Traditional General Linear Model Research Articles

Non-Differentiable Loss Function Optimization and Interaction Effect Discovery in Insurance Pricing Using the Genetic Algorithm

Non-Differentiable Loss Function Optimization and Interaction Effect Discovery in Insurance Pricing Using the Genetic Algorithm

Robust Inference and Modeling of Mean and Dispersion for Generalized Linear Models

Generalized Linear Models (GLMs) are a popular class of regression models when the responses follow a distribution in the exponential family. In real data the variability often deviates from the relation imposed by the exponential family distribution, which results in over- or underdispersion. Dispersion effects may even vary in the data. Such datasets do not follow the traditional GLM distributional assumptions, leading to unreliable inference. Therefore, the family of double exponential distributions has been proposed, which models both the mean and the dispersion as a function of covariates in the GLM framework. Since standard maximum likelihood inference is highly susceptible to the possible presence of outliers, we propose the robust double exponential (RDE) estimator. Asymptotic properties and robustness of the RDE estimator are discussed. A generalized robust quasi-deviance measure is introduced which constitutes the basis for a stable robust test. Simulations for binomial and Poisson models show the excellent performance of the RDE estimator and corresponding robust tests. Penalized versions of the RDE estimator are developed for sparse estimation with high-dimensional data and for flexible estimation via generalized additive models (GAMs). Real data applications illustrate the relevance of robust inference for dispersion effects in GLMs and GAMs. Supplementary materials for this article are available online.

Identifying Determinants of Dyslexia: An Ultimate Attempt Using Machine Learning

Research based on traditional linear techniques has yet not been able to clearly identify the role of cognitive skills in reading problems, presumably because the process of reading and the factors that are associated with reading reside within a system of multiple interacting and moderating factors that cannot be captured within traditional statistical models. If cognitive skills are indeed indicative of reading problems, the relatively new nonlinear techniques of machine learning should make better predictions. The aim of the present study was to investigate whether cognitive factors play any role in reading skill, questioning (1) the extent to what cognitive skills are indicative of present reading level, and (2) the extent to what cognitive skills are indicative of future reading progress. In three studies with varying groups of participants (average school-aged and poor readers), the results of four supervised machine learning techniques were compared to the traditional General Linear Models technique. Results of all models appeared to be comparable, producing poor to acceptable results, which are however inadequate for making a thorough prediction of reading development. Assumably, cognitive skills are not predictive of reading problems, although they do correlate with one another. This insight has consequences for scientific theories of reading development, as well as for the prevention and remediation of reading difficulties.

Catch per unit effort standardization using spatio-temporal models for Australia’s Eastern Tuna and Billfish Fishery

AbstractThe majority of catch per unit effort (cpue) standardizations use generalized linear models (GLMs) or generalized additive models (GAMs). We develop geostatistical models that model catch locations as continuous Gaussian random fields (GRFs) and apply them to standardizing cpue in Australia’s Eastern Tuna and Billfish Fishery (ETBF). The results are compared with the traditional GLMs currently used in ETBF assessments as well as GAMs. Specifically, we compare seven models in three groups: two GLMs, two GAMs, and three GRF models. Within each group, one model treats spatial and temporal variables independently, while the other model(s) treats them together as an interaction term. The two spatio-temporal GRF models differ in treating the spatial–temporal interaction: either as a random process or as an autoregressive process. We simulate catch rate data for five pelagic species based on real fishery catch rates so that the simulated data reflect real fishery patterns while the “true” annual abundance levels are known. The results show that within each group, the model with a spatial–temporal interaction term significantly outperforms the other model treating spatial and temporal variables independently. For spatial–temporal models between the three groups, prediction accuracy tends to improve from GLM to GAM and to the GRF models. Overall, the spatio-temporal GRF autoregressive model reduces mean relative predictive error by 43.4% from the GLM, 33.9% from the GAM, and reduces mean absolute predictive error by 23.5% from the GLM and 3.3% from the GAM, respectively. The comparison suggests a promising direction for further developing the geostatistical models for the ETBF.

Efeitos moderadores duplos e triplos e plots em análise de regressão

Distinguished international published papers examine mediator, moderator, moderator-mediator, mediator-moderator variables and indirect effects over the causal relationship in social sciences. Among the possible different ways of data interpretation, understand the moderating effect using linear regression analysis is an alternative. The main objective of this article is to discuss and to clarify theconcept of moderation, when using the multiple regression analysis instead of the traditional general linear models – GLM (e.g., MANOVA, ANCOVA, ANOVA, ANCOVA). The second goal is to apply three estimates: (a) two-way moderating effect with independent continuous variables, (b) two-way moderating effect with a continuous and a dummy variable as independent variables and (c) three-waymoderating effect with independent continuous variables, all using regression analysis. Third, the paper discusses the ordinal moderation and cross-over effects.The results showed that three-way interactions demand group analysis and were not used.

Use of Geographically Weighted Poisson Regression to examine the effect of distance on Tuberculosis incidence: A case study in Nam Dinh, Vietnam.

ObjectivesThis study aimed to examine the potential of combining routine tuberculosis (TB) surveillance and demographic and socioeconomic variables into the Geographic Information System (GIS) to describe the geographical distribution of TB notified incidence in relation to distances to health services as well as local demographic and socioeconomic factors, including population density, urban/rural status, and household poverty rates in Nam Dinh, Vietnam. It also aimed to compare the conventional Generalized Linear Models (GLM) Poisson regression model and Geographically Weighted Poisson Regression (GWPR) models in order to determine the best fitting model that can be used to investigate the relationship between TB notified incidence and distances and the social risk factors.MethodsThe data of new and relapse patients with all forms of TB aged ≥15 years residing in Nam Dinh (Vietnam) from 2012 to 2015 were collected from the Administration of Medical Services’ (Ministry of Health of Vietnam) TB surveillance database. Data on the population and household poverty rates from 2012 to 2015 were gathered from the Nam Dinh Statistical Office. Distances between communes and the nearest TB diagnostic facilities in districts were computed. The TB notified incidence per 100,000 population was denoted by indirect age and sex standardized incidence ratio. GLM Poisson regression and GWPR were performed to assess the relationship between distance and TB incidence.ResultsThe average notified TB incidence level measured from 2012 to 2015 is 82 per 100,000 population (range: 79-84/100,000). The distance to the nearest TB diagnosis presents a negative effect on TB notified incidence. By capturing spatial heterogeneity, the GWPR may be better at fitting data (corrected Aikake information criterion [AICc] = 245.71, residual deviance = 221.12) than the traditional GLM (AICc = 251.53, residual deviance = 241.21)ConclusionsGIS technologies benefit TB surveillance system. Distances should be considered when planning methods of improving access for those who live far from TB diagnostic services, thereby improving TB detection. Additional studies must confirm the association between geographic distance and TB case detection and must explore other factors that may affect TB notified incidence.

Spatial modeling improves understanding patterns of invasive species defoliation by a biocontrol herbivore

Spatial modeling has proven to be useful in understanding the drivers of plant populations in the field of ecology, but has yet to be applied to understanding variation in biocontrol impact. In this study, we employ multi-scale analysis (Moran’s Eigenvector Maps) to better understand the variation in tree canopy exposed to defoliation by a biocontrol beetle (Diorhabda spp.). The control of the exotic tree Tamarix in riparian areas has long been a priority for land managers and ecologists in the American southwest. Diorhabda spp. was introduced as a bio-control agent beginning in 2001 and has since become an inseparable part of Tamarix-dominated river systems in the southwest. Between 2013 and 2016 tamarisk dieback was assessed at 79 sites across Grand County, Utah, arguably the epicenter of Diorhabda impact in the U.S. Canopy cover of Tamarix was between 73 and 81% at these sites, with the percent that was live cover fluctuating by year with a minimum of 42%. Using a traditional general linear model, we found that readily and commonly measured environmental factors could explain only up to 26% of the variation in Tamarix live canopy each year. The number of defoliations was correlated with an increase rather than a decrease in percent live canopy, suggesting compensatory growth. Spatial structure alone explained 22–40% of variation. We found fine scale spatial structure at less than 10 km and broad scale spatial structure from 10 to 30 km. Combining both traditional and novel spatial statistical methods we increased that percentage to 43–63%, depending on year. These results suggest that scientists and land managers must look beyond commonly measured environmental variables to explain non-random biocontrol impact in this system. In particular, this study points to the potential for biotic interactions and variation in flood cycles for further exploration of the identified spatial structure.

Intersubject synchronisation analysis of brain activity associated with the instant effects of acupuncture: an fMRI study.

To use a promising analytical method, namely intersubject synchronisation (ISS), to evaluate the brain activity associated with the instant effects of acupuncture and compare the findings with traditional general linear model (GLM) methods. 30 healthy volunteers were recruited for this study. Block-designed manual acupuncture stimuli were delivered at SP6, and de qi sensations were measured after acupuncture stimulation. All subjects underwent functional MRI (fMRI) scanning during the acupuncture stimuli. The fMRI data were separately analysed by ISS and traditional GLM methods. All subjects experienced de qi sensations. ISS analysis showed that the regions activated during acupuncture stimulation at SP6 were mainly divided into five clusters based on the time courses. The time courses of clusters 1 and 2 were in line with the acupuncture stimulation pattern, and the active regions were mainly involved in the sensorimotor system and salience network. Clusters 3, 4 and 5 displayed an almost contrary time course relative to the stimulation pattern. The brain regions activated included the default mode network, descending pain modulation pathway and visual cortices. GLM analysis indicated that the brain responses associated with the instant effects of acupuncture were largely implicated in sensory and motor processing and sensory integration. The ISS analysis considered the sustained effect of acupuncture and uncovered additional information not shown by GLM analysis. We suggest that ISS may be a suitable approach to investigate the brain responses associated with the instant effects of acupuncture.

Application of generalized estimating equations for crash frequency modeling with temporal correlation

Traditional crash frequency modeling uses crash frequency data averaged across multiple years. When data size is small, crash data in each year are used in the modeling to extend the size of the samples. The extension of sample size could create a temporal correlation among crash frequencies of the different years, which could affect the modeling accuracy. The primary objective of this study is to evaluate the application of the generalized estimating equation (GEE) procedures to account for the temporal correlation in the longitudinal crash frequency data. Four-year crash data at exit ramps on a freeway in China were collected for modeling. Based on the same data, traditional generalized linear models (GLMs) were estimated for model com- parison. Results showed that traditional GLM underestimated the standard errors of coefficients for explanatory variables. The GEE procedure with an exchangeable correlation structure successively captured the temporal correlation among the crash fre- quencies of the different years. The GLM with GEE outperformed the traditional GLM in providing a good fit for the crash fre- quency data. Results of this study can help researchers better understand how various factors affect the crash frequencies at freeway divergent areas and propose effective countermeasures.

Effects of spatial smoothing on inter-subject correlation based analysis of FMRI

This study evaluates the effects of spatial smoothing on inter-subject correlation (ISC) analysis for FMRI data using the traditional model based analysis as a reference. So far within ISC analysis the effects of smoothing have not been studied systematically and linear Gaussian filters with varying kernel widths have been used without better knowledge about the effects of filtering. Instead, with the traditional general linear model (GLM) based analysis, the effects of smoothing have been studied extensively.In this study, ISC and GLM analyses were computed with two experimental and one simulated block-design datasets. The test statistics and the detected activation areas were compared numerically with correlation and Dice similarity measures, respectively. The study verified that 1) the choice of the filter substantially affected the activations detected by ISC analysis, 2) the detected activations according to ISC and GLM methods were highly similar regardless of the smoothing kernel and 3) the effect of spatial smoothing was mildly smaller on ISC than GLM analysis. Our results indicated that a good selection of the full width at half maximum of the Gaussian smoothing kernel for ISC was slightly larger than double the original voxel size.

A comparison of three empirically based, spatially explicit predictive models of residential soil Pb concentrations in Baltimore, Maryland, USA: understanding the variability within cities

In many older US cities, lead (Pb) contamination of residential soil is widespread; however, contamination is not uniform. Empirically based, spatially explicit models can assist city agencies in addressing this important public health concern by identifying areas predicted to exceed public health targets for soil Pb contamination. Sampling of 61 residential properties in Baltimore City using field portable X-ray fluorescence revealed that 53% had soil Pb that exceeded the USEPA reportable limit of 400ppm. These data were used as the input to three different spatially explicit models: a traditional general linear model (GLM), and two machine learning techniques: classification and regression trees (CART) and Random Forests (RF). The GLM revealed that housing age, distance to road, distance to building, and the interactions between variables explained 38% of the variation in the data. The CART model confirmed the importance of these variables, with housing age, distance to building, and distance to major road networks determining the terminal nodes of the CART model. Using the same three predictor variables, the RF model explained 42% of the variation in the data. The overall accuracy, which is a measure of agreement between the model and an independent dataset, was 90% for the GLM, 83% for the CART model, and 72% for the RF model. A range of spatially explicit models that can be adapted to changing soil Pb guidelines allows managers to select the most appropriate model based on public health targets.

Spatial ICA reveals functional activity hidden from traditional fMRI GLM-based analyses

OPINION article Front. Neurosci., 27 August 2013Sec. Brain Imaging Methods https://doi.org/10.3389/fnins.2013.00154

Inter-Subject Correlation in fMRI: Method Validation against Stimulus-Model Based Analysis

Within functional magnetic resonance imaging (fMRI), the use of the traditional general linear model (GLM) based analysis methods is often restricted to strictly controlled research setups requiring a parametric activation model. Instead, Inter-Subject Correlation (ISC) method is based on voxel-wise correlation between the time series of the subjects, which makes it completely non-parametric and thus suitable for naturalistic stimulus paradigms such as movie watching. In this study, we compared an ISC based analysis results with those of a GLM based in five distinct controlled research setups. We used International Consortium for Brain Mapping functional reference battery (FRB) fMRI data available from the Laboratory of Neuro Imaging image data archive. The selected data included measurements from 37 right-handed subjects, who all had performed the same five tasks from FRB. The GLM was expected to locate activations accurately in FRB data and thus provide good grounds for investigating relationship between ISC and stimulus induced fMRI activation. The statistical maps of ISC and GLM were compared with two measures. The first measure was the Pearson's correlation between the non-thresholded ISC test-statistics and absolute values of the GLM Z-statistics. The average correlation value over five tasks was 0.74. The second was the Dice index between the activation regions of the methods. The average Dice value over the tasks and three threshold levels was 0.73. The results of this study indicated how the data driven ISC analysis found the same foci as the model-based GLM analysis. The agreement of the results is highly interesting, because ISC is applicable in situations where GLM is not suitable, for example, when analyzing data from a naturalistic stimuli experiment.

Statistical epistasis and progressive brain change in schizophrenia: an approach for examining the relationships between multiple genes

Although schizophrenia is generally considered to occur as a consequence of multiple genes that interact with one another, very few methods have been developed to model epistasis. Phenotype definition has also been a major challenge for research on the genetics of schizophrenia. In this report we use novel statistical techniques to address the high dimensionality of genomic data, and we apply a refinement in phenotype definition by basing it on the occurrence of brain changes during the early course of the illness, as measured by repeated MR scans (i.e., an “intermediate phenotype.” The method combines a machine learning algorithm, the ensemble method using stochastic gradient boosting, with traditional general linear model statistics. We began with fourteen genes that are relevant to schizophrenia based on association studies or their role in neurodevelopment and then used statistical techniques to reduce them to five genes and 17 SNPs that had a significant statistical interaction: 5 for PDE4B, 4 for RELN, 4 for ERBB4, 3 for DISC1, and one for NRG1. Five of the SNPs involved in these interactions replicate previous research, in that these five SNPs have previously been identified as schizophrenia vulnerability markers or implicate cognitive processes relevant to schizophrenia. This ability to replicate previous work suggests that our method has potential for detecting a meaningful epistatic relationships among the genes that influence brain abnormalities in schizophrenia.

Abnormal ERD/ERS but Unaffected BOLD Response in Patients with Unverricht–Lundborg Disease During Index Extension: A Simultaneous EEG-fMRI Study

Electrophysiological studies indicate that Unverricht-Lundborg's disease (ULD), the most common form of progressive myoclonus epilepsy in Europe, is characterized by the involvement of multiple cortical regions in degenerative changes that lead to enhanced excitation and deficient inhibition. We searched for the haemodynamic correlates of these effects using functional MRI (fMRI) of self-paced index extensions, a well-accepted task highlighting significant differences. EEG and fMRI were simultaneously acquired in 11 ULD patients and 16 controls, performing the index extensions individually (event-related task) as well as repetitively (block task). ERD/ERS analysis was performed for the EEG data in the alpha and beta bands. fMRI time-series were analyzed using the traditional general linear model, as well as with an assumption-free approach, and by means of cross-region correlations representing functional connectivity. In line with the existing literature, ULD patients had enhanced desynchronization in the alpha band and reduced post-movement synchronization in the beta band. By contrast, fMRI did not reveal any difference between the two groups; there were no activation intensity, latency or extent effects, no significant engagement of additional regions, and no changes to functional connectivity. We conclude that, so long as the patients are executing a task which does not induce obvious action myoclonus, the hypothesized abnormalities in pyramidal neuron and interneuron dynamics are relatively subtle, embodied in processes which are not metabolically-demanding and take place at a time-scale invisible to fMRI.

Multivariate Pattern Analysis of Functional Magnetic Resonance Imaging Data Reveals Deficits in Distributed Representations in Schizophrenia

Multivariate pattern analysis is an alternative method of analyzing functional magnetic resonance imaging (fMRI) data, which is capable of decoding distributed neural representations. We applied this method to test the hypothesis of the impairment in distributed representations in schizophrenia. We also compared the results of this method with traditional general linear model (GLM)-based univariate analysis. Nineteen schizophrenia and 15 control subjects viewed two runs of stimuli-exemplars of faces, scenes, objects, and scrambled images. To verify engagement with stimuli, subjects completed a 1-back matching task. A multivoxel pattern classifier was trained to identify category-specific activity patterns on one run of fMRI data. Classification testing was conducted on the remaining run. Correlation of voxelwise activity across runs evaluated variance over time in activity patterns. Patients performed the task less accurately. This group difference was reflected in the pattern analysis results with diminished classification accuracy in patients compared with control subjects, 59% and 72%, respectively. In contrast, there was no group difference in GLM-based univariate measures. In both groups, classification accuracy was significantly correlated with behavioral measures. Both groups showed highly significant correlation between interrun correlations and classification accuracy. Distributed representations of visual objects are impaired in schizophrenia. This impairment is correlated with diminished task performance, suggesting that decreased integrity of cortical activity patterns is reflected in impaired behavior. Comparisons with univariate results suggest greater sensitivity of pattern analysis in detecting group differences in neural activity and reduced likelihood of nonspecific factors driving these results.

A method for multi-group inter-participant correlation: Abnormal synchrony in patients with schizophrenia during auditory target detection

The general linear model (GLM) approach is the most commonly used method in functional magnetic resonance imaging analysis in predicting a particular response. Recently, a novel method of analysis, referred to as inter-participant correlation (IPC), was developed which attempts to determine the level of blood oxygen level-dependent (BOLD) synchrony among subjects. The IPC approach enables detection of changes in inter-participant BOLD synchrony in a manner that does not rely on an explicit model of the hemodynamic activity. In this paper, we extend IPC to the case of two groups and derive an approach for thresholding the resulting maps. We demonstrate our approach by comparing 35 patients with paranoid schizophrenia (DSM-IV sub-type 295.30) to 35 healthy matched controls during an auditory target detection paradigm. Results showed significantly lower inter-participant BOLD synchrony in patients versus healthy controls in areas including bilateral temporal lobes, medial frontal gyrus, anterior cingulate cortex, dorsolateral prefrontal cortex, thalamus, insula, and cerebellum. The IPC approach is straightforward to use and provides a useful complement to traditional GLM techniques. This approach may also be sensitive to underlying, but unpredictable, changes in inter-participant BOLD synchrony between patients and controls.

Incidence and Practical Issues of Mental Health for School-Aged Youth in Juvenile Justice Detention

This study documents rates of youth referred for adjudication to a state juvenile justice system who have coexisting—and often unidentified—mental illnesses. The project examined records for 1,411 youth who were admitted over a 1-year period. All were screened with an instrument that allowed multidimensional appraisal along relevant mental health concerns. Approximately 70% of the youth exhibited a caution or warning in one or more (out of six) categories of mental health concern. These incidents were cross-referenced with categories of offense as well as incidents of using psychotropic medication. Sex, age, and ethnic heritage were also tracked. Results for each category show wide differences. Statistically, variances among the variables were analyzed by traditional general linear model techniques (e.g., ANOVA, regression) and differences in underlying constructs were confirmed by structural equation modeling. Schoolteachers, counselors, psychologists and psychiatrists, and policymakers can employ this information when working with youth in the juvenile justice system or those who are at risk.

Actuarial statistics with generalized linear mixed models

Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics and Applied Probability. Chapman and Hall, New York]. Traditional GLMs however model a sample of independent random variables. Since actuaries very often have repeated measurements or longitudinal data (i.e. repeated measurements over time) at their disposal, this article considers statistical techniques for modelling such data within the framework of GLMs. Use is made of generalized linear mixed models (GLMMs) which model a transformation of the mean as a linear function of both fixed and random effects. The likelihood and Bayesian approaches to GLMMs are explained. The models are illustrated by considering classical credibility models and more general regression models for non-life ratemaking in the context of GLMMs. Details on computation and implementation (in SAS and WinBugs) are provided.

Semi-blind ICA of fMRI: A method for utilizing hypothesis-derived time courses in a spatial ICA analysis

Independent component analysis (ICA) is a data-driven approach utilizing high-order statistical moments to find maximally independent sources that has found fruitful application in functional magnetic resonance imaging (fMRI). Being a blind source separation technique, ICA does not require any explicit constraints upon the fMRI time courses. However, for some fMRI data analysis applications, such as for the analysis of an event-related paradigm, it would be useful to flexibly incorporate paradigm information into the ICA analysis. In this paper, we present an approach for constrained or semi-blind ICA (sbICA) analysis of event-related fMRI data by imposing regularization on certain estimated time courses using the paradigm information. We demonstrate the performance of our approach using both simulations and fMRI data from a three-stimulus auditory oddball paradigm. Simulation results suggest that (1) a regression approach slightly outperforms ICA when prior information is accurate and ICA outperforms the general linear model (GLM)-based approach when prior information is not completely accurate, (2) prior information improves the robustness of ICA in the presence of noise, and (3) ICA analysis using prior information with temporal constraints can outperform a regression approach when the prior information is not completely accurate. Using fMRI data, we compare a regression-based conjunction analysis of target and novel stimuli, both of which elicit an orienting response, to an sbICA approach utilizing both the target and novel stimuli to constrain the ICA time courses. Results show similar positive associations for both GLM and sbICA, but sbICA detects additional negative associates consistent with regions implicated in a default mode of brain activity. This suggests that task-related default mode decreases have a more “complex” signal that benefits from a flexible modeling approach. Compared with a traditional GLM approach, the sbICA approach provides a flexible way to analyze fMRI data that reduces the assumptions placed upon the hemodynamic response of the brain. The advantages and limitations of our technique are discussed in detail in the manuscript to provide guidelines to the reader for developing useful applications. The use of prior time course information in a spatial ICA analysis, which combines elements of both a regression approach and a blind ICA approach, may prove to be a useful tool for fMRI analysis.