General Linear Model

Measurement error occurs when one or more regression model covariates are measured with error, and is a common problem in occupational health and other fields. If the effects of measurement error are not corrected, estimates of the regression coefficients and their variances are biased. We consider the situation when an external validation study provides information about the measurement error process. Two related approaches for correcting measurement error, both called regression calibration, have been proposed. Although the estimators for the corrected regression coefficients can be shown to be the same under the two approaches, the asymptotic variances are derived using two different methods and have not been compared. In this paper, we show that these two methods give algebraically identical estimators for the corrected regression coefficients and their asymptotic variances, in the general case of multiple covariates measured with error, for a generalized linear model of exponen...

We present models predicting the potential distribution of a threatened ant species, Formica exsecta Nyl., in the Swiss National Park (SNP). Data to fit the models have been collected according to a random-stratified design with an equal number of replicates per stratum. The basic aim of such a sampling strategy is to allow the formal testing of biological hypotheses about those factors most likely to account for the distribution of the modeled species. The stratifying factors used in this study were: vegetation, slope angle and slope aspect, the ...

The increase of violence in present-day society calls for adequate crisis interventions for students with behavioral problems. Life Space Crisis Intervention (LSCI) is a systematic and formatted response to a student's crisis, based on cognitive, behavioral, psychodynamic and developmental theory. The following research article evaluates a LSCI Program with students referred to special schools with residential treatment because of severe behavioral problems. The evaluation was conducted using a quasi experimental pre-test-post-test control group design. Thirty-one match paired students were pre-tested before the interventions started and post-tested after a period of 11 months. Five standardized questionnaires were examined to assess the effectiveness of the LSCI Program. General Linear Model (GLM) with repeated measures was used to analyze all data. For the total group of subjects (n = 62) it was found that students' perception about their athletic competence decrease significantly after 11 months in residential care. A positive effect of LSCI was found on direct aggression and social desirability.

Alterations in VO(2) or VCO(2) are amongst the more polemical physiological adaptations ascribed to insects. Generally, metabolic rate is thought to be lowered in response to arid conditions, and elevated in species from cold environments compared to their more temperate relatives. However, most studies have rarely addressed the influence of both environmental factors in unison. To this end, standard metabolic rate and its temperature dependence were measured (at 4 degrees C intervals from 16 to 32 degrees C) in six Scarabaeus dung beetle species (three flightless, three volant) from a variety of habitats (warm, arid to cool, mesic) in southern Africa using flow-through respirometry. Mass specific VCO(2) varied from 0.0158 ml g(-1) h(-1) at 16 degrees C to 0.1839 ml g (-1) h(-1) at 32 degrees C. The slopes of the rate temperature curves were similar for all species (Q(10)s of 2.14-2.84), although the intercepts differed significantly in the direction (warm arid to cool mesic): S. gariepinus<S. hippocrates<S. striatum<S. galenus<S. rusticus<S. westwoodi. General linear models were fitted to the VCO(2) data with treatment temperature, wing status, mean annual rainfall and mean annual temperature as the independent variables. For all six species, the best fit model included treatment temperature and wing status only. Flightless species had significantly lower VCO(2)s than did winged ones. Amongst the flightless species, S. gariepinus, from the driest area, had the lowest VCO(2). Among the winged species it was impossible to determine whether environmental temperature or water availability were most important in influencing VCO(2); both were significant. We conclude that investigations of metabolic rate modulation, and especially metabolic cold adaptation, in insects must take both temperature and water availability into account.

Summary. I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother. By making use of Lanczos iteration the basis change and truncation are computationally efficient. The smoothers allow the use of approximate thin plate spline models with large data sets, avoid the problems that are associated with ‘knot placement’ that usually complicate modelling with regression splines or penalized regression splines, provide a sensible way of modelling interaction terms in generalized additive models, provide low rank approximations to generalized smoothing spline models, appropriate for use with large data sets, provide a means for incorporating smooth functions of more than one variable into non-linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines. Given that the approach produces spline-like models with a sparse basis, it also provides a natural way of incorporating unpenalized spline-like terms in linear and generalized linear models, and these can be treated just like any other model terms from the point of view of model selection, inference and diagnostics.

Background Air pollution in Darwin, Northern Australia, is dominated by smoke from seasonal fires in the surrounding savanna that burn during the dry season from April to November. Our aim was to study the association between particulate matter less than or equal to 10 microns diameter (PM10) and daily emergency hospital admissions for cardio-respiratory diseases for each fire season from 1996 to 2005. We also investigated whether the relationship differed in indigenous Australians; a disadvantaged population sub-group. Methods Daily PM10 exposure levels were estimated for the population of the city from visibility data using a previously validated model. We used over-dispersed Poisson generalized linear models with parametric smoothing functions for time and meteorology to examine the association between admissions and PM10 up to three days prior. An interaction between indigenous status and PM10 was included to examine differences in the impact on indigenous people. Results We found both positive and negative associations and our estimates had wide confidence intervals. There were generally positive associations between respiratory disease and PM10 but not with cardiovascular disease. An increase of 10 μg/m3 in same-day estimated ambient PM10 was associated with a 4.81% (95%CI: -1.04%, 11.01%) increase in total respiratory admissions. When the interaction between indigenous status and PM10 was assessed a statistically different association was found between PM10 and admissions three days later for respiratory infections of indigenous people (15.02%; 95%CI: 3.73%, 27.54%) than for non-indigenous people (0.67%; 95%CI: -7.55%, 9.61%). There were generally negative estimates for cardiovascular conditions. For non-indigenous admissions the estimated association with total cardiovascular admissions for same day ambient PM10 and admissions was -3.43% (95%CI: -9.00%, 2.49%) and the estimate for indigenous admissions was -3.78% (95%CI: -13.4%, 6.91%), although ambient PM10 did have positive (non-significant) associations with cardiovascular admissions of indigenous people two and three days later. Conclusion We observed positive associations between vegetation fire smoke and daily hospital admissions for respiratory diseases that were stronger in indigenous people. While this study was limited by the use of estimated rather than measured exposure data, the results are consistent with the currently small evidence base concerning this source of air pollution.

Cotton is the world’s leading cash crop, but it lags behind other major crops for marker-assisted breeding due to limited polymorphisms and a genetic bottleneck through historic domestication. This underlies a need for characterization, tagging, and utilization of existing natural polymorphisms in cotton germplasm collections. Here we report genetic diversity, population characteristics, the extent of linkage disequilibrium (LD), and association mapping of fiber quality traits using 202 microsatellite marker primer pairs in 335 G. hirsutum germplasm grown in two diverse environments, Uzbekistan and Mexico. At the significance threshold (r 2 ≥ 0.1), a genome-wide average of LD extended up to genetic distance of 25 cM in assayed cotton variety accessions. Genome wide LD at r 2 ≥ 0.2 was reduced to ~5–6 cM, providing evidence of the potential for association mapping of agronomically important traits in cotton. Results suggest linkage, selection, inbreeding, population stratification, and genetic drift as the potential LD-generating factors in cotton. In two environments, an average of ~20 SSR markers was associated with each main fiber quality traits using a unified mixed liner model (MLM) incorporating population structure and kinship. These MLM-derived significant associations were confirmed in general linear model and structured association test, accounting for population structure and permutation-based multiple testing. Several common markers, showing the significant associations in both Uzbekistan and Mexican environments, were determined. Between 7 and 43% of the MLM-derived significant associations were supported by a minimum Bayes factor at ‘moderate to strong’ and ‘strong to very strong’ evidence levels, suggesting their usefulness for marker-assisted breeding programs and overall effectiveness of association mapping using cotton germplasm resources.

Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set $\Theta \subset $IR$^p$ and some function set ${\cal G}$ of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linear model, a partial linear model, a single index model, but also the selection of explanatory variables can be considered as a special case of this hypothesis. To test this null hypothesis, we make use of the so-called marked empirical process introduced by \citeD and studied by \citeSt for the particular case of parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure. The asymptotic validity of the proposed test is established, and its finite sample performance is compared with other existing tests by means of a simulation study.