Linear Latent Variable Models Research Articles

GLAMLE: inference for multiview network data in the presence of latent variables, with an application to commodities trading

The statistical analysis of multiview network data provides researchers with insights on the mechanism governing many complex systems of interconnected elements. A graph is routinely applied to model this type of data: this poses several statistical challenges. Among them, there is the need for considering that some unobservable factors may determine the network connections and the graph topology. This requirement entails both complex models and computationally heavy inference procedures. To cope with these inference issues, a novel and flexible class of latent variable models labeled Graph Generalized Linear Latent Variable Model (GGLLVM) is introduced. Then, its parameters are estimated via the maximization of the Laplace-approximated likelihood. This leads to the creation of an M-estimator which is named Graph Laplace-Approximated Maximum Likelihood Estimator (GLAMLE). The statistical properties of this new estimator are characterized, and numerical experiments on simulated networks are performed to illustrate that the GLAMLE yields fast and accurate inference, in comparison to other widely used approaches. A real data application to commodities trading in European countries illustrates how the use of GGLLVM and GLAMLE unveils the import/export propensity that each node of the network has toward other nodes, along with additional information specific to each traded commodity.

Enhancing LS-PIE’s Optimal Latent Dimensional Identification: Latent Expansion and Latent Condensation

The Latent Space Perspicacity and Interpretation Enhancement (LS-PIE) framework enhances dimensionality reduction methods for linear latent variable models (LVMs). This paper extends LS-PIE by introducing an optimal latent discovery strategy to automate identifying optimal latent dimensions and projections based on user-defined metrics. The latent condensing (LCON) method clusters and condenses an extensive latent space into a compact form. A new approach, latent expansion (LEXP), incrementally increases latent dimensions using a linear LVM to find an optimal compact space. This study compares these methods across multiple datasets, including a simple toy problem, mixed signals, ECG data, and simulated vibrational data. LEXP can accelerate the discovery of optimal latent spaces and may yield different compact spaces from LCON, depending on the LVM. This paper highlights the LS-PIE algorithm’s applications and compares LCON and LEXP in organising, ranking, and scoring latent components akin to principal component analysis or singular value decomposition. This paper shows clear improvements in the interpretability of the resulting latent representations allowing for clearer and more focused analysis.

Network analysis of gut microbial communities reveal key genera for a multiple sclerosis cohort with Mycobacterium avium subspecies paratuberculosis infection

BackgroundIn gut ecosystems, there is a complex interplay of biotic and abiotic interactions that decide the overall fitness of an individual. Divulging the microbe-microbe and microbe-host interactions may lead to better strategies in disease management, as microbes rarely act in isolation. Network inference for microbial communities is often a challenging task limited by both analytical assumptions as well as experimental approaches. Even after the network topologies are obtained, identification of important nodes within the context of underlying disease aetiology remains a convoluted task. We therefore present a network perspective on complex interactions in gut microbial profiles of individuals who have multiple sclerosis with and without Mycobacterium avium subspecies paratuberculosis (MAP) infection. Our exposé is guided by recent advancements in network-wide statistical measures that identify the keystone nodes. We have utilised several centrality measures, including a recently published metric, Integrated View of Influence (IVI), that is robust against biases.ResultsThe ecological networks were generated on microbial abundance data (n = 69 samples) utilising 16 S rRNA amplification. Using SPIEC-EASI, a sparse inverse covariance estimation approach, we have obtained networks separately for MAP positive (+), MAP negative (-) and healthy controls (as a baseline). Using IVI metric, we identified top 20 keystone nodes and regressed them against covariates of interest using a generalised linear latent variable model. Our analyses suggest Eisenbergiella to be of pivotal importance in MS irrespective of MAP infection. For MAP + cohort, Pyarmidobacter, and Peptoclostridium were predominately the most influential genera, also hinting at an infection model similar to those observed in Inflammatory Bowel Diseases (IBDs). In MAP- cohort, on the other hand, Coprostanoligenes group was the most influential genera that reduces cholesterol and supports the intestinal barrier.ConclusionsThe identification of keystone nodes, their co-occurrences, and associations with the exposome (meta data) advances our understanding of biological interactions through which MAP infection shapes the microbiome in MS individuals, suggesting the link to the inflammatory process of IBDs. The associations presented in this study may lead to development of improved diagnostics and effective vaccines for the management of the disease.

Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables.

Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.

Predicting niche overlap with model‐based ordination

The ecological niche is a fundamental concept in ecology that can be used in order better understand species relationships. The overlap in species niches provides a measure of the likelihood for species to co‐occur. Most approaches that quantify niche overlap have been based on distance and similarity indices, for pairwise combinations of species. In this paper, we suggest that niche overlap can be calculated from the predictions of a model. Using a statistical model to predict niche overlap provides various benefits, includes the possibility to adjust the model to properties of the data. We demonstrate this using an example dataset of an ecological community of Foraminifera species, to which we fit a generalized linear latent variable model (GLLVM). GLLVMs are a flexible class of models that allow to estimate the distribution of species using both measured environmental predictors and residual covariation between species. We demonstrate how to calculate niche overlap from GLLVMs for any combination of species, and separately for different environments. Predicting niche overlap from a model further expands the toolset available to ecologists for the exploration of species co‐occurrence patterns.

Gut microbial ecology and exposome of a healthy Pakistani cohort.

Pakistan is a multi-ethnic society where there is a disparity between dietary habits, genetic composition, and environmental exposures. The microbial ecology of healthy Pakistani gut in the context of anthropometric, sociodemographic, and dietary patterns holds interest by virtue of it being one of the most populous countries, and also being a Lower Middle Income Country (LMIC). 16S rRNA profiling of healthy gut microbiome of normo-weight healthy Pakistani individuals from different regions of residence is performed with additional meta-data collected through filled questionnaires. The current health status is then linked to dietary patterns through [Formula: see text] test of independence and Generalized Linear Latent Variable Model (GLLVM) where distribution of individual microbes is regressed against all recorded sources of variability. To identify the core microbiome signature, a dynamic approach is used that considers into account species occupancy as well as consistency across assumed grouping of samples including organization by gender and province of residence. Fitting neutral modeling then revealed core microbiome that is selected by the environment. A strong determinant of disparity is by province of residence. It is also established that the male microbiome is better adapted to the local niche than the female microbiome, and that there is microbial taxonomic and functional diversity in different ethnicities, dietary patterns and lifestyle habits. Some microbial genera, such as, Megamonas, Porphyromonas, Haemophilus, Klebsiella and Finegoldia showed significant associations with consumption of pickle, fresh fruits, rice, and cheese. Our analyses suggest current health status being associated with the diet, sleeping patterns, employment status, and the medical history. This study provides a snapshot of the healthy core Pakistani gut microbiome by focusing on the most populous provinces and ethnic groups residing in predominantly urban areas. The study serves a reference dataset for exploring variations in disease status and designing personalized dietary and lifestyle interventions to promote gut health, particularly in LMICs settings.

Generative models for anomaly detection and design-space dimensionality reduction in shape optimization

Our work presents a novel approach to shape optimization, with the twofold objective to improve the efficiency of global optimization algorithms while promoting the generation of high-quality designs during the optimization process free of geometrical anomalies. This is accomplished by reducing the number of the original design variables defining a new reduced subspace where the geometrical variance is maximized and modeling the underlying generative process of the data via probabilistic linear latent variable models such as factor analysis and probabilistic principal component analysis. We show that the data follows approximately a Gaussian distribution when the shape modification method is linear and the design variables are sampled uniformly at random, due to the direct application of the central limit theorem. The degree of anomalousness is measured in terms of Mahalanobis distance, and the paper demonstrates that abnormal designs tend to exhibit a high value of this metric. This enables the definition of a new optimization model where anomalous geometries are penalized and consequently avoided during the optimization loop. The procedure is demonstrated for hull shape optimization of the DTMB 5415 model, extensively used as an international benchmark for shape optimization problems. The global optimization routine is carried out using Bayesian optimization and the DIRECT algorithm. From the numerical results, the new framework improves the convergence of global optimization algorithms, while only designs with high-quality geometrical features are generated through the optimization routine thereby avoiding the wastage of precious computationally expensive simulations.

Environmental Conditions and Vehicle Disturbance Influence Stress Behaviors in a Working Harris’s Hawk (Parabuteo unicinctus)

ABSTRACT Harris’s hawk (Parabuteo unicinctus) is used for pest control, as their presence can deter wild birds such as gulls. Working Harris’s hawk on UK waste sites is permitted in accordance with regulations and legislation. This study investigated the general environment of a waste site compound yard where a single Harris’s hawk was flown for pest control. The hawk’s behaviors were evaluated in an ethogram, alongside environmental measures, and disturbance levels. Data was analyzed using Generalised Linear Latent Variable Models (GLLVM) to elucidate the effects of disturbance and environment on hawk behaviors. Results suggested cloudy conditions encouraged grooming responses that were normal and relaxed in their nature. Rain, sun and wind conditions increased recognized stress behaviors. Frequency of disturbance by construction vehicles inside the compound increased stress behaviors, such that keepers are recommended to revise welfare conditions. Increased stress behaviors by birds worked in dynamic environments like waste recycling yards could potentially elicit damaging illness such as feather breaking behavior. Reducing stress factors for Harris’s hawk in industrial working yards combined with amending husbandry practices will improve welfare for the species.

Co-infection patterns in the ectoparasitic community affecting the Iberian ibex Capra pyrenaica

BackgroundSarcoptic mange is one of the main parasitic diseases affecting the Iberian ibex Capra pyrenaica. Scabietic animals suffer a decline in body condition and reproductive fitness and in severe cases may die. Although several previous studies of the pathology of this disease and the physiological changes it produces in ibex have been carried out in recent years, our knowledge of the relationship between Sarcoptes scabiei and other ectoparasites of this host is still limited.MethodsWe analysed 430 Iberian ibex skin samples. Ectoparasites were removed, counted and identified. Mite (S. scabiei) numbers were obtained after digesting the skin samples in a 5% KOH solution. We modelled mite numbers in terms of host sex and age, site, year, season and the presence of other ectoparasites such as ticks and lice using generalized linear mixed models (GLMMs) and ectoparasite co-occurrence patterns using two different models: the probabilistic model species co-occurrence and the generalized linear latent variable model (GLLVM).ResultsThe ectoparasite community was mainly composed of S. scabiei, six ticks (Haemaphysalis sulcata, Haemaphysalis punctata, Rhipicephalus bursa, Rhipicephalus turanicus, Dermacentor marginatus and Ixodes ricinus) and two lice (Bovicola crassipes and Linognathus stenopsis). Adult male ibex harboured more mites than females. Mite numbers varied greatly spatially and seasonally and increased with the presence of other parasites. Some positive co-occurrence relationships between pairs of different ectoparasites were observed, particularly between ticks. The presence of S. scabiei negatively affected lice and H. sulcata numbers.ConclusionsSarcoptic mange has spread above all in ibex populations in and around the Mediterranean Basin, where it is now found in almost a third of its host’s range. Mite numbers varied seasonally and spatially and were higher in male hosts. The presence of S. scabiei had a negative effect on lice numbers but favoured the presence of ticks.Graphical

Somatotype altitudinal variation and its relationship with the nutritional status of children in the Jujuy province, Argentina.

To study the somatotype variations adjusted by altitude, age, sex, and BMI categories, and to assess the health status of the children population. A sample of 460 children aged 8-13 years was assessed in a cross-sectional study conducted on anthropometric measurements between 2011 and 2015. Data were categorized into two age groups: Group 8-10, Group 11-13 and two altitudes: Highland (>2000 masl), lowland (<2000 masl). The somatotypic profile was determined by the Heath and Carter's study method and the Body Mass Index was used to assess children nutritional status. Generalized linear latent variable models (GLLVM) were performed to test the association between somatotype and geographic altitude. Individual age-sex specific somatotypes were plotted in a two-dimension somatochart, and group dispersion was displayed by the somatotype attitudinal mean. The sample has an overall endomorph-mesomorph body type, exhibiting different patterns when altitude and sex were considered. The GLLVM showed that the whole somatotype was different by altitude. Highland children occupied central to endomorphic-mesomorphic places in the somatochart with lower variation. In both altitudes, girls exhibited higher endomorphy than boys. Several discrepancies between the BMI categorization and the somatotype were observed. Jujenean children show differential body patterns across geographic altitude which exhibit age and sex variations. Children have a differential tendency to a fat mass gain. The BMI showed some inconsistencies with somatotype, leading to a misclassification of the child nutritional status, this highlights the importance of not to treat the BMI in isolation but with other determinants of the health status.

Association between brain serotonin 4 receptor binding and reactivity to emotional faces in depressed and healthy individuals

Brain serotonergic (5-HT) signaling is posited to modulate neural responses to emotional stimuli. Dysfunction in 5-HT signaling is implicated in major depressive disorder (MDD), a disorder associated with significant disturbances in emotion processing. In MDD, recent evidence points to altered 5-HT4 receptor (5-HT4R) levels, a promising target for antidepressant treatment. However, how these alterations influence neural processing of emotions in MDD remains poorly understood. This is the first study to examine the association between 5-HT4R binding and neural responses to emotions in patients with MDD and healthy controls. The study included one hundred and thirty-eight participants, comprising 88 outpatients with MDD from the NeuroPharm clinical trial (ClinicalTrials.gov identifier: NCT02869035) and 50 healthy controls. Participants underwent an [11C]SB207145 positron emission tomography (PET) scan to quantify 5-HT4R binding (BPND) and a functional magnetic resonance imaging (fMRI) scan during which they performed an emotional face matching task. We examined the association between regional 5-HT4R binding and corticolimbic responses to emotional faces using a linear latent variable model, including whether this association was moderated by depression status. We observed a positive correlation between 5-HT4R BPND and the corticolimbic response to emotional faces across participants (r = 0.20, p = 0.03). This association did not differ between groups (parameter estimate difference = 0.002, 95% CI = −0.008: 0.013, p = 0.72). Thus, in the largest PET/fMRI study of associations between serotonergic signaling and brain function, we found a positive association between 5-HT4R binding and neural responses to emotions that appear unaltered in MDD. Future clinical trials with novel pharmacological agents targeting 5-HT4R are needed to confirm whether they ameliorate emotion processing biases in MDD.

Fast estimation of multiple group generalized linear latent variable models for categorical observed variables

A computationally efficient method for marginal maximum likelihood estimation of multiple group generalized linear latent variable models for categorical data is introduced. The approach utilizes second-order Laplace approximations of the integrals in the likelihood function. It is demonstrated how second-order Laplace approximations can be utilized highly efficiently for generalized linear latent variable models by considering symmetries that exist for many types of model structures. In a simulation with binary observed variables and four correlated latent variables in four groups, the method has similar bias and mean squared error compared to adaptive Gauss-Hermite quadrature with five quadrature points while substantially improving computational efficiency. An empirical example from a large-scale educational assessment illustrates the accuracy and computational efficiency of the method when compared against adaptive Gauss-Hermite quadrature with three, five, and 13 quadrature points.

Causal discovery of 1-factor measurement models in linear latent variable models with arbitrary noise distributions

The problem of causal discovery is especially challenging when the variables of interest cannot be directly measured. In measurement models, the measured variables were generated by latent causal variables that are causally related to each other, and by estimating the measurement model from measured data, one is able to recover the latent variables and their causal relations. In this paper, we provide precise sufficient identifiability conditions for the linear pure measurement model, and show what information of the causal structure can be recovered from observed data without prior knowledge of data distributions. In particular, we first show that, based on second-order statistics, although the pure measurement model is in general not fully identifiable under the assumption of two pure measurement variables, we can identify the set of all candidate measurement models. We then further prove that the pure measurement model can be identified uniquely based on higher-order statistics. Next, to address more general situations, we offer the identifiability conditions of linear measurement models with arbitrary noise distributions. We finally develop a unified method to learn pure measurement models from data. Experimental results on both synthetic and real-world data demonstrate the usefulness of our theory and the effectiveness of our approach.

Fast and universal estimation of latent variable models using extended variational approximations

Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., in the analysis of multivariate abundance data in ecology. One of the main features of GLLVMs is their capacity to handle a variety of responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, and proportions data. On the other hand, the inclusion of unobserved latent variables poses a major computational challenge, as the resulting marginal likelihood function involves an intractable integral for non-normally distributed responses. This has spurred research into a number of approximation methods to overcome this integral, with a recent and particularly computationally scalable one being that of variational approximations (VA). However, research into the use of VA for GLLVMs has been hampered by the fact that fully closed-form variational lower bounds have only been obtained for certain combinations of response distributions and link functions. In this article, we propose an extended variational approximations (EVA) approach which widens the set of VA-applicable GLLVMs dramatically. EVA draws inspiration from the underlying idea behind the Laplace approximation: by replacing the complete-data likelihood function with its second order Taylor approximation about the mean of the variational distribution, we can obtain a fully closed-form approximation to the marginal likelihood of the GLLVM for any response type and link function. Through simulation studies and an application to a species community of testate amoebae, we demonstrate how EVA results in a “universal” approach to fitting GLLVMs, which remains competitive in terms of estimation and inferential performance relative to both standard VA (where any intractable integrals are either overcome through reparametrization or quadrature) and a Laplace approximation approach, while being computationally more scalable than both methods in practice.

Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

Abstract In community ecology, unconstrained ordination can be used to indirectly explore drivers of community composition, while constrained ordination can be used to directly relate predictors to an ecological community. However, existing constrained ordination methods do not explicitly account for community composition that cannot be explained by the predictors, so that they have the potential to misrepresent community composition if not all predictors are available in the data. We propose and develop a set of new methods for ordination and joint species distribution modelling (JSDM) as part of the generalized linear latent variable model (GLLVM) framework, that incorporate predictors directly into an ordination. This includes a new ordination method that we refer to as concurrent ordination, as it simultaneously constructs unconstrained and constrained latent variables. Both unmeasured residual covariation and predictors are incorporated into the ordination by simultaneously imposing reduced rank structures on the residual covariance matrix and on fixed‐effects. We evaluate the method with a simulation study, and show that the proposed developments outperform canonical correspondence analysis (CCA) for Poisson and Bernoulli responses, and perform similar to redundancy analysis (RDA) for normally distributed responses, the two most popular methods for constrained ordination in community ecology. Two examples with real data further demonstrate the benefits of concurrent ordination, and the need to account for residual covariation in the analysis of multivariate data. This article contextualizes the role of constrained ordination in the GLLVM and JSDM frameworks, while developing a new ordination method that incorporates the best of unconstrained and constrained ordination, and which overcomes some of the deficiencies of existing classical ordination methods.

Identification of Linear Latent Variable Model with Arbitrary Distribution

An important problem across multiple disciplines is to infer and understand meaningful latent variables. One strategy commonly used is to model the measured variables in terms of the latent variables under suitable assumptions on the connectivity from the latents to the measured (known as measurement model). Furthermore, it might be even more interesting to discover the causal relations among the latent variables (known as structural model). Recently, some methods have been proposed to estimate the structural model by assuming that the noise terms in the measured and latent variables are non-Gaussian. However, they are not suitable when some of the noise terms become Gaussian. To bridge this gap, we investigate the problem of identification of the structural model with arbitrary noise distributions. We provide necessary and sufficient condition under which the structural model is identifiable: it is identifiable iff for each pair of adjacent latent variables Lx, Ly, (1) at least one of Lx and Ly has non-Gaussian noise, or (2) at least one of them has a non-Gaussian ancestor and is not d-separated from the non-Gaussian component of this ancestor by the common causes of Lx and Ly. This identifiability result relaxes the non-Gaussianity requirements to only a (hopefully small) subset of variables, and accordingly elegantly extends the application scope of the structural model. Based on the above identifiability result, we further propose a practical algorithm to learn the structural model. We verify the correctness of the identifiability result and the effectiveness of the proposed method through empirical studies.

Brain serotonin transporter is associated with cognitive-affective biases in healthy individuals.

Cognitive affective biases describe the tendency to process negative information or positive information over the other. These biases can be modulated by changing extracellular serotonin (5‐HT) levels in the brain, for example, by pharmacologically blocking and downregulating the 5‐HT transporter (5‐HTT), which remediates negative affective bias. This suggests that higher levels of 5‐HTT are linked to a priority of negative information over positive, but this link remains to be tested in vivo in healthy individuals. We, therefore, evaluated the association between 5‐HTT levels, as measured with [11C]DASB positron emission tomography (PET), and affective biases, hypothesising that higher 5‐HTT levels are associated with a more negative bias. We included 98 healthy individuals with measures of [11C]DASB binding potential (BPND) and affective biases using The Emotional Faces Identification Task by subtracting the per cent hit rate for happy from that of sad faces (EFITAB). We evaluated the association between [11C]DASB BPND and EFITAB in a linear latent variable model, with the latent variable (5‐HTTLV) modelled from [11C]DASB BPND in the fronto‐striatal and fronto‐limbic networks implicated in affective cognition. We observed an inverse association between 5‐HTTLV and EFITAB (β = −8% EFITAB per unit 5‐HTTLV, CI = −14% to −3%, p = .002). These findings show that higher 5‐HTT levels are linked to a more negative bias in healthy individuals. High 5‐HTT supposedly leads to high clearance of 5‐HT, and thus, a negative bias could result from low extracellular 5‐HT. Future studies must reveal if a similar inverse association exists in individuals with affective disorders.

GEE-Assisted Forward Regression for Spatial Latent Variable Models

Multivariate spatial data, where multiple responses are recorded at a set of spatial locations, are widely collected in many disciplines. One common approach for analyzing such data is spatial generalized linear latent variable models (spatial GLLVMs), where the latent variables are used to model both the spatial correlation between locations and correlations between responses. However, inference such as variable selection for spatial GLLVMs is computationally demanding, as the marginal likelihood involves a high-dimensional and often intractable integral. To overcome this, we propose to use spatial generalized estimating equations (GEEs) to perform fast, GEE-assisted forward regression for spatial GLLVMs. Focusing on counts and nonnegative continuous responses, we use spatial GEEs to build a forward solution path by choosing the candidate variable which maximizes a score statistic at each point on the path. A model is then selected from this path based on a modified score information criterion. The proposed approach is computationally efficient, relying only on GEEs which are quick to update, coupled with a novel theoretical result linking the coefficients from spatial GEEs to that of spatial GLLVMs. We show that the proposed approach can asymptotically identify all truly important nonzero predictors in the underlying spatial GLLVM. Simulations demonstrate that, when the data are generated from a sparse spatial GLLVM, GEE-assisted forward regression performs well at recovering this sparsity, while taking only a fraction of the computation time required to fit just a single (saturated) spatial GLLVM. Supplementary materials for this article are available online.

Controlling the familywise error rate when performing multiple comparisons in a linear latent variable model

In latent variable models (LVMs) it is possible to analyze multiple outcomes and to relate them to several explanatory variables. In this context many parameters are estimated and it is common to perform multiple tests, e.g. to investigate outcome-specific effects using Wald tests or to check the correct specification of the modeled mean and variance using a forward stepwise selection (FSS) procedure based on Score tests. Controlling the family-wise error rate (FWER) at its nominal level involves adjustment of the p-values for multiple testing. Because of the correlation between test statistics, the Bonferroni procedure is often too conservative. In this article, we extend the max-test procedure to the LVM framework for Wald and Score tests. Depending on the correlation between the test statistics, the max-test procedure is equivalent or more powerful than the Bonferroni procedure while also providing, asymptotically, a strong control of the FWER for non-iterative procedures. Using simulation studies, we assess the finite sample behavior of the max-test procedure for Wald and Score tests in LVMs. We apply our procedure to quantify the neuroinflammatory response to mild traumatic brain injury in nine brain regions.

Big data ordination towards intensive care event count cases using fast computing GLLVMS

BackgroundIn heart data mining and machine learning, dimension reduction is needed to remove multicollinearity. Meanwhile, it has been proven to improve the interpretation of the parameter model. In addition, dimension reduction can also increase the time of computing in high dimensional data.MethodsIn this paper, we perform high dimensional ordination towards event counts in intensive care hospital for Emergency Department (ED 1), First Intensive Care Unit (ICU1), Second Intensive Care Unit (ICU2), Respiratory Care Intensive Care Unit (RICU), Surgical Intensive Care Unit (SICU), Subacute Respiratory Care Unit (RCC), Trauma and Neurosurgery Intensive Care Unit (TNCU), Neonatal Intensive Care Unit (NICU) which use the Generalized Linear Latent Variable Models (GLLVM’s).ResultsDuring the analysis, we measure the performance and calculate the time computing of GLLVM by employing variational approximation and Laplace approximation, and compare the different distributions, including Negative Binomial, Poisson, Gaussian, ZIP, and Tweedie, respectively. GLLVMs (Generalized Linear Latent Variable Models), an extended version of GLMs (Generalized Linear Models) with latent variables, have fast computing time. The major challenge in latent variable modelling is that the function fleft(varTheta right)=int fleft(uvarTheta right)hleft(uright)du is not trivial to solve since the marginal likelihood involves integration over the latent variable u.ConclusionsIn a nutshell, GLLVMs lead as the best performance reaching the variance of 98% comparing other methods. We get the best model negative binomial and Variational approximation, which provides the best accuracy by accuracy value of AIC, AICc, and BIC. In a nutshell, our best model is GLLVM-VA Negative Binomial with AIC 7144.07 and GLLVM-LA Negative Binomial with AIC 6955.922.