Approximate likelihood ratios for general estimating functions

The method of estimating functions (Godambe, 1991) is commonlyused when one desires to conduct inference about some parametersof interest but the full distribution of the observations isunknown. However, this approach may have limited utility, dueto multiple roots for the estimating function, a poorly behavedWald test, or lack of a goodness-of-fit test. This paper presentsapproximate likelihood ratios that can be used along with estimatingfunctions when any of these three problems occurs. We show thatthe approximate likelihood ratio provides correct large sampleinference under very general circumstances, including clustereddata and misspecified weights in the estimating function. Twomethods of constructing the approximate likelihood ratio, onebased on the quasi-likelihood approach and the other based onthe linear projection approach, are compared and shown to beclosely related. In particular we show that quasi-likelihoodis the limit of the projection approach. We illustrate the techniquewith two applications.     

Markov regression models for time series: a quasi-likelihood approach

This paper discusses a quasi-likelihood (QL) approach to regression analysis with time series data. We consider a class of Markov models, referred to by Cox (1981, Scandinavian Journal of Statistics 8, 93-115) as "observation-driven" models in which the conditional means and variances given the past are explicit functions of past outcomes. The class includes autoregressive and Markov chain models for continuous and categorical observations as well as models for counts (e.g., Poisson) and continuous outcomes with constant coefficient of variation (e.g., gamma). We focus on Poisson and gamma data for illustration. Analogous to QL for independent observations, large-sample properties of the regression coefficients depend only on correct specification of the first conditional moment.     

Fitting Mixed Poisson Regression Models Using Quasi-Likelihood Methods

This paper is to investigate the use of the quasi-likelihood, extended quasi-likelihood, and pseudo-likelihood approach to estimating and testing the mean parameters with respect to two variance models, M1: φ μ^θ(1+μphis;) and M2: φ μ^θ(1+τ). Simulation was conducted to compare the bias and standard deviation, and type I error of the Wald tests, based on the model-based and robust variance estimates, using the three semi-parametric approaches under four mixed Poisson models, two variance structures, and two sample sizes. All methods perform reasonably well in terms of bias. Type I error of the Wald test, based on either the model-based or robust estimate, tends to be larger than the nominal level when over-dispersion is moderate. The extended quasi-likelihood method with the variance model M1 performs more consistently in terms of the efficiency and controlling the type I error than with the model M2, and better than the pseudo-likelihood approach with either the M1 or M2 model. The model-based estimate seems to perform better than the robust estimate when the sample size is small.     

A stochastic catch-effort method for estimating animal abundance

A method for estimating the size of a heavily exploited animal population from catch data and relative-harvest-effort data is presented. The method assumes a competing-risk model of adult deaths and captures that is similar to the hazard-regression model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220). This model avoids making any assumptions about birth rates or juvenile mortality rates, and allows the user to incorporate an arbitrary number of time-dependent covariates into the natural and catch hazard functions. Estimates of the population's size, together with asymptotic error bounds and predictions of subsequent catches, are derived from maximum likelihood estimates of the parameters of the model. A simulation study is presented which indicates that this method is far more accurate than previously available catch-effort techniques. The method is illustrated with some fisheries data. A series of models is fitted to the data with the objective of improving the goodness of fit while maintaining biologic plausibility of the model. In this example a 68% reduction in the mean sum of squares for error is obtained and the accuracy of future catch predictions is greatly improved. This method is particularly appropriate for estimating the sizes of commercially exploited aquatic populations whose sizes are too large to make mark-recapture techniques feasible, and which are not amenable to line-transect techniques.     

Quantification of catch composition in fisheries: A methodology and its application to compare biodegradable and nylon gillnets

When evaluating fishing gear catches, the focus is often on a few species as opposed to the entire catch. In some fisheries this can lead to ignoring major part of catch composition. Thus, there is a need for a more holistic approach when evaluating the ecological impact of using a specific fishing gear and when comparing two or more gears. In this context, it is relevant to have a method that describes the total catch and quantifies proportions of the catch being wanted and unwanted. In this study, we outline such a method and demonstrate its applicability to catch data from a small-scale coastal gillnet fishery targeting European plaice (Pleuronectes platessa, Linnaeus, 1758) by comparing catch composition when using nylon and biodegradable gillnets. The results showed no significant differences in catch composition between gillnets made of the two materials. Therefore, the catch composition obtained using the more environmentally friendly biodegradable materials does not represent a barrier in this specific gillnet fishery. However, species selectivity of gillnets is still of concern as the primary target species constituted only half of the total catch composition in numbers while the rest was unwanted catch. The presented approach for quantifying and inferring the differences in catch composition can be further applied for assessing the performance of different fishing gears and their modifications.     

Gear type,species composition and economic value of fisheries in the mangroves of Pak Phanang,Thailand

Fishing gear and methods, catch composition, annual catch numbers and the monetary value of fisheries based in the mangroves of Pak Phanang, Nakhon Si Thamarat province, Thailand, were studied from September 2004 to February 2005. The fishing gear and methods were surveyed by visual observation and interviews. Sample catches were taken for each type of fishing gear and method. Semi-closed questionnaire surveys were conducted among fishers, local traders, local administrative officers and related organizations to derive information on utilized species, gear and methods, fisher and fishery status, and trading and catch price. The Pak Phanang mangrove fishery has three types of multi-species capture gear: channel traps, gill nets and lift nets. It also has three kinds of single-species (group) gear/methods: crab traps, catfish hooks and hand capture using a long tail fishing boat. A total of 57 fish species in 27 families, and 23 shell fish species in 8 families were recorded from the catch samples. Penaeid shrimp (25%), and ambassid (31%) and mugilid (24%) fishes were the abundant groups in the channel traps, while ariid (36%) and mugilid (19%) fishes were abundant in the lift net catches. Ambassid (42%) fish dominated the gill net catches. Species richness (number of species) varied depending on sampling month and type of fishing gear. The total annual catch and its monetary value were estimated to be 442–551 tons and US $368,038–733,973, respectively. The estimated annual catch per unit area of mangrove was 63–79 kg ha⁻¹, which generated a market value of US $368,038–733,973, respectively. The estimated annual catch per unit area of mangrove was 63–79 kg ha⁻¹, which generated a market value of US 52–105.     

Modelling the impact of the regulation of estuarine drift‐netting on the declared rod catch of Atlantic salmon Salmo salar L. in the River Usk

1. A novel method was used to determine if the statutory regulation of drift‐netting at the mouth of the River Usk in Wales was associated with a significant improvement in the stock and rod catch of salmon in the river upstream.
2. A linear regression model was constructed, in which the annual rod catch of salmon declared from the Usk between 1977 and 1988 was the dependent variable and the simultaneous annual catch declared from the nearby River Wye was the independent variable. The model was extrapolated to project the annual rod catches of salmon on the Usk, relative to the Wye, between 1989 and 1995.
3. The model accurately projected the actual rod catches declared from the Usk in 1989, 1990 and 1991. However, between 1992 and 1995 the declared catches deviated significantly ( P ≤ 0.05) from those projected by the model. The upsurge in rod catches declared after 1992 from the Usk, relative to the Wye was concomitant with the regulation of estuarine drift‐netting.
4. It was concluded that diminished estuarine exploitation had a beneficial impact on salmon angling success on the Usk. However, the utility of the model was restricted by inconsistencies in the methods used to generate the data, by changes in fishery management policies and by a lack of essential information on the interrelationships between catch, effort, stock and environmental conditions.     

Extended Mantel-Haenszel estimating procedure for multivariate logistic regression models

A class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case-control studies. It reduces to the well-known Mantel-Haenszel estimator when there is a single binary risk factor. Large-sample properties of the solutions to the proposed estimating equations are established for two distinct situations. Efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered. Application of the proposed method to family data and longitudinal data, where the conditional likelihood approach fails, is discussed. Two examples from case-control studies and one example from a study on familial aggregation are presented.     

Some covariance models for longitudinal count data with overdispersion

A family of covariance models for longitudinal counts with predictive covariates is presented. These models account for overdispersion, heteroscedasticity, and dependence among repeated observations. The approach is a quasi-likelihood regression similar to the formulation given by Liang and Zeger (1986, Biometrika 73, 13-22). Generalized estimating equations for both the covariate parameters and the variance-covariance parameters are presented. Large-sample properties of the parameter estimates are derived. The proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures.     

Model Selection in Estimating Equations

Model selection is a necessary step in many practical regression analyses. But for methods based on estimating equations, such as the quasi-likelihood and generalized estimating equation (GEE) approaches, there seem to be few well-studied model selection techniques. In this article, we propose a new model selection criterion that minimizes the expected predictive bias (EPB) of estimating equations. A bootstrap smoothed cross-validation (BCV) estimate of EPB is presented and its performance is assessed via simulation for overdispersed generalized linear models. For illustration, the method is applied to a real data set taken from a study of the development of ewe embryos.     

Robust tests for treatment effects based on censored recurrent event data observed over multiple periods

We derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods. These methods are based on estimating functions motivated by a working "mixed-Poisson" assumption under which conditioning can eliminate subject-specific random effects. Robust pseudoscore test statistics are obtained via "sandwich" variance estimation. The relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time-homogeneous Poisson model. The robustness and empirical power of the semiparametric approach are assessed through simulation. Adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two-period crossover trial of patients with bronchial asthma.     

Applications of DNA barcoding to fish landings: authentication and diversity assessment

DNA barcoding methodologies are being increasingly applied not only for scientific purposes but also for diverse real-life uses. Fisheries assessment is a potential niche for DNA barcoding, which serves for species authentication and may also be used for estimating within-population genetic diversity of exploited fish. Analysis of single-sequence barcodes has been proposed as a shortcut for measuring diversity in addition to the original purpose of species identification. Here we explore the relative utility of different mitochondrial sequences (12S rDNA, COI, cyt b, and D-Loop) for application as barcodes in fisheries sciences, using as case studies two marine and two freshwater catches of contrasting diversity levels. Ambiguous catch identification from COI and cyt b was observed. In some cases this could be attributed to duplicated names in databases, but in others it could be due to mitochondrial introgression between closely related species that may obscure species assignation from mtDNA. This last problem could be solved using a combination of mitochondrial and nuclear genes. We suggest to simultaneously analyze one conserved and one more polymorphic gene to identify species and assess diversity in fish catches.     

First use of pheromones to detect phenology patterns and density relationships of pine sawflies in German forests

1 Monitoring studies of pine sawflies with pheromone traps were performed for the first time in Germany. Pheromone traps baited with species‐specific pheromone substances were installed in pine forests at different locations in Bavaria, Brandenburg and Lower Saxony during two years. 2 It was possible to track the flight phenology of Diprion pini, Gilpinia pallida and Neodiprion sertifer reliably and to get information about the number of generations of these species in 1997 and 1998. 3 A clear relationship between trap catch and population density could not be detected, but qualitative changes in trap catch caused by different density levels were observed. 4 For D. pini, trap catches were different among endemic populations of different forest types. Furthermore, catches of males reflected the results from the regular cocoon collections by foresters during the previous winter. 5 For N. sertifer, trap catches in endemic populations were well separated from trap catches on sites with higher sawfly densities. However, no significant correlation between trap catch and sawfly density or defoliation level could be found. These results suggest that the efficacy of the pheromone traps probably varied with biological features (sex ratio, density level, immigration) of the particular population.     

Incidental capture of bottlenose dolphins (Tursiops truncatus) in shark nets: an assessment of some possible causes

A minimum of 250 bottlenose dolphins, Tursiops truncatus , was caught in anti-shark nets off Natal, South Africa between January 1980 and December 1988. Males and females constituted 45.4% and 54.6% of the catch, respectively. Sexually mature males and females constituted 18.2% and 24% of the total catch, respectively. Of the latter, 65% were lactating and a further 10.3% were pregnant. Adolescents, three or more years old but not mature, contributed 12.4% of the catch. Calves, two growth layer groups (GLGs) or less in the dentine, constituted the greatest portion of the catch, almost 43%, and of these almost 70% were either weaned or weaning at capture. Analyses of biological, environmental and physiographic data for each capture suggest a number of reasons for the catch of bottlenose dolphins. The distribution of catches was random but catch rates were proportional to the number of nets. The stomachs of most dolphins were almost full at the time of capture, suggesting that enmeshing occurred either during or subsequent to feeding. Most captures were of single animals, but lactating females with calves constituted more than 25% of catches. The direction of the prevailing current was significantly related to captures. These data are examined in relation to existing knowledge of bottlenose dolphins in this area and suggest that capture may be a consequence of prey abundance at and around the nets, dolphin capture occurring either during or directly after feeding. Possible methods of reducing captures are proposed.     

Sphaeroceridae (Diptera) caught in light traps at Rothamsted Experimental Station, Herts., 1980–83

ABSTRACT.

• 1 A total of 7063 specimens of Sphaeroceridae representing forty species were caught in four light traps, two in woodland and two in the open, at Rothamsted Experimental Station between December 1980 and December 1983.
• 2 A complete list of species and the numbers of individuals of each is provided.
• 3 The catches in the two traps in woodland were less diverse than the catches in the two traps in the open.
• 4 Two-way analysis of variance demonstrated a significant difference in catch from trap to trap.
• 5 When their similarities were compared, the four light trap catches formed two groups, corresponding with habitat type.
• 6 The majority of the catch were Copromyza similis (Collin) (5555 specimens or 78.64% of the total). The species was most abundant in winter from mid-December to early February, although there were slight differences in times of maximum abundance between open and woodland habitats.

     

Estimating equations with nonignorably missing response data

Troxel, Lipsitz, and Brennan (1997, Biometrics 53, 857-869) considered parameter estimation from survey data with nonignorable nonresponse and proposed weighted estimating equations to remove the biases in the complete-case analysis that ignores missing observations. This paper suggests two alternative modifications for unbiased estimation of regression parameters when a binary outcome is potentially observed at successive time points. The weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association 90, 106-121) is also modified to obtain unbiased estimating functions. The suggested estimating functions are unbiased only when the missingness probability is correctly specified, and misspecification of the missingness model will result in biases in the estimates. Simulation studies are carried out to assess the performance of different methods when the covariate is binary or normal. For the simulation models used, the relative efficiency of the two new methods to the weighting methods is about 3.0 for the slope parameter and about 2.0 for the intercept parameter when the covariate is continuous and the missingness probability is correctly specified. All methods produce substantial biases in the estimates when the missingness model is misspecified or underspecified. Analysis of data from a medical survey illustrates the use and possible differences of these estimating functions.     

Longitudinal data analysis for discrete and continuous outcomes

Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. This paper proposes a unifying approach to such analysis for a variety of discrete and continuous outcomes. A class of generalized estimating equations (GEEs) for the regression parameters is proposed. The equations are extensions of those used in quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) methods. The GEEs have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as we often expect. A consistent variance estimate is presented. We illustrate the use of the GEE approach with longitudinal data from a study of the effect of mothers' stress on children's morbidity.     

Distribution and dynamics of Japanese beetles along the Indianapolis Airport perimeter and the influence of land use on trap catch

As part of a program to minimize the accidental transportation of Japanese beetles (Popillia japonica) through cargo aircraft to areas where they are not established, a 4-yr trapping project was initiated to study the relative distribution and dynamics of the beetles along a trap line around the Indianapolis International Airport. Land use influence on beetle abundance (trap catch) was assessed using a geographic information system. Trap catch was consistently high in some locations and low in others. In general, high trap catches occurred near agronomic land planted with corn or soybeans, which are both preferred hosts of adult beetles. Low trap catches generally occurred in areas lacking preferred host plants. The amount of agronomic land within 500 m of the traps was always positively correlated with trap catch. Average trap catches were highly correlated by location from year to year, indicating stability of the relative distribution of the beetles along the trap line. Because high trap catches consistently occurred in the same locations, it can be inferred that trapping can be an effective method to monitor Japanese beetle populations. Taking airport-owned agronomic land out of corn and soybean production near the cargo terminals may reduce beetle activity in these areas.     

Catch and discards from experimental trawl and longline fishing in the deep water of the Rockall Trough

Comparative bottom trawl and longline surveys were carried out on two chartered commercial fishing vessels in the deep waters (350-1300 m) of the Rockall Trough, an area subjected to heavy commercial exploitation. The species composition, catch rates and length distributions from each survey were very different and reflected the fundamental difference in the two types of fishing operations. Bottom-trawled catches produced greater species diversity and higher discard rates. Longline catches produced larger specimens of teleost fish and were dominated by squalid shark. Trawl discards, expressed as kgs of discards per tonne of roundnose grenadier Coryphaenoides rupestris landed, were calculated for a broad range of the most abundant species taken in the catch. First estimates of total international discarding from deep-water trawling operations in the Rockall Trough area (7530 tonnes; 26.5 million individuals) were made by raising the discard rates using international grenadier landings for 1995. The outlook for the continued exploitation of the deep-water fish resource in the Rockall Trough and possible management options are discussed.     

Phenological and geographical relationships between catches of pea moth in sex-attractant traps

Traps containing a sex attractant of the pea moth (Cydia nigricana) were used to monitor numbers of male moths in individual fields in south-eastern and eastern England from 1976 to 1978 at 16 or more sites/yr. Data concerning catches at different sites on several occasions over the flight season, and dates on which a ‘threshold catch’ was achieved were examined, and were related weakly to site locations within areas. Area spray warnings, based on trap catches at a few sites within a large area, provide a less reliable indication of the need to spray than on-site monitoring (two traps) in each pea field. On-site monitoring may be improved by specialist interpretation of trap catches.