized nonlinear models based on maximum L_q-likelihood estimation

In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.

Interannual and Seasonal Variability of Winter-Spring Cohort of Neon Flying Squid Abundance in the Northwest Pacific Ocean During 1995–2011

The neon flying squid, Ommastrephes bartramii, is a species of economically important cephalopod in the Northwest Pacific Ocean. Its short lifespan increases the susceptibility of the distribution and abundance to the direct impact of the environmental conditions. Based on the generalized linear model(GLM) and generalized additive model(GAM), the commercial fishery data from the Chinese squid-jigging fleets during 1995 to 2011 were used to examine the interannual and seasonal variability in the abundance of O. bartramii, and to evaluate the influences of variables on the abundance(catch per unit effort, CPUE). The results from GLM suggested that year, month, latitude, sea surface temperature(SST), mixed layer depth(MLD), and the interaction term(SST×MLD) were significant factors. The optimal model based on GAM included all the six significant variables and could explain 42.43% of the variance in nominal CPUE. The importance of the six variables was ranked by decreasing magnitude: year, month, latitude, SST, MLD and SST×MLD. The squid was mainly distributed in the waters between 40?N and 44?N in the Northwest Pacific Ocean. The optimal ranges of SST and MLD were from 14 to 20℃ and from 10 to 30 m, respectively. The squid abundance greatly fluctuated from 1995 to 2011. The CPUE was low during 1995–2002 and high during 2003–2008. Furthermore, the squid abundance was typically high in August. The interannual and seasonal variabilities in the squid abundance were associated with the variations of marine environmental conditions and the life history characteristics of squid.

Evaluating the impact of spatio-temporal scale on CPUE standardization

This study focused on the quantitative evaluation of the impact of the spatio-temporal scale used in data collection and grouping on the standardization of CPUE(catch per unit effort).We used the Chinese squid-jigging fishery in the northwestern Pacific Ocean as an example to evaluate 24 scenarios at different spatio-temporal scales,with a combination of four levels of temporal scale(weekly,biweekly,monthly,and bimonthly)and six levels of spatial scale(longitude×latitude:0.5°×0.5°,0.5°×1°,0.5°×2°,1°×0.5°,1°×1°,and 1°×2°).We applied generalized additive models and generalized linear models to analyze the24 scenarios for CPUE standardization,and then the differences in the standardized CPUE among these scenarios were quantified.This study shows that combinations of different spatial and temporal scales could have different impacts on the standardization of CPUE.However,at a fine temporal scale(weekly)different spatial scales yielded similar results for standardized CPUE.The choice of spatio-temporal scale used in data collection and analysis may create added uncertainty in fisheries stock assessment and management.To identify a cost-effective spatio-temporal scale for data collection,we recommend a similar study be undertaken to facilitate the design of effective monitoring programs.

Estimation of the Volume of Coarse Woody Debris in Eucalyptus Forest using LiDAR Derived Forest Structure Variables

CWD （coarse woody debris） plays an important role in nutrient cycling, habitat for species and more recently carbon accounting in forest ecosystems. LiDAR （light detection and ranging） technology has demonstrated utility in capturing forest structure information. This paper proposes an indirect method of assessing downed CWD using LiDAR derived forest structure variables. Fieldwork was conducted to measure CWD volume in an Eucalyptus forest in Tasmania. A GLM （generalized linear model） to statistically estimate CWD volume in the Eucalyptus forest was developed using a LiDAR derived FCS （forest characterisation scheme）： the openings above the ground, low and medium vegetation, canopy cover, presence of understorey and mid-storey vegetation and high trees, and the vertical canopy density of high trees. Five structural variables were selected for the best model based on AIC （Akaike＇s Information Criterion） by stepwise selection. The applicability of the model was then compared to the outcome of model using field derived variables such as diameter at breast height of trees. The results show that the model using LiDAR derived variables better estimated the amount of CWD. It is concluded that LiDAR derived forest structural variables has the potential to predict the amount of downed CWD in Eucalyptus forest.

Susceptibility of pine stands to bark stripping by chacma baboons Papio ursinus in the Eastern Highlands of Zimbabwe

The aim of this study was to determine the susceptibility, intensity and distribution of pine trees to bark stripping by chacma baboons Papio ursinus in three plantations in the Eastern Highlands of Zimbabwe. The number of plots/ha, stripped trees/ plot and stripped trees/ha was recorded during the pre-rainy, rainy and post-rainy seasons from August 2006 to May 2007. During data collection, altitude, aspect, season and other site predictor variables （e. g., roads and fire traces, water points, indigenous vegetation conservation areas, crop felds, human settlements, wattle scrubs, rocky areas, open grasslands, earlier stripped sites and roost sites） were recorded for each plot in association with selected predictor variables within plantation estates. Data on the number of stripped plots/ha, stripped trees/plot and stripped trees/ha were analysed as dependent variables using the Generalised Linear Model （GLM） through SPSS version 15 （2006） to determine which predictor variables were significantly related to bark stripping. Differences between means were tested using Bonferroni tests with a 5 % level of significance. Our findings show that bark stripping of pine trees by baboons occurred at all altitudes and aspects. Overall, the number of bark stripped trees/ha did not significandy vary by season. The number of bark stripped plots/ha was lower during the pre-rainy season than the rainy season, whereas the number of bark stripped trees/plot was higher during the pre-rainy than the rainy season. Bark stripping of pines occurred more often in the vicinities of areas with abundant food and water

A Comparison of Several 5-Minute Radar-Rainfall Estimation Models

For the Z-R relationship in radar-based rainfall estimation, the distribution of corresponding R values for a given Z value (or the corresponding Z value for a given R value) may be highly skewed. However, the traditional power-law model is physically deduced and fitted under the normal-distribution presumption of radar wave echoes associated with a rain rate value, and it may not be very appropriate. Considering this problem, the authors devised several generalized linear models with different forms and distribution presumptions to represent the Z-R relationship. Radar-reflectivity scans observed by a CINRAD/SC Doppler radar and 5-minute rainfall accumulation recorded by 10 ground gauges were used to fit these models. All data used in this study were collected during some large rainfalls of the period from 2005 to 2007. The radar and all gauges were installed in the catchment of the Yishu River, a branch of the Huaihe River in China. Three models based on normal distribution and a dBZ presumption of gamma distribution were fitted using maximum-likelihood techniques, which were resolved by genetic algorithms. Comparisons of estimated maximized likelihoods based on assumptions of gamma and normal distribution showed that all generalized linear models (GLMs) of presumed gamma distribution were better fitted than GLMs based on normal distribution. In a comparison of maximum-likelihood, the differences between these three models were small. Three error statistics were used to assess the agreement between radar estimated rainfall and gauge rainfall: relative bias (B), root mean square error (RMSE), and correlation coefficient (r). The results showed that no one model was excellent in all criteria. On the whole, the GLM-based models gave smaller relative bias than the traditional power-law model. It is suggested that validations conducted in many previous works should have been made against a specific criterion but overlooked others.

A Model-calibration Approach to Using Complete Auxiliary Information from Stratified Sampling Survey Data

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.

Oscillating Solitons for （2＋1）-Dimensional Nonlinear Models

Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.

Influence and Local Influence for Explained Variation in Survival Analysis

The amount of explained variation R2 is an overall measure used to quantify the information in a model and especially how useful the model might be when predicting future observations, explained variation is useful in guiding model choice for all types of predictive regression models, including linear and generalized linear models and survival analysis. In this work we consider how individual observations in a data set can influence the value of various R2 measures proposed for survival analysis including local influence to assess mathematically the effect of small changes. We discuss methodologies for assessing influence on Graf et al.＇s R2G measure, Harrell＇s C-index and Nagelkerke＇s R2N. The ideas are illustrated on data on 1391 patients diagnosed with Diffuse Large B-cell Lymphoma （DLBCL）, a major subtype ofNon-Hodgkin＇s Lymphoma （NHL）.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance for the General Linear Model

In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.

Approximate Conditional Likelihood for Generalized Linear Models with General Missing Data Mechanism

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate.Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.

ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS

For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.

Dispersal behavior correlates with personality of a North American fish

The process of dispersal is determined by the interaction of individual （intrinsic） traits and environmental （extrinsic） factors. Although many studies address and quantify dispersal, few evaluate both intrinsic and extrinsic factors jointly. We test the relative importance of intrinsic traits （exploration tendency and size） and extrinsic factors （population density and habitat quality） on dispersal of a medium-sized western United States minnow, southern leatherside chub Lepidomeda aliciae. A generalized linear model with a binomial response was used to determine the probability of individuals dispersing one year after tagging. Medium-sized individuals that were more prone to explore novel environments were 10.7 times more likely to be recaptured outside of their original capture area after a year （dispersal） compared to non-explorer individuals of the same size class. Differences be- tween explorer classifications within the small and large size classes were negligible. Open habitat within 50 m upstream also in- creased the probability of dispersal relative to controls. Relative location within the study reach, and population density were not significantly related to dispersal probabilities of individuals. Our results indicate that understanding of personality may illuminate patterns of dispersal within and among populations

ASYMPTOTIC NORMALITY OF MAXIMUM QUASI-LIKELIHOOD ESTIMATORS IN GENERALIZED LINEAR MODELS WITH FIXED DESIGN

In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.

Sequential Estimate for Generalized Linear Models with Uncertain Number of Effective Variables

For the generalized linear model,the authors propose a sequential sampling procedure based on an adaptive shrinkage estimate of parameter.This method can determine a minimum sample size under which effective variables contributing to the model are identified and estimates of regression parameters achieve the required accuracy.The authors prove that the proposed sequential procedure is asymptotically optimal.Numerical simulation studies show that the proposed method can save a large number of samples compared to the traditional sequential approach.

glmm.hp: an R package for computing individual effect of predictors in generalized linear mixed models

Generalized linear mixed models(GLMMs)have been widely used in contemporary ecology studies.However,determination of the relative importance of collinear predictors(i.e.fixed effects)to response variables is one of the challenges in GLMMs.Here,we developed a novel R package,glmm.hp,to decompose marginal R2^(2)explained by fixed effects in GLMMs.The algorithm of glmm.hp is based on the recently proposed approach‘average shared variance’i.e.used for multivariate analysis.We explained the principle and demonstrated the use of this package by simulated dataset.The output of glmm.hp shows individual marginal R2^(2)s that can be used to evaluate the relative importance of predictors,which sums up to the overall marginal R2^(2).Overall,we believe the glmm.hp package will be helpful in the interpretation of GLMM outcomes.

Time till death affects spider mobility and web-building behavior during web construction in an orb-web spider

It is well known that age influences organism mobility. This was demonstrated in vertebrates （such as mammals and birds） but has been less studied in invertebrates with the exception of Drosophila and the nematode Caenorhabditis elegans. Here we studied the influence of age on the mobility of the orb-weaving spider Zygiella x-notata during web construction. The orb-web is a good model because it has a characteristic geometrical structure and video tracking can be used to easily follow the spider＇s movements during web building. We investigated the influence of age （specifically chronological age, life span, and time till death） on different parameters of spider mobility during the construction of the capture spiral （distance traveled, duration of construction, spider velocity, spider movement, and spider inactivity） with a generalized linear model （GLM） procedure adjusted for the spider mass. The re- sults showed that neither chronological age, nor life span affected the mobility parameters. However, when the time till death decreased, there was a decrease in the distance traveled, the duration of the construction of the capture spiral, and the spider movement. The spider velocity and the time of inactivity were not affected. These results could be correlated with a decrease in the length of the silky thread deposited for the construction of the capture spiral. Spiders with a shorter time till death built smaller web using less silk. Thus, our study suggests strongly that time till death affects spider mobility during web construction but not the chronological age and thus may be a good indicator of senescence.

GENERALIZED p-VALUES FOR TESTING REGRESSION COEFFICIENTS IN PARTIALLY LINEAR MODELS

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.

INFERENCE ON COEFFICIENT FUNCTION FOR VARYING-COEFFICIENT PARTIALLY LINEAR MODEL

One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.