Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models.

The use of Poisson regression in the sociological study of suicide

This paper explains how Poisson regression can be used in studies in which the dependent variable describes the number of occurrences of some rare event such as suicide. After pointing out why ordinary linear regression is inappropriate for treating dependent variables of this sort, we go on to present the basic Poisson regression model and show how it fits in the broad class of generalized linear models. Then we turn to discussing a major problem of Poisson regression known as overdispersion and suggest possible solutions, including the correction of standard errors and negative binomial regression. The paper ends with a detailed empirical example, drawn from our own research on suicide.

Variables affecting the success of older applicants for employment in a public organization: An age -cued cognitive model of administrative decision-making

The dissertation takes a multivariate approach to answer the question of how applicant age, after controlling for other variables, affects employment success in a public organization. In addition to applicant age, there are five other categories of variables examined: organization/applicant variables describing the relationship of the applicant to the organization; organization/position variables describing the target position as it relates to the organization; episodic variables such as applicant age relative to the ages of competing applicants; economic variables relating to the salary needs of older applicants; and cognitive variables that may affect the decision maker's evaluation of the applicant. ^ An exploratory phase of research employs archival data from approximately 500 decisions made in the past three years to hire or promote applicants for positions in one public health administration organization. A logit regression model is employed to examine the probability that the variables modify the effect of applicant age on employment success. A confirmatory phase of the dissertation is a controlled experiment in which hiring decision makers from the same public organization perform a simulated hiring decision exercise to evaluate hypothetical applicants of similar qualifications but of different ages. The responses of the decision makers to a series of bipolar adjective scales add support to the cognitive component of the theoretical model of the hiring decision. A final section contains information gathered from interviews with key informants. ^ Applicant age has tended to have a curvilinear relationship with employment success. For some positions, the mean age of the applicants most likely to succeed varies with the values of the five groups of moderating variables. The research contributes not only to the practice of public personnel administration, but is useful in examining larger public policy issues associated with an aging workforce. ^

Nonparametric Evaluation of Quantitative Traits in Population-Based Association Studies when the Genetic Model is Unknown

Statistical association between a single nucleotide polymorphism (SNP) genotype and a quantitative trait in genome-wide association studies is usually assessed using a linear regression model, or, in the case of non-normally distributed trait values, using the Kruskal-Wallis test. While linear regression models assume an additive mode of inheritance via equi-distant genotype scores, Kruskal-Wallis test merely tests global differences in trait values associated with the three genotype groups. Both approaches thus exhibit suboptimal power when the underlying inheritance mode is dominant or recessive. Furthermore, these tests do not perform well in the common situations when only a few trait values are available in a rare genotype category (disbalance), or when the values associated with the three genotype categories exhibit unequal variance (variance heterogeneity). We propose a maximum test based on Marcus-type multiple contrast test for relative effect sizes. This test allows model-specific testing of either dominant, additive or recessive mode of inheritance, and it is robust against variance heterogeneity. We show how to obtain mode-specific simultaneous confidence intervals for the relative effect sizes to aid in interpreting the biological relevance of the results. Further, we discuss the use of a related all-pairwise comparisons contrast test with range preserving confidence intervals as an alternative to Kruskal-Wallis heterogeneity test. We applied the proposed maximum test to the Bogalusa Heart Study dataset, and gained a remarkable increase in the power to detect association, particularly for rare genotypes. Our simulation study also demonstrated that the proposed non-parametric tests control family-wise error rate in the presence of non-normality and variance heterogeneity contrary to the standard parametric approaches. We provide a publicly available R library nparcomp that can be used to estimate simultaneous confidence intervals or compatible multiplicity-adjusted p-values associated with the proposed maximum test.

Explaining dinophysis cf. acuminata abundance in Antifer (Normandy, France) using dynamic linear regression

Classical regression analysis can be used to model time series. However, the assumption that model parameters are constant over time is not necessarily adapted to the data. In phytoplankton ecology, the relevance of time-varying parameter values has been shown using a dynamic linear regression model (DLRM). DLRMs, belonging to the class of Bayesian dynamic models, assume the existence of a non-observable time series of model parameters, which are estimated on-line, i.e. after each observation. The aim of this paper was to show how DLRM results could be used to explain variation of a time series of phytoplankton abundance. We applied DLRM to daily concentrations of Dinophysis cf. acuminata, determined in Antifer harbour (French coast of the English Channel), along with physical and chemical covariates (e.g. wind velocity, nutrient concentrations). A single model was built using 1989 and 1990 data, and then applied separately to each year. Equivalent static regression models were investigated for the purpose of comparison. Results showed that most of the Dinophysis cf. acuminata concentration variability was explained by the configuration of the sampling site, the wind regime and tide residual flow. Moreover, the relationships of these factors with the concentration of the microalga varied with time, a fact that could not be detected with static regression. Application of dynamic models to phytoplankton time series, especially in a monitoring context, is discussed.

A demand-driven analysis of tourist accommodation price: A quantile regression of room bookings

Tourist accommodation expenditure is a widely investigated topic as it represents a major contribution to the total tourist expenditure. The identification of the determinant factors is commonly based on supply-driven applications while little research has been made on important travel characteristics. This paper proposes a demand-driven analysis of tourist accommodation price by focusing on data generated from room bookings. The investigation focuses on modeling the relationship between key travel characteristics and the price paid to book the accommodation. To accommodate the distributional characteristics of the expenditure variable, the analysis is based on the estimation of a quantile regression model. The findings support the econometric approach used and enable the elaboration of relevant managerial implications.

Applying Least Absolute Shrinkage Selection Operator and Akaike Information Criterion Analysis to Find the Best Multiple Linear Regression Models between Climate Indices and Components of Cow’s Milk

This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.

Obtaining environmental favourability functions from logistic regression

Logistic regression is a statistical tool widely used for predicting species’ potential distributions starting from presence/absence data and a set of independent variables. However, logistic regression equations compute probability values based not only on the values of the predictor variables but also on the relative proportion of presences and absences in the dataset, which does not adequately describe the environmental favourability for or against species presence. A few strategies have been used to circumvent this, but they usually imply an alteration of the original data or the discarding of potentially valuable information. We propose a way to obtain from logistic regression an environmental favourability function whose results are not affected by an uneven proportion of presences and absences. We tested the method on the distribution of virtual species in an imaginary territory. The favourability models yielded similar values regardless of the variation in the presence/absence ratio. We also illustrate with the example of the Pyrenean desman’s (Galemys pyrenaicus) distribution in Spain. The favourability model yielded more realistic potential distribution maps than the logistic regression model. Favourability values can be regarded as the degree of membership of the fuzzy set of sites whose environmental conditions are favourable to the species, which enables applying the rules of fuzzy logic to distribution modelling. They also allow for direct comparisons between models for species with different presence/absence ratios in the study area. This makes themmore useful to estimate the conservation value of areas, to design ecological corridors, or to select appropriate areas for species reintroductions.

Sustainable Australia : containing travel in master planned estates

Low density suburban development and excessive use of automobiles are associated with serious urban and environmental problems. These problems include traffic congestion, longer commuting times, high automobile dependency, air and water pollution, and increased depletion of natural resources. Master planned development suggests itself as a possible palliative for the ills of low density and high travel. The following study examines the patterns and dynamics of movement in a selection of master planned estates in Australia. The study develops new approaches for assessing the containment of travel within planned development. Its key aim is to clarify and map the relationships between trip generation and urban form and structure. The initial conceptual framework of the paper is developed in a review of literature related to urban form and travel behaviour. These concepts are tested empirically in a pilot study of suburban travel activity in master planned estates. A geographical information systems methodology is used to determine regional journey-to-work patterns and travel containment rates. Factors that influence selfcontainment patterns are estimated with a regression model. This research is a useful preliminary examination of travel self-containment in Australian master planned estates.

Research Monograph : Sustainable Australia : Containing travel in master planned estates

Low density suburban development and excessive use of automobiles are associated with serious urban and environmental problems. These problems include traffic congestion, longer commuting times, high automobile dependency, air and water pollution, and increased depletion of natural resources. Master planned development suggests itself as a possible palliative for the ills of low density and high travel. The following study examines the patterns and dynamics of movement in a selection of master planned estates in Australia. The study develops new approaches for assessing the containment of travel within planned development. Its key aim is to clarify and map the relationships between trip generation and urban form and structure. The initial conceptual framework of the report is developed in a review of literature related to urban form and travel behaviour. These concepts are tested empirically in a pilot study of suburban travel activity in master planned estates. A geographical information systems (GIS) methodology is used to determine regional journey-to-work patterns and travel containment rates. Factors that influence self-containment patterns are estimated with a regression model. The key research findings of the pilot study are: - There is a strong relation between urban structural form and patterns of trip generation; - The travel self-containment of Australian master planned estates is lower than the scholarly literature implies would occur if appropriate planning principles to achieve sustainable urban travel were followed; - Proximity to the central business district, income level and education status are positively correlated with travel containment; - Master planned estates depend more on local and regional centres for employment than on the central business district; - The service sector is the major employer in and around master planned estates. It tends to provide part-time and casual employment rather than full-time employment; - Travel self-containment is negative correlated with car dependency. Master planned estates with less car dependent residents, and with good access to public transport, appear to be more self-contained and, consequently, more sustainable than the norm. This research is a useful preliminary examination of travel self-containment in Australian master planned estates. It by no means exhausts the subject. In future research we hope to further assess sustainable travel patterns with more detailed spatial analysis.

Examination of the influence of personal attributes on consumer use on m-services

The rapid uptake of mobile devices has created the capacity to provide services to consumers while they are on the move, and new mobile services (m-services) are constantly emerging. In past research, personal attributes have been found to be import ant in the adoption and use of information and communication technology. However, little research has been conducted in the area of m-services. To explore factors influencing the use of these services, this paper examines personal attributes in terms of motivational, attitudinal and demographic characteristics. Specifically, it investigates the influence of innovativeness, self- efficacy, involvement and impulsiveness, as well as age and gender on m-services use . Data were collected from a convenience sample of 250 respondents using an online survey and a modified snowball procedure. Age and gender were quite well balanced in the sample. The multiple regression model was significant and the hypotheses relating to the positive relationship between impulsiveness, involvement and gender and m-services were supported. Findings are discussed, further implications for managers are suggested and directions for future research are proposed.

Using Trauma Injury Severity Score (TRISS) variables to predict length of hospital stay following trauma in New Zealand

Aim – To develop and assess the predictive capabilities of a statistical model that relates routinely collected Trauma Injury Severity Score (TRISS) variables to length of hospital stay (LOS) in survivors of traumatic injury. Method – Retrospective cohort study of adults who sustained a serious traumatic injury, and who survived until discharge from Auckland City, Middlemore, Waikato, or North Shore Hospitals between 2002 and 2006. Cubic-root transformed LOS was analysed using two-level mixed-effects regression models. Results – 1498 eligible patients were identified, 1446 (97%) injured from a blunt mechanism and 52 (3%) from a penetrating mechanism. For blunt mechanism trauma, 1096 (76%) were male, average age was 37 years (range: 15-94 years), and LOS and TRISS score information was available for 1362 patients. Spearman’s correlation and the median absolute prediction error between LOS and the original TRISS model was ρ=0.31 and 10.8 days, respectively, and between LOS and the final multivariable two-level mixed-effects regression model was ρ=0.38 and 6.0 days, respectively. Insufficient data were available for the analysis of penetrating mechanism models. Conclusions – Neither the original TRISS model nor the refined model has sufficient ability to accurately or reliably predict LOS. Additional predictor variables for LOS and other indicators for morbidity need to be considered.

The effect of Amblyopia on motor and psychosocial skills in children

Background/Aims: In an investigation of the functional impact of amblyopia on children, the fine motor skills, perceived self-esteem and eye movements of amblyopic children were compared with that of age-matched controls. The influence of amblyogenic condition or treatment factors that might predict any decrement in outcome measures was investigated. The relationship between indirect measures of eye movements that are used clinically and eye movement characteristics recorded during reading was examined and the relevance of proficiency in fine motor skills to performance on standardised educational tests was explored in a sub-group of the control children. Methods: Children with amblyopia (n=82; age 8.2 ± 1.3 years) from differing causes (infantile esotropia n=17, acquired strabismus n=28, anisometropia n=15, mixed n=13 and deprivation n=9), and a control group of children (n=106; age 9.5 ± 1.2 years) participated in this study. Measures of visual function included monocular logMAR visual acuity (VA) and stereopsis assessed with the Randot Preschool Stereoacuity test, while fine motor skills were measured using the Visual-Motor Control (VMC) and Upper Limb Speed and Dexterity (ULSD) subtests of the Brunicks-Oseretsky Test of Motor Proficiency. Perceived self esteem was assessed for those children from grade 3 school level with the Harter Self Perception Profile for Children and for those in younger grades (preschool to grade 2) with the Pictorial Scale of Perceived Competence and Acceptance for Young Children. A clinical measure of eye movements was made with the Developmental Eye Movement (DEM) test for those children aged eight years and above. For appropriate case-control comparison of data, the results from amblyopic children were compared with age-matched sub-samples drawn from the group of children with normal vision who completed the tests. Eye movements during reading for comprehension were recorded by the Visagraph infra-red recording system and results of standardised tests of educational performance were also obtained for a sub-set of the control group. Results Amblyopic children (n=82; age 8.2 ± 1.7 years) performed significantly poorer than age-matched control children (n=37; age 8.3 ± 1.3 years) on 9 of 16 fine motor skills sub-items and for the overall age-standardised scores for both VMC and ULSD items (p<0.05); differences were most evident on timed manual dexterity tasks. The underlying aetiology of amblyopia and level of stereoacuity significantly affected fine motor skill performance on both items. However, when examined in a multiple regression model that took into account the inter-correlation between visual characteristics, poorer fine motor skills performance was only associated with strabismus (F1,75 = 5.428; p =0. 022), and not with the level of stereoacuity, refractive error or visual acuity in either eye. Amblyopic children from grade 3 school level and above (n=47; age 9.2 ± 1.3 years), particularly those with acquired strabismus, had significantly lower social acceptance scores than age-matched control children (n=52; age 9.4 ± 0.5 years) (F(5,93) = 3.14; p = 0.012). However, the scores of the amblyopic children were not significantly different to controls for other areas related to self-esteem, including scholastic competence, physical appearance, athletic competence, behavioural conduct and global self worth. A lower social acceptance score was independently associated with a history of treatment with patching but not with a history of strabismus or wearing glasses. Amblyopic children from pre-school to grade 2 school level (n=29; age = 6.6 ± 0.6 years) had similar self-perception scores to their age-matched peers (n=20; age = 6.4 ± 0.5 years). There were no significant differences between the amblyopic (n=39; age 9.1 ± 0.9 years) and age-matched control (n = 42; age = 9.3 ± 0.38 years) groups for any of the DEM outcome measures (Vertical Time, Horizontal Time, Number of Errors and Ratio (Horizontal time/Vertical time)). Performance on the DEM did not significantly relate to measures of VA in either eye, level of binocular function, history of strabismus or refractive error. Developmental Eye Movement test outcome measures Horizontal Time and Vertical Time were significantly correlated with reading rates measured by the Visagraph for both reading for comprehension and naming numbers (r>0.5). Some moderate correlations were also seen between the DEM Ratio and word reading rates as recorded by Visagraph (r=0.37). In children with normal vision, academic scores in mathematics, spelling and reading were associated with measures of fine motor skills. Strongest effect sizes were seen with the timed manual dexterity domain, Upper Limb Speed and Dexterity. Conclusions Amblyopia may have a negative impact on a child’s fine motor skills and an older child’s sense of acceptance by their peers may be influenced by treatment that includes eye patching. Clinical measures of eye movements were not affected in amblyopic children. A number of the outcome measures of the DEM are associated with objective recordings of reading rates, supporting its clinical use for identification of children with slower reading rates. In children with normal vision, proficiency on clinical measures of fine motor skill are associated with outcomes on standardised measures of educational performance. Scores on timed manual dexterity tasks had the strongest association with educational performance. Collectively, the results of this study indicate that, in addition to the reduction in visual acuity and binocular function that define the condition, amblyopes have functional impairment in childhood development skills that underlie proficiency in everyday activities. The study provides support for strategies aimed at early identification and remediation of amblyopia and the co-morbidities that arise from abnormal visual neurodevelopment.

Socio-environmental factors and suicide in Queensland, Australia

Suicide has drawn much attention from both the scientific community and the public. Examining the impact of socio-environmental factors on suicide is essential in developing suicide prevention strategies and interventions, because it will provide health authorities with important information for their decision-making. However, previous studies did not examine the impact of socio-environmental factors on suicide using a spatial analysis approach. The purpose of this study was to identify the patterns of suicide and to examine how socio-environmental factors impact on suicide over time and space at the Local Governmental Area (LGA) level in Queensland. The suicide data between 1999 and 2003 were collected from the Australian Bureau of Statistics (ABS). Socio-environmental variables at the LGA level included climate (rainfall, maximum and minimum temperature), Socioeconomic Indexes for Areas (SEIFA) and demographic variables (proportion of Indigenous population, unemployment rate, proportion of population with low income and low education level). Climate data were obtained from Australian Bureau of Meteorology. SEIFA and demographic variables were acquired from ABS. A series of statistical and geographical information system (GIS) approaches were applied in the analysis. This study included two stages. The first stage used average annual data to view the spatial pattern of suicide and to examine the association between socio-environmental factors and suicide over space. The second stage examined the spatiotemporal pattern of suicide and assessed the socio-environmental determinants of suicide, using more detailed seasonal data. In this research, 2,445 suicide cases were included, with 1,957 males (80.0%) and 488 females (20.0%). In the first stage, we examined the spatial pattern and the determinants of suicide using 5-year aggregated data. Spearman correlations were used to assess associations between variables. Then a Poisson regression model was applied in the multivariable analysis, as the occurrence of suicide is a small probability event and this model fitted the data quite well. Suicide mortality varied across LGAs and was associated with a range of socio-environmental factors. The multivariable analysis showed that maximum temperature was significantly and positively associated with male suicide (relative risk [RR] = 1.03, 95% CI: 1.00 to 1.07). Higher proportion of Indigenous population was accompanied with more suicide in male population (male: RR = 1.02, 95% CI: 1.01 to 1.03). There was a positive association between unemployment rate and suicide in both genders (male: RR = 1.04, 95% CI: 1.02 to 1.06; female: RR = 1.07, 95% CI: 1.00 to 1.16). No significant association was observed for rainfall, minimum temperature, SEIFA, proportion of population with low individual income and low educational attainment. In the second stage of this study, we undertook a preliminary spatiotemporal analysis of suicide using seasonal data. Firstly, we assessed the interrelations between variables. Secondly, a generalised estimating equations (GEE) model was used to examine the socio-environmental impact on suicide over time and space, as this model is well suited to analyze repeated longitudinal data (e.g., seasonal suicide mortality in a certain LGA) and it fitted the data better than other models (e.g., Poisson model). The suicide pattern varied with season and LGA. The north of Queensland had the highest suicide mortality rate in all the seasons, while there was no suicide case occurred in the southwest. Northwest had consistently higher suicide mortality in spring, autumn and winter. In other areas, suicide mortality varied between seasons. This analysis showed that maximum temperature was positively associated with suicide among male population (RR = 1.24, 95% CI: 1.04 to 1.47) and total population (RR = 1.15, 95% CI: 1.00 to 1.32). Higher proportion of Indigenous population was accompanied with more suicide among total population (RR = 1.16, 95% CI: 1.13 to 1.19) and by gender (male: RR = 1.07, 95% CI: 1.01 to 1.13; female: RR = 1.23, 95% CI: 1.03 to 1.48). Unemployment rate was positively associated with total (RR = 1.40, 95% CI: 1.24 to 1.59) and female (RR=1.09, 95% CI: 1.01 to 1.18) suicide. There was also a positive association between proportion of population with low individual income and suicide in total (RR = 1.28, 95% CI: 1.10 to 1.48) and male (RR = 1.45, 95% CI: 1.23 to 1.72) population. Rainfall was only positively associated with suicide in total population (RR = 1.11, 95% CI: 1.04 to 1.19). There was no significant association for rainfall, minimum temperature, SEIFA, proportion of population with low educational attainment. The second stage is the extension of the first stage. Different spatial scales of dataset were used between the two stages (i.e., mean yearly data in the first stage, and seasonal data in the second stage), but the results are generally consistent with each other. Compared with other studies, this research explored the variety of the impact of a wide range of socio-environmental factors on suicide in different geographical units. Maximum temperature, proportion of Indigenous population, unemployment rate and proportion of population with low individual income were among the major determinants of suicide in Queensland. However, the influence from other factors (e.g. socio-culture background, alcohol and drug use) influencing suicide cannot be ignored. An in-depth understanding of these factors is vital in planning and implementing suicide prevention strategies. Five recommendations for future research are derived from this study: (1) It is vital to acquire detailed personal information on each suicide case and relevant information among the population in assessing the key socio-environmental determinants of suicide; (2) Bayesian model could be applied to compare mortality rates and their socio-environmental determinants across LGAs in future research; (3) In the LGAs with warm weather, high proportion of Indigenous population and/or unemployment rate, concerted efforts need to be made to control and prevent suicide and other mental health problems; (4) The current surveillance, forecasting and early warning system needs to be strengthened, to trace the climate and socioeconomic change over time and space and its impact on population health; (5) It is necessary to evaluate and improve the facilities of mental health care, psychological consultation, suicide prevention and control programs; especially in the areas with low socio-economic status, high unemployment rate, extreme weather events and natural disasters.