Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

Secchi depth maps for the Baltic Sea, 2003-2012, with links to GeoTIFs

Secchi depth is a measure of water transparency. In the Baltic Sea region, Secchi depth maps are used to assess eutrophication and as input for habitat models. Due to their spatial and temporal coverage, satellite data would be the most suitable data source for such maps. But the Baltic Sea's optical properties are so different from the open ocean that globally calibrated standard models suffer from large errors. Regional predictive models that take the Baltic Sea's special optical properties into account are thus needed. This paper tests how accurately generalized linear models (GLMs) and generalized additive models (GAMs) with MODIS/Aqua and auxiliary data as inputs can predict Secchi depth at a regional scale. It uses cross-validation to test the prediction accuracy of hundreds of GAMs and GLMs with up to 5 input variables. A GAM with 3 input variables (chlorophyll a, remote sensing reflectance at 678 nm, and long-term mean salinity) made the most accurate predictions. Tested against field observations not used for model selection and calibration, the best model's mean absolute error (MAE) for daily predictions was 1.07 m (22%), more than 50% lower than for other publicly available Baltic Sea Secchi depth maps. The MAE for predicting monthly averages was 0.86 m (15%). Thus, the proposed model selection process was able to find a regional model with good prediction accuracy. It could be useful to find predictive models for environmental variables other than Secchi depth, using data from other satellite sensors, and for other regions where non-standard remote sensing models are needed for prediction and mapping. Annual and monthly mean Secchi depth maps for 2003-2012 come with this paper as Supplementary materials.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

Comparing linear and non linear wind flow models

Assessing wind conditions on complex terrain has become a hard task as terrain complexity increases. That is why there is a need to extrapolate in a reliable manner some wind parameters that determine wind farms viability such as annual average wind speed at all hub heights as well as turbulence intensities. The development of these tasks began in the early 90´s with the widely used linear model WAsP and WAsP Engineering especially designed for simple terrain with remarkable results on them but not so good on complex orographies. Simultaneously non-linearized Navier Stokes solvers have been rapidly developed in the last decade through CFD (Computational Fluid Dynamics) codes allowing simulating atmospheric boundary layer flows over steep complex terrain more accurately reducing uncertainties. This paper describes the features of these models by validating them through meteorological masts installed in a highly complex terrain. The study compares the results of the mentioned models in terms of wind speed and turbulence intensity.

Deforestación y Pérdida de hábitat en Bosques de montaña en la Cuenca alta del Río Zamora (Loja, Ecuador)

Los bosques húmedos de montaña se encuentran reconocidos como uno de los ecosistemas más amenazados en el mundo, llegando inclusive a ser considerado como un “hotspot” por su alta diversidad y endemismo. La acelerada pérdida de cobertura vegetal de estos bosques ha ocasionado que, en la actualidad, se encuentren restringidos a una pequeña fracción de su área de distribución histórica. Pese a esto, los estudios realizados sobre cual es efecto de la deforestación, fragmentación, cambios de uso de suelo y su efecto en las comunidades de plantas presentes en este tipo de vegetación aún son muy escuetos, en comparación a los realizados con sus similares amazónicos. En este trabajo, el cual se encuentra dividido en seis capítulos, abordaremos los siguientes objetivos: a) Comprender cuál es la dinámica que han seguido los diferentes tipos de bosques montanos andinos de la cuenca del Rio Zamora, Sur de Ecuador durante entre 1976 y 2002. b) Proveer de evidencia de las tasas de deforestación y fragmentación de todos los tipos diferentes de bosques montanos andinos presentes en la cuenca del Rio Zamora, Sur de Ecuador entre 1976 y 2002. c) Determinar qué factores inducen a la fragmentación de bosques de montaña en la cuenca alta del río Zamora entre 1976 y 2002. d) Determinar cuáles son y cómo afectan los factores ambientales y socioeconómicos a la dinámica de la deforestación y regeneración (pérdida y recuperación del hábitat) sufrida por los bosques de montaña dentro de la zona de estudio y e) Determinar si la deforestación y fragmentación actúan sobre la diversidad y estructura de las comunidades de tres tipos de organismos (comunidades de árboles, comunidades de líquenes epífitos y comunidades de hepáticas epífitas). Este estudio se centró en el cuenca alta del río Zamora, localizada al sur de Ecuador entre las coordenadas 3º 00´ 53” a 4º 20´ 24.65” de latitud sur y 79º 49´58” a 78º 35´ 38” de longitud oeste, que cubre alrededor de 4300 km2 de territorio situado entre las capitales de las provincias de Loja y Zamora-Chinchipe. Con objeto de predecir la dinámica futura de la deforestación en la región de Loja y cómo se verán afectados los diferentes tipos de hábitat, así como para detectar los factores que más influyen en dicha dinámica, se han construido modelos basados en la historia de la deforestación derivados de fotografías aéreas e imágenes satelitales de tres fechas (1976, 1989 y 2002). La cuantificación de la deforestación se realizó mediante la tasa de interés compuesto y para la caracterización de la configuración espacial de los fragmentos de bosque nativo se calcularon índices de paisaje los cuales fueron calculados utilizando el programa Fragstats 3.3. Se ha clasificado el recubrimiento del terreno en forestal y no forestal y se ha modelado su evolución temporal con Modelos Lineales Generalizados Mixtos (GLMM), empleando como variables explicativas tanto variables ambientales espacialmente explícitas (altitud, orientación, pendiente, etc) como antrópicas (distancia a zonas urbanizadas, deforestadas, caminos, entre otras). Para medir el efecto de la deforestación sobre las comunidades modelo (de árboles, líquenes y hepáticas) se monitorearon 11 fragmentos de vegetación de distinto tamaño: dos fragmentos de más de cien hectáreas, tres fragmentos de entre diez y noventa ha y seis fragmentos de menos de diez hectáreas. En ellos se instalaron un total de 38 transectos y 113 cuadrantes de 20 x 20 m a distancias que se alejaban progresivamente del borde en 10, 40 y 80 m. Nuestros resultados muestran una tasa media anual de deforestación del 1,16% para todo el período de estudio, que el tipo de vegetación que más alta tasa de destrucción ha sufrido, es el páramo herbáceo, con un 2,45% anual. El análisis de los patrones de fragmentación determinó un aumento en 2002 de más del doble de fragmentos presentes en 1976, lo cual se repite en el análisis del índice de densidad promedio. El índice de proximidad media entre fragmentos muestra una reducción progresiva de la continuidad de las áreas forestadas. Si bien las formas de los fragmentos se han mantenido bastante similares a lo largo del período de estudio, la conectividad entre estos ha disminuido en un 84%. Por otro lado, de nuestros análisis se desprende que las zonas con mayor probabilidad de deforestarse son aquellas que están cercanas a zonas previamente deforestadas; la cercanía a las vías también influye significativamente en la deforestación, causando un efecto directo en la composición y estructura de las comunidades estudiadas, que en el caso de los árboles viene mediado por el tamaño del fragmento y en el caso del componente epífito (hepáticas y líquenes), viene mediado tanto por el tamaño del fragmento como por la distancia al borde del mismo. Se concluye la posibilidad de que, de mantenerse esta tendencia, este tipo de bosques desaparecerá en corto tiempo y los servicios ecosistémicos que prestan, se verán seriamente comprometidos. ABSTRACT Mountain rainforests are recognized as one of the most threatened ecosystems in the world, and have even come to be considered as a “hotspot” due to their high degree of diversity and endemism. The accelerated loss of plant cover of these forests has caused them to be restricted today to a small fraction of their area of historic distribution. In spite of this, studies done on the effect of deforestation, fragmentation, changes in soil use and their effect on the plant communities present in this type of vegetation are very brief compared to those done on their analogues in the Amazon region. In this study, which is divided into six chapters, we will address the following objectives: a) To understand what the dynamic followed by the different types of Andean mountain forests in the Zamora River watershed of southern Ecuador has been between 1976 and 2002. b) To provide evidence of the rates of deforestation and fragmentation of all the different types of Andean mountain forests existing in the upper watershed of the Zamora River between 1976 and 2002. c) To determine the factors that induces fragmentation of all different types of Andean mountain forests existing in the upper watershed of the Zamora River between 1976 and 2002. d) To determine what the environmental and anthropogenic factors are driving the dynamic of deforestation and regeneration (loss and recuperation of the habitat) suffered by the mountain forests in the area of the study and e) To determine if the deforestation and fragmentation act upon the diversity and structure of three model communities: trees, epiphytic lichens and epiphytic liverworts. This study is centered on the upper Zamora River watershed, located in southern Ecuador between 3º 00´ 53” and 4º 20´ 24.65 south latitude and 79º 49´ 58” to 78º 35´ 38” west longitude, and covers around 4,300 km2 of territory located between Loja and Zamora-Chinchipe provinces. For the purpose of predicting the future dynamic of deforestation in the Loja region and how different types of habitats will be affected, as well as detecting the environmental and socioeconomic factors that influence landscape dynamics, models were constructed based on deforestation history, derived from aerial photographs and satellite images for three dates (1976, 1989 and 2002). Quantifying the deforestation was done using the compound interest rate; to characterize the spatial configuration of fragments of native forest, landscape indices were calculated with Fragstats 3.3 program. Land cover was classified as forested and not forested and its evolution over time was modeled with Generalized Linear Mixed Models (GLMM), using spatially explicit environmental variables (altitude, orientation, slope, etc.) as well as anthropic variables (distance to urbanized, deforested areas and roads, among others) as explanatory variables. To measure the effects of fragmentation on three types of model communities (forest trees and epiphytic lichen and liverworts), 11 vegetation fragments of different sizes were monitored: two fragments of more than one hundred hectares, three fragments of between ten and ninety ha and six fragments of fewer than ten hectares . In these fragments, a total of 38 transects and 113 20 x 20 m quadrats were installed at distances that progressively moved away from the edge of the fragment by 10, 40 and 80 m. Our results show an average annual rate of deforestation of 1.16% for the entire period of the study, and that the type of vegetation that suffered the highest rate of destruction was grassy paramo, with an annual rate of 2.45%. The analysis of fragmentation patterns determined the number of fragments in 2002 more than doubled the number of fragments present in 1976, and the same occurred for the average density index. The variation of the average proximity index among fragments showed a progressive reduction of the continuity of forested areas. Although fragment shapes have remained quite similar over the period of the study, connectivity among them has diminished by 84%. On the other hand, it emerged from our analysis that the areas of greatest probability of deforestation were those that are close to previously deforested areas; proximity to roads also significantly favored the deforestation causing a direct effect on the composition of our model communities, that in the case of forest trees is determined by the size of the fragment, and in the case of the epiphyte communities (liverworts and lichens), is determined, by the size of the fragment as well as the distance to edge. A subject under discussion is the possibility that if this tendency continues, this type of forest will disappear in a short time, and the ecological services it provides, will be seriously endangered.

Análise genética da produção in vitro de embriões em bovinos Guzerá

O objetivo dessa pesquisa foi avaliar aspectos genéticos que relacionados à produção in vitro de embriões na raça Guzerá. O primeiro estudo focou na estimação de (co) variâncias genéticas e fenotípicas em características relacionadas a produção de embriões e na detecção de possível associação com a idade ao primeiro parto (AFC). Foi detectada baixa e média herdabilidade para características relacionadas à produção de oócitos e embriões. Houve fraca associação genética entre características ligadas a reprodução artificial e a idade ao primeiro parto. O segundo estudo avaliou tendências genéticas e de endogamia em uma população Guzerá no Brasil. Doadoras e embriões produzidos in vitro foram considerados como duas subpopulações de forma a realizar comparações acerca das diferenças de variação anual genética e do coeficiente de endogamia. A tendência anual do coeficiente de endogamia (F) foi superior para a população geral, sendo detectado efeito quadrático. No entanto, a média de F para a sub- população de embriões foi maior do que na população geral e das doadoras. Foi observado ganho genético anual superior para a idade ao primeiro parto e para a produção de leite (305 dias) entre embriões produzidos in vitro do que entre doadoras ou entre a população geral. O terceiro estudo examinou os efeitos do coeficiente de endogamia da doadora, do reprodutor (usado na fertilização in vitro) e dos embriões sobre resultados de produção in vitro de embriões na raça Guzerá. Foi detectado efeito da endogamia da doadora e dos embriões sobre as características estudadas. O quarto (e último) estudo foi elaborado para comparar a adequação de modelos mistos lineares e generalizados sob método de Máxima Verossimilhança Restrita (REML) e sua adequação a variáveis discretas. Quatro modelos hierárquicos assumindo diferentes distribuições para dados de contagem encontrados no banco. Inferência foi realizada com base em diagnósticos de resíduo e comparação de razões entre componentes de variância para os modelos em cada variável. Modelos Poisson superaram tanto o modelo linear (com e sem transformação da variável) quanto binomial negativo à qualidade do ajuste e capacidade preditiva, apesar de claras diferenças observadas na distribuição das variáveis. Entre os modelos testados, a pior qualidade de ajuste foi obtida para o modelo linear mediante transformação logarítmica (Log10 X +1) da variável resposta.

Fate and Transport of Naproxen in a Sandy Aquifer Material: Saturated Column Studies and Model Evaluation

Naproxen-C14H14O3 is a nonsteroidal anti-inflammatory drug which has been found at detectable concentrations in wastewater, surface water, and groundwater. Naproxen is relatively hydrophilic and is in anionic form at pH between 6 and 8. In this study, column experiments were performed using an unconsolidated aquifer material from an area near Barcelona (Spain) to assess transport and reaction mechanisms of Naproxen in the aquifer matrix under different pore water fluxes. Results were evaluated using HYDRUS-1D, which was used to estimate transport parameters. Batch sorption isotherms for Naproxen conformed with the linear model with a sorption coefficient of 0.42 (cm3 g−1), suggesting a low sorption affinity. Naproxen breakthrough curves (BTCs) measured in soil columns under steady-state, saturated water flow conditions displayed similar behavior, with no apparent hysteresis in sorption or dependence of retardation (R, 3.85-4.24) on pore water velocities. Soil sorption did not show any significant decrease for increasing flow rates, as observed from Naproxen recovery in the effluent. Sorption parameters estimated by the model suggest that Naproxen has a low sorption affinity to aquifer matrix. Most sorption of Naproxen occurred on the instantaneous sorption sites, with the kinetic sorption sites representing only about 10 to 40% of total sorption.

Modelling inpatient length of stay by a hierarchical mixture regression via the EM algorithm

The modelling of inpatient length of stay (LOS) has important implications in health care studies. Finite mixture distributions are usually used to model the heterogeneous LOS distribution, due to a certain proportion of patients sustaining-a longer stay. However, the morbidity data are collected from hospitals, observations clustered within the same hospital are often correlated. The generalized linear mixed model approach is adopted to accommodate the inherent correlation via unobservable random effects. An EM algorithm is developed to obtain residual maximum quasi-likelihood estimation. The proposed hierarchical mixture regression approach enables the identification and assessment of factors influencing the long-stay proportion and the LOS for the long-stay patient subgroup. A neonatal LOS data set is used for illustration, (C) 2003 Elsevier Science Ltd. All rights reserved.

Feeding ecology of the fish ectoparasite Gnathia sp. (Crustacea: Isopoda) from the Great Barrier Reef, and its implications for fish cleaning behaviour

The feeding rate of a parasitic gnathiid isopod on fish was examined. Individual fish, Hemigymnus melapterus, were exposed to gnathiid larvae and sampled after 5, 10, 30, 60, and 240 min. I recorded whether larvae had an engorged gut, an engorged gut containing red material, or had dropped off the fish after having completed engorgement; variation among sampling times and larval stages was analyzed using generalized linear mixed model analyses. The likelihood that larvae had an engorged gut increased with time and varied with larval stage. First stage (1.45 mm) larvae. After 30 min, however, most (>93%) larvae had an engorged gut regardless of their larval stage. The likelihood of red material in the gut of third stage larvae increased over time (46% after 30 min, 70% after 60 min, and 86% after 240 min) while that of first and second stage larvae remained relatively low (

Application of a generalized thermodynamic approach to characterize mesoporous materials

Equilibrium adsorption and desorption in mesoporous adsorbents is considered on the basis of rigorous thermodynamic analysis, in which the curvature-dependent solid-fluid potential and the compressibility of the adsorbed phase are accounted for. The compressibility of the adsorbed phase is considered for the first time in the literature in the framework of a rigorous thermodynamic approach. Our model is a further development of continuum thermodynamic approaches proposed by Derjaguin and Broekhoff and de Boer, and it is based on a reference isotherm of a non-porous material having the same chemical structure as that of the pore wall. In this improved thermodynamic model, we incorporated a prescription for transforming the solid-fluid potential exerted by the flat reference surface to the potential inside cylindrical and spherical pores. We relax the assumption that the adsorbed film density is constant and equal to that of the saturated liquid. Instead, the density of the adsorbed fluid is allowed to vary over the adsorbed film thickness and is calculated by an equation of state. As a result, the model is capable to describe the adsorption-desorption reversibility in cylindrical pores having diameter less than 2 nm. The generalized thermodynamic model may be applied to the pore size characterization of mesoporous materials instead of much more time-consuming molecular approaches. (c) 2005 Elsevier B.V. All rights reserved.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Fluidization characteristics of moist food particles

Changes in fluidization behaviour of green peas particulates with change in moisture content during drying were investigated using a fluidized bed dryer. All drying experiments were conducted at 50 + 2 0C and 13 + 2 % RH using a heat pump dehumidifier system. Fluidization experiments were undertaken for the bedheights of 100, 80, 60 and 40 mm and at 10 moisture content levels. Fluidization behaviour was best fitted to the linear model of Umf = A + B m. A generalized model was also formulated using the height variation. Also generalized equation and Ergun equation was used to compare minimum fluidization velocity. Copyright ©2006 The Berkeley Electronic Press. All rights reserved.

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.