Likelihood Ratio Test Approach Research Articles

DIF Statistical Inference Without Knowing Anchoring Items

Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also on the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require knowing several anchor items that are DIF-free in order to draw inferences on whether each of the rest is a DIF item, where the anchor items are used to identify the latent trait distributions. When no prior information on anchor items is available, or some anchor items are misspecified, item purification methods and regularized estimation methods can be used. The former iteratively purifies the anchor set by a stepwise model selection procedure, and the latter selects the DIF-free items by a LASSO-type regularization approach. Unfortunately, unlike the methods based on a correctly specified anchor set, these methods are not guaranteed to provide valid statistical inference (e.g., confidence intervals and p-values). In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal L_1 norm condition for identifying the latent trait distributions. Without requiring prior knowledge about an anchor set, it can accurately estimate the DIF effects of individual items and further draw valid statistical inferences for quantifying the uncertainty. Specifically, the inference results allow us to control the type-I error for DIF detection, which may not be possible with item purification and regularized estimation methods. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is applied to analysing the three personality scales of the Eysenck personality questionnaire-revised (EPQ-R).

Comparison of Methods Used in Detection of DIF in Cognitive Diagnostic Models with Traditional Methods: Applications in TIMSS 2011

This study aims to compare the Wald test and likelihood ratio test (LRT) approaches with Classical Test Theory (CTT) and Item Response Theory (IRT) based differential item functioning (DIF) detection methods in the context of cognitive diagnostic models (CDMs), using the TIMSS 2011 dataset as a retrofitting study. CDMs, which have a significant potential when determining the DIF and their contribution to validity, can give confidence under the strong methodological background condition is met. Therefore, it is hoped that this study will contribute to the literature to ensure the correct usage of CDMs and evaluate the compatibility of these new approaches with traditional methods. According to the analysis results, thirty-one items showed differences between the cognitive diagnosis assessments and the traditional methods. The item with the largest DIF was found in the Raju Unsigned Area Measures technique in IRT, whereas the item with the lowest DIF was found in the Wald test technique developed for CDMs. In general, the analyses show that methods not based on CDMs detect more items with DIF, but the Wald test and LRT methods based on CDMs detect fewer items with DIF. This study conducted DIF analyses to determine the test's psychometric properties within the framework of CDMs rather than the source of the bias. Researchers can take the study one step further and make more specific assessments about the items' bias regarding the test structure, test scope, and subgroups. In addition, DIF analyses in this study were carried out using only the gender variable, and researchers can use different variables to conduct studies specific to their purpose.

Adaptive Radar Detection and Bearing Estimation in the Presence of Unknown Mutual Coupling

This paper deals with joint adaptive radar detection and target bearing estimation in the presence of mutual coupling among the array elements. First of all, a suitable model of the signal received by the multichannel radar is developed via a linearization procedure of the Uniform Linear Array (ULA) manifold around the nominal array looking direction together with the use of symmetric Toeplitz structured matrices to represent the mutual coupling effects. Hence, the Generalized Likelihood Ratio Test (GLRT) detector is evaluated under the assumption of homogeneous radar environment. Its computation leverages a specific Minorization-Maximization (MM) framework, with proven convergence properties, to optimize the concentrated likelihood function under the target presence hypothesis. Besides, when the number of active mutual coupling coefficients is unknown, a Multifamily Likelihood Ratio Test (MFLRT) approach is invoked. During the analysis phase, the performance of the new detectors is compared with benchmarks as well as with counterparts available in the open literature which neglect the mutual coupling phenomenon. The results indicate that it is necessary to consider judiciously the coupling effect since the design phase, to guarantee performance levels close to the benchmark.

Gaussian universal likelihood ratio testing

Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of the log-likelihood is one of the fundamental tools of statistical inference. A recent universal likelihood ratio test approach based on sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute the split likelihood ratio statistic, or, more generally, an upper bound on the null maximum likelihood. The universal likelihood ratio test is valid in finite samples and without regularity conditions. This test empowers statisticians to construct tests in settings for which no valid hypothesis test previously existed. For the simple, but fundamental, case of testing the population mean of $d$-dimensional Gaussian data with an identity covariance matrix, the classical likelihood ratio test itself applies. Thus, this setting serves as a perfect test bed to compare the classical likelihood ratio test against the universal likelihood ratio test. This work presents the first in-depth exploration of the size, power and relationships between several universal likelihood ratio test variants. We show that a repeated subsampling approach is the best choice in terms of size and power. For large numbers of subsamples, the repeated subsampling set is approximately spherical. We observe reasonable performance even in a high-dimensional setting, where the expected squared radius of the best universal likelihood ratio test’s confidence set is approximately 3/2 times the squared radius of the classical likelihood ratio test’s spherical confidence set. We illustrate the benefits of the universal likelihood ratio test through testing a nonconvex doughnut-shaped null hypothesis, where a universal inference procedure can have higher power than a standard approach.

On the use of the likelihood ratio test methodology in pharmacovigilance.

The safety of medical products due to adverse events (AE) from drugs, therapeutic biologics, and medical devices is a major public health concern worldwide. Likelihood ratio test (LRT) approaches to pharmacovigilance constitute a class of rigorous statistical tools that permit objective identification of AEs of a specific drug and/or a class of drugs cataloged in spontaneous reporting system databases. However, the existing LRT approaches encounter certain theoretical and computational challenges when an underlying Poisson model assumption is violated, including in cases of zero-inflated data. We briefly review existing LRT approaches and propose a novel class of (pseudo-) LRT methods to address these challenges. Our approach uses an alternative parametrization to formulate a unified framework with a common test statistic that can handle both Poisson and zero-inflated Poisson (ZIP) models. The proposed framework is computationally efficient, and it reveals deeper insights into the comparative behaviors of the Poisson and the ZIP models for handling AE data. Our extensive simulation studies document notably superior performances of the proposed methods over existing approaches particularly under zero-inflation, both in terms of statistical (eg, much better control of the nominal level and false discovery rate with substantially enhanced power) and computational ( 100-500-fold gains in average running times) performance metrics. An application of our method on the statin drug class from the FDA FAERS database reveals interesting insights on potential AEs. An R package, pvLRT, implementing our methods has been released in the public domain.

Robust Copula-Based Detection of Shallow-Buried Landmines With Forward-Looking Radar

We propose a technique for landmine detection using forward-looking ground-penetrating radar. The detector is applied to radar images obtained from multiple viewpoints of the region of interest and is based on a robust version of the likelihood ratio test (LRT). We incorporate the statistical dependence between multiview images into the test via copula-based model. The test is designed to maximize the worst-case performance over all feasible pairs of target and clutter distributions, thereby eliminating the need for strong assumptions about the image statistics. We evaluate the detection performance of the proposed technique for different copula functions representing the dependence structure. Using electromagnetic modeled data of shallow-buried targets under varying ground surface roughness profiles, we demonstrate the superiority of the robust copula-based detector over existing parametric and robust LRT approaches designed under the assumption of statistical independence of multiview images.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

Predictive Added Value of Selected Plasma Lipids to a Re-estimated Minimal Risk Tool.

Background: Lipidomics is emerging for biomarker discovery in cardiovascular disease, and circulating lipids are increasingly incorporated in risk models to predict cardiovascular events. Moreover, specific classes of lipids, such as sphingomyelins, ceramides, and triglycerides, have been related to coronary artery disease (CAD) severity and plaque characteristics. To avoid unnecessary testing, it is important to identify individuals at low CAD risk. The only pretest model available so far to rule out the presence of coronary atherosclerosis in patients with chest pain, but normal coronary arteries, is the minimal risk tool (MRT).Aim: Using state-of-the-art statistical methods, we aim to verify the additive predictive value of a set of lipids, derived from targeted plasma lipidomics of suspected CAD patients, to a re-estimated version of the MRT for ruling out the presence of coronary atherosclerosis assessed by coronary CT angiography (CCTA).Methods: Two hundred and fifty-six subjects with suspected stable CAD recruited from five European countries within H2020-SMARTool, undergoing CCTA and blood sampling for clinical biochemistry and lipidomics, were selected. The MRT was validated by regression methods and then re-estimated (reMRT). The reMRT was used as a baseline model in a likelihood ratio test approach to assess the added predictive value of each lipid from 13 among ceramides, triglycerides, and sphingomyelins. Except for one lipid, the analysis was carried out on more than 240 subjects for each lipid. A sensitivity analysis was carried out by considering two alternative models developed on the cohort as baseline models.Results: In 205 subjects, coronary atherosclerosis ranged from minimal lesions to overt obstructive CAD, while in 51 subjects (19.9%) the coronary arteries were intact. Four triglycerides and seven sphingomyelins were significantly (p < 0.05) and differentially expressed in the two groups and, at a lesser extent, one ceramide (p = 0.067). The probability of being at minimal risk was significantly better estimated by adding either Cer(d18:1/16:0) (p = 0.01), SM(40:2) (p = 0.04), or SM(41:1) at a lesser extent (p = 0.052) to reMRT than by applying the reMRT alone. The sensitivity analysis confirmed the relevance of these lipids. Furthermore, the addition of SM(34:1), SM(38:2), SM(41:2), and SM(42:4) improved the predictive performance of at least one of the other baseline models. None of the selected triglycerides was found to provide an added value.Conclusions: Plasma lipidomics can be a promising source of diagnostic and prognostic biomarkers in cardiovascular disease, exploitable not only to assess the risk of adverse events but also to identify subjects without coronary atherosclerosis, thus reducing unnecessary further testing in normal subjects.

Alternative classification rules for two normal populations with a common mean and ordered variances

The problem of classification into two normal populations with a common mean and ordered variances is revisited. So far in the literature, authors have proposed classification rules which are based on either the Graybill-Deal estimator or its improved version of the common mean under order restricted variances. Surprisingly, the maximum likelihood estimator (MLE) of the common mean has not been used for classification purposes. However, it is interesting to know that the MLE has better performance than the Graybill-Deal estimator in most of the parameter ranges. In this article, utilizing the MLE and its plug-in type restricted version of the common mean, two new classification rules have been proposed. Further, a classification rule based on the generalized likelihood ratio test approach has been obtained. Moreover, certain rules based on some of the improved existing estimators of the common mean under order restricted variances have been proposed. More importantly, a simulation study has been carried out to numerically compare the probabilities of misclassification for all the classification rules, including the existing ones. It has been observed that the classification rules which are based on the MLE and its restricted version perform quite satisfactorily (if not the best) compared to other rules.

Bivariate Poisson Inverse Gaussian Regression Model with Exposure Variable: Infant and Maternal Death Case Study

One of appropriate methods that could be used to model positive integers response and its corresponding predictors is Poisson regression. This method has a strict assumption to be achieved, that is the mean and variance of response variable must be equal (equidispersion). In many practical issues, sometimes, the variance is larger than the mean (overdispersion). Bivariate Poisson Inverse Gaussian Regression (BPIGR) is proposed to overcome the overdispersion issue. In this study, the BPIGR model is developed by adding the exposure variable as the weight of each sample unit. This study applies the proposed method to model the infant and maternal death data (as the responses) and the factors that influence them. The data of East Java 2017 are used for the application. Maximum Likelihood Estimation (MLE) method is used to estimate the parameters, while the hypothesis testing of the BPIGR model is derived using Maximum Likelihood Ratio Test (MLRT) approach. The results showed that the BPIGR model is a proper model for modeling the number of infant and maternal deaths. Furthermore, all predictor variables significantly influence those two responses.

Monitoring Attributed Social Networks Based on Count Data and Random Effects

This paper presents a novel approach for the statistical monitoring of online social networks where the edges represent the count of communications between ties at each time stamp. Since the available methods in the literature are limited to the assumption that the set of all interacting individuals is fixed during the monitoring horizon and their corresponding attributes do not change over time, the proposed method tackles these limitations due to the properties of the random effects concepts. Applying appropriate parameters estimation technique involved in a likelihood ratio testing (LRT) approach considering two different statistics, the longitudinal network data are monitored. The performance of the proposed method is verified using numerical examples including simulation studies as well as an illustrative example.

PCA likelihood ratio test approach for attributed social networks monitoring

One of the most important factors in building and changing communication mechanisms in social networks is considering features of the members of social networks. Most of the existing methods in network monitoring don’t consider effects of features in network formation mechanisms and others don’t lead to reliable results when the features abound or when there are correlations among them. In this article, we combined two methods principal component analysis (PCA) and likelihood method to monitor the underlying network model when the features of individuals abound and when some of them have high correlations with each other.

Statistical Methods for Clinical Study Site Selection.

The US Food and Drug Administration conducts on-site inspections and data audits through Bioresearch Monitoring program for assurance of the quality and integrity of data in the pre- and postapproval processes. It is important to inspect the study sites that are different compared with other sites in clinical studies and identify the problems related to those sites. Usually one cannot inspect all the sites in a clinical study because of limited resources, and statistical tools are needed to help in selecting sites for inspection. We propose two technical approaches, namely Fisher combination approach and likelihood ratio test (LRT) approach, for site selection, with each approach integrating the information obtained from a P value matrix. The proposed approaches produce site rankings, and the sites with highest rankings may be selected for inspection. The application of the approaches is demonstrated through a hypothetical data set reflecting the pattern of the real data in a premarket approval submission for a diagnostic device. The proposed methods are shown, through extensive simulations, to control false discovery rate, while maintaining good sensitivity. The proposed approaches will be useful for site selection process. However, limitations exist when only using the statistical approaches proposed here. In practice, investigators will select the site for inspection by considering the outputs from the statistical approaches along with other important factors. Future research topic is discussed to facilitate practical application of the approaches.

Spectrum sensing in a calibrated multi-antenna cognitive radio: Exact LRT approaches

This paper addresses the spectrum sensing problem in a calibrated multi-antenna cognitive radio. To do so, a composite hypothesis testing problem is formulated according to the covariance matrix of the received signal. Then, we resort to the likelihood ratio test (LRT) principle to derive some new LRT tests. This problem has been previously solved based on two-step Generalized LRT (2S-GLRT), leading to different detection strategies in comparison to this study; thus the proposed method is referred to as an exact spectrum sensing method. We provide some simulation results to show that the detection performance of the proposed detectors is better than their counterparts, derived based on the 2S-GLRT, as well as some other state-of-the-art approaches given in the literature.

Moving target detection with polarimetric distributed MIMO radar in heterogeneous clutter

In this study, the authors consider the problem of moving target detection in the presence of heterogeneous clutter. The knowledge-aided method has been extended to derive the polarimetric multiple-input multiple-output (MIMO) radar detector. And the polarimetric clutter covariance matrix was modelled as a complex inverse Wishart distribution. More precisely, the clutter covariance matrices between different transmitter–receiver (Tx–Rx) pairs are assumed to follow the distribution which shares a prior clutter covariance matrix structure while with different values of the power levels. Under this assumption, the generalised likelihood ratio test (GLRT) approach has been adopted to develop the polarimetric knowledge-aided detector without secondary data. Numerical results are shown to illustrate the effectiveness of the polarimetric knowledge-aided GLRT detector in heterogeneous clutter.

Multi-Antenna Spectrum Sensing using Bootstrap on Cognitive Radio for Internet of Things Application

Cognitive Radio (CR) is a technology used for other developing technologies like Internet of Things (IoT), one part of CR is spectrum sensing which is useful as an empty spectrum searcher. The use of spectrum is now considered very minimal and raises the problem of scarcity of spectrum. But after testing the real problem is the spectrum in utilization. This problem can be overcome by using efficient utilization of CR technology using Spectrum Sensing. Sensing algorithms that are usually used such as: a suitable filter, energy detector and cyclostationary are not enough because there are many antennas to be detected. In the case of multi-antenna detection, research usually uses the Generalized likelihood ratio test (GLRT) approach. The GLRT Approach Detector also has three types of detectors, type-3 detectors do not determine statistical tests. However, if you use monte carlo or the literacy algorithm, you need a lot of data to get the detector performance. this research will combine algorithms using bootstrap to determine detector performance using small data because using Bootstrap basically only requires a small resampling. The research wants to show if a type-3 detector can help the detector produce good probabilities using little data. The expected result is that the GLRT approach can be combined with a bootstrap for type-3 detectors such as: arithmetic and geometric statistical tests (TAGM) and GLRT time code space code statistical tests (TSTBCGLRT) to help determine assumptions Pd assumptions. Then an experiment was carried out to determine the threshold, by comparing bootstrap with monte carlo, research is expected to show that bootstrap works without a known H0 distribution and set the same threshold at all times.

Impropriety-Based Multiantenna Spectrum Sensing With I/Q Imbalanced Radios

Direct conversion radios are widely recognized as the most appealing approach for reducing the hardware cost as well as power consumption in upcoming communication systems. However, such radios are known to entail gain and phase uncertainties along the analog inphase/quadrature (I/Q) paths. In this paper, we address the effects of the transmitter (TX) and receiver (RX) I/Q errors or mismatches on the improperness of the transmitted and received signals, respectively. We analytically show how the properness of a transmitted signal and the receiver thermal noise can be destroyed, respectively, under the transmitter and receiver I/Q errors, given that the corresponding ideal signals are proper under perfect I/Q balance. Then, we address the spectrum sensing problem in cognitive radio systems through modeling it as a composite binary hypothesis testing task, and apply the likelihood ratio test approach to solve it. To this end, we propose three impropriety-based multiantenna spectrum sensing algorithms under the transmitter and receiver I/Q uncertainties. The principle of invariance is exploited to examine the potential constant false alarm rate (CFAR) behavior of the proposed detectors. We analytically prove that all the proposed sensing methods possess CFAR behavior against the noise variance uncertainty, while only two of them have CFAR property against the receiver I/Q mismatch values. The achievable sensing performance of the proposed methods is then analyzed through extensive numerical experiments, and the devised alternative detectors are mutually compared. Finally, analytical solutions are derived to quantify the improvement/degradation in the effective received signal SNR under I/Q imbalanced radios.

Inference of admixed ancestry with Ancestry Informative Markers

Analysis of Ancestry Informative Markers (AIMs) is of interest to forensic geneticists for the purpose of assessing the origin of individuals. Often AIMs are used to produce investigative leads for potential suspects in crime cases and identification in missing persons mass disaster cases.We have previously suggested to assess the origin of the profile of interest by a likelihood ratio test on Fisher's exact test. The likelihood ratio test assesses the likelihood of the data under two competing hypotheses, where the null hypothesis assume common origin of the profile of interest and those in a specified population. However, in the case of a profile of an individual of admixed ancestry, there is an increased risk that the profile will be rejected in the constituting populations.The likelihood ratio test approach is extended by allowing for profile admixture implying the profile of interest is a mixture of profiles from two populations. The Expectation-Maximisation (EM) algorithm is used to handle the ambiguity of allocation of alleles at heterozygous markers. To demonstrate the approach, admixed profiles are simulated using AIMs genotypes in eight global meta populations.

Statistical Methods for Clinical Study Site Selection

The US Food and Drug Administration conducts on-site inspections and data audits through Bioresearch Monitoring program for assurance of the quality and integrity of data in the pre- and postapproval processes. It is important to inspect the study sites that are different compared with other sites in clinical studies and identify the problems related to those sites. Usually one cannot inspect all the sites in a clinical study because of limited resources, and statistical tools are needed to help in selecting sites for inspection. We propose two technical approaches, namely Fisher combination approach and likelihood ratio test (LRT) approach, for site selection, with each approach integrating the information obtained from a P value matrix. The proposed approaches produce site rankings, and the sites with highest rankings may be selected for inspection. The application of the approaches is demonstrated through a hypothetical data set reflecting the pattern of the real data in a premarket approval submission for a diagnostic device. The proposed methods are shown, through extensive simulations, to control false discovery rate, while maintaining good sensitivity. The proposed approaches will be useful for site selection process. However, limitations exist when only using the statistical approaches proposed here. In practice, investigators will select the site for inspection by considering the outputs from the statistical approaches along with other important factors. Future research topic is discussed to facilitate practical application of the approaches.

Efficient GLRT/DOA spectrum sensing algorithm for single primary user detection in cognitive radio systems

Spectrum sensing is a fundamental requirement for cognitive radio systems. In this paper, a new spectrum sensing technique with multiple antenna elements is proposed for further performance enhancement. The proposed technique is based on direction of arrival (DOA) knowledge and beamforming of the received signals. In this context, the Signal to Noise Ratio (SNR) will be significantly improved. The proposed technique is developed to detect only one primary user. Test statistics which determine the absence/presence of the Primary User (PU) are derived by using generalized likelihood ratio test (GLRT) approach. Two test statistics are developed with and without prior knowledge of noise power. Theoretical analysis for probability of detection, probability of false alarm, and their associated threshold are performed based on the statistical theory. Under a few samples scenario, simulations revealed that the proposed technique outperforms the other existing techniques particularly at low SNR regimes. In addition, it consumed less sensing time. Further, simulation results have confirmed theoretical analysis.