Maximum Likelihood Ratio Test Research Articles

The Comparison of Inverse Gaussian and Gamma Regression: Application on Stunting Data in Jepara

Many research data have distributions other than the normal distribution, called exponential family distributions. The exponential family of distributions includes the inverse Gaussian and Gamma distributions. There are parallels between these two distributions in terms of the kind of random variable and how well they work. Finding the optimal model using inverse Gaussian and Gamma regression on stunting data in Jepara is the goal of this study. Maximum Likelihood Estimation is used for parameter estimation, Maximum Likelihood Ratio Test is used for simultaneous parameter testing, and Wald testing is used for partial parameter testing. For this case, the best model is inverse Gaussian regression. Exclusive breastfeeding, low birth weight babies, clean drinking water facilities, and the number of Integrated Service Post (Posyandu) influence the percentage of stunting in Jepara..

Spatial clustering based on geographically weighted multivariate generalized gamma regression

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:•A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.•Goodness of fit test to test the spatial effects in GWMGGR model.•Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

Parameter Estimation and Hypothesis Testing on Bivariate Log-Normal Regression Models

This study aims to introduce a bivariate Log-Normal regression model and to develop a technique for parameter estimation and hypothesis testing. We term the model Bivariate Log-Normal Regression (BLNR). The estimation procedure is conducted by the standard Maximum Likelihood Estimation (MLE) employing the Newton-Raphson method. To perform hypothesis testing, we adapt the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing with test statistics which, for large n, follows Chi-Square distribution with degrees of freedom p. In addition, the partial testing is derived from a central limit theorem which results in a Z-test statistic.
 Keywords: parameter estimation, hypothesis testing, bivariate log, normal regression

Paternal age and first trimester placental size and growth: The Rotterdam Periconceptional Cohort

IntroductionDespite a noticeable trend of delayed fatherhood, less is known about the impact of paternal age on the paternally programmed placenta. We hypothesize that paternal aging affects seminal quality and as such induces ageing-related epigenetic alterations that influence placental growth. Our main aim is to investigate associations between paternal age and first trimester (vascular) placental growth trajectories. MethodsPregnant women were enrolled before 10 weeks of gestation in the Rotterdam Periconceptional Cohort (Predict study). Placental volumes (PV) and utero-placental vascular volumes (uPVV) were measured at 7, 9, and 11 weeks gestation. Associations between paternal age and PV and uPVV were investigated using linear mixed models and the maximum likelihood ratio test to test non-linear relationships. We adjusted for gestational age, fetal sex, parental smoking and maternal age, BMI, education and parity, and stratified for conception mode. ResultsFrom 808 pregnancies we obtained 1313 PV and from 183 pregnancies 345 uPVV measurements. We show no associations between paternal age and PV (p = 0.934) and uPVV (p = 0.489) in our total population or in pregnancies conceived naturally (PV p = 0.166; uPVV p = 0.446) and after IVF/ICSI (PV p = 0.909; uPVV p = 0.749). For example, PV was 0.9% smaller (95% CI -5.7%—7.1%) in fathers aged 40 compared to 30 years old at 9 weeks gestation in the total study population. DiscussionWe are not demonstrating a significant impact of paternal age on first trimester placental growth in a tertiary care population. Given the trend of increasing paternal age, our study should be repeated in the general population.

Exact testing for heteroscedasticity in a two‐way layout in variety frost trials when incorporating a covariate

SummaryTwo‐way layouts are common in grain industry research where it is often the case that there are one or more covariates. It is widely recognised that when estimating fixed effect parameters, one should also examine for possible extra error variance structure. An exact test for heteroscedasticity, when there is a covariate, is illustrated for a data set from frost trials in Western Australia. While the general algebra for the test is known, albeit in past literature, there are computational aspects of implementing the test for the two way when there are covariates. In this scenario the test is shown to have greater power than the industry standard, and because of its exact size, is preferable to use of the restricted maximum likelihood ratio test (REMLRT) based on the approximate asymptotic distribution in this instance. Formulation of the exact test considered here involves creation of appropriate contrasts in the experimental design. This is illustrated using specific choices of observations corresponding to an index set in the linear model for the two‐way layout. Also an algorithm supplied complements the test. Comparisons of size and power then ensue. The test has natural extensions when there are unbalanced data, and more than one covariate may be present. Results can be extended to Balanced Incomplete Block Designs.

Analyzing cellwise weighted data

Often the rows (cases, objects) of a dataset have weights. For instance, the weight of a case may reflect the number of times it has been observed, or its reliability. For analyzing such data many rowwise weighted techniques are available, the most well known being the weighted average. But there are also situations where the individual cells (entries) of the data matrix have weights assigned to them. An approach to analyze such data is proposed. A cellwise weighted likelihood function is defined, that corresponds to a transformation of the dataset which is called unpacking. Using this weighted likelihood one can carry out multivariate statistical methods such as maximum likelihood estimation and likelihood ratio tests. Particular attention is paid to the estimation of covariance matrices, because these are the building blocks of much of multivariate statistics. An R implementation of the cellwise maximum likelihood estimator is provided, which employs a version of the EM algorithm. Also a faster approximate method is proposed, which is asymptotically equivalent to it.

Parameter Estimation and Hypothesis Testing of The Bivariate Polynomial Ordinal Logistic Regression Model

Logistic regression is one of statistical methods that used to analyze the correlation between categorical response variables and predictor variables which are categorical or continuous. Many studies on logistic regression have been carried out by assuming that the predictor variable and its logit link function have a linear relationship. However, in several cases it was found that the relationship was not always linear, but could be quadratic, cubic, or in the form of other curves, so that the assumption of linearity was incorrect. Therefore, this study will develop a bivariate polynomial ordinal logistic regression (BPOLR) model which is an extension of ordinal logistic regression, with two correlated response variables in which the relationship between the continuous predictor variable and its logit is modeled as a polynomial form. There are commonly two correlated response variables in scientific research. In this study, each response variable used consisted of three categories. This study aims to obtain parameter estimators of the BPOLR model using the maximum likelihood estimation (MLE) method, obtain test statistics of parameters using the maximum likelihood ratio test (MLRT) method, and obtain algorithms of estimating and hypothesis testing for parameters of the BPOLR model. The results of the first partial derivatives are not closed-form, thus, a numerical optimization such as the Berndt–Hall–Hall–Hausman (BHHH) method is needed to obtain the maximum likelihood estimator. The distribution statistically test is followed the Chi-square limit distribution, asymptotically.

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis.

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than . We show that our analytic expressions reproduce the p-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as an energy versus entropy competition.

Inference of Intensity-Based Models for Load-Sharing Systems With Damage Accumulation

To model damage accumulation for load-sharing systems, two models given by intensity functions of self-exciting point processes are proposed: a model with additive damage accumulation and a model with multiplicative damage accumulation. Both models include the model without damage accumulation as a special case. For both models, the likelihood functions are derived and maximum likelihood estimators and likelihood ratio tests are given in a scale-invariant version and a scale-dependent version. Furthermore, a Bayesian approach using Markov chain Monte Carlo methods for posterior computation is provided. The frequentist and Bayesian methods are applied to a data set of failures of tension wires of concrete beams where a significant damage accumulation effect is confirmed by both additive and multiplicative damage accumulation models. This is all the more remarkable as a simulation study indicates that the tests for an existing damage accumulation effect are rather conservative. Moreover, prediction intervals for the failure times of the tension wires in a new experiment are given, which improve former prediction intervals derived without damage accumulation. The simulation study considers a scenario with a fixed time horizon and one with fixed numbers of failed components of the systems.

ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESIS MODEL GEOGRAPHICALLY WEIGHTED GENERALIZED GAMMA REGRESSION

Each location has unique characteristics, which are different from other locations which give rise to spatial effects between locations. Therefore, the Generalized Gamma Regression (GGR) model is not suitable to be applied to this problem. The solution is to use a Geographically Weighted Generalized Gamma Regression (GWGGR) model which produces different parameters for each observation location. This study aims to estimate GWGGR parameters using the Berndt-Hall-Hall-Hausman (BHHH) algorithm. After parameter estimation is performed, the hypothesis testing procedure is used to test the similarity of parameters between the generalized gamma regression and GWGGR and to test the significance of the independent variables in the model, either simultaneously using the Maximum Likelihood Ratio Test (MLRT) or partially using the Z-test. Keywords: BHHH, Generalized Gamma, GGR, GWGGR, MLRT.

MIXED-EFFECT MODELS FOR VOLUMETRIC ESTIMATION OF LUMBER FROM NATIVE AMAZONIAN SPECIES

The objective of the present work is to test fixed effect models and compare them with different configurations of mixed models to predict lumber volume. The database came from a medium-sized sawmill located in the rural area of the municipality of Porto Grande, Amapá, Brazil. A total of 50 logs of 9 native species were used, with their volume being measured by the Smalian method. A fixed effect model proposed by Lima et al. (2018) was fitted andcompared to mixed linear models with species as a random effect. The fitting of the fixed model and the mixed models were performed using the maximum restricted likelihood method. Akaike information criteria (AIC), correlation coefficient, Maximum Likelihood Ratio Test, Square Root of the Mean Square Error (RMSE), absolute mean distance and bias were used to select the best model. According to the established criteria, the mixed models obtained better fits when compared to the fixed model, providing a reduction in the RMSE of 0.3 for an average between the mixed models of 0.26. According to the results achieved, the mixed linear models were more efficient and accurate for volume estimation. The M7 mixed model was the best fit model. The use of mixed models enables greater accuracy in estimating volume.

Bartlett correction of an independence test in a multivariate Poisson model

We consider a system of dependent Poisson variables, where each variable is the sum of an independent variate and a common variate. It is the common variate that creates the dependence. Within this system, a test of independence may be constructed where the null hypothesis is that the common variate is identically zero. In the present paper, we consider the maximum log likelihood ratio test. For this test, it is well‐known that the asymptotic distribution of the test statistic is an equal mixture of zero and a chi‐square distribution with one degree of freedom. We examine a Bartlett correction of the test, in the hope that we will get better approximation of the nominal size for moderately large sample sizes. A correction of this type is explicitly derived, and its usefulness is explored in a simulation study. For practical purposes, the correction is found to be useful in dimension two, but not in higher dimensions.

Three-Dimensional Myocardial Strain for the Prediction of Clinical Events in Patients With ST-Segment Elevation Myocardial Infarction.

BACKGROUNDTwo-dimensional (2D) strain provides more predictive power than ejection fraction (EF) in patients with ST-elevation myocardial infarction (STEMI). 3D strain and EF are also expected to have better clinical usefulness and overcome several inherent limitations of 2D strain. We aimed to clarify the prognostic significance of 3D strain analysis in patients with STEMI.METHODSPatients who underwent successful revascularization for STEMI were retrospectively recruited. In addition to conventional parameters, 3D EF, global longitudinal strain (GLS), global area strain (GAS), as well as 2D GLS were obtained. We constructed a composite outcome consisting of all-cause death or re-hospitalization for acute heart failure or ventricular arrhythmia.RESULTSOf 632 STEMI patients, 545 patients (86.2%) had a reliable 3D strain analysis. During median follow-up of 49.5 months, 55 (10.1%) patients experienced the adverse outcome. Left ventricle EF, 2D GLS, 3D EF, 3D GLS, and 3D GAS were significantly associated with poor outcomes. (all, p < 0.001) The maximum likelihood-ratio test was performed to evaluate the additional prognostic value of 2D GLS or 3D GLS over the prognostic model consisting of clinical characteristics and EF, and the likelihood ratio was 15.9 for 2D GLS (p < 0.001) and 1.49 for 3D GLS (p = 0.22).CONCLUSIONSThe predictive power of 3D strain was slightly lower than the 2D strain. Although we can obtain 3D strains, volume, and EF simultaneously in same cycle, the clinical implications of 3D strains in STEMI need to be investigated further.

Bootstrap-Based Between-Study Heterogeneity Tests in Meta-Analysis

Meta-analysis combines pertinent information from existing studies to provide an overall estimate of population parameters/effect sizes, as well as to quantify and explain the differences between studies. However, testing between-study heterogeneity is one of the most challenging tasks in meta-analysis research. Existing methods for testing heterogeneity, such as the Q test and likelihood ratio (LR) test, have been criticized for their failure to control Type I error rate and/or failure to attain enough statistical power. Although better reference distribution approximations have been proposed in the literature, their application is limited. Additionally, when the interest is to test whether the size of the heterogeneity is larger than a specific level, existing methods are far from mature. To address these issues, we propose new heterogeneity tests. Specifically, we combine bootstrap methods with existing heterogeneity tests (i.e., the maximum LR test, the restricted maximum LR test, and the Q test) to overcome the reference distribution issue and denote them as B-ML-LRT, B-REML-LRT, and B-Q, respectively. Simulation studies were conducted to examine and compare the performance of the proposed methods with the regular LR test, the regular Q test, and the Kulinskaya’s improved Q test in both random- and mixed-effects meta-analyses. Based on the results of Type I error rates and statistical power, B-REML-LRT is recommended. Additionally, the improved Q test is also recommended when it is applicable. An R package is provided to facilitate the implementation of the proposed tests.

Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model

We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables.

Prognostic factors related to clinical outcome following thrombectomy in ischemic stroke

Background: Acute ischemic stroke continues to be one of the leading causes of disability and death and is a financial burden to an already taxed health care system. Early intra-arterial treatment with mechanical thrombectomy devices is safe and effective for reducing disability and is superior to standard treatment with intravenous thrombolysis alone for the treatment large artery occlusion stroke. Nevertheless prognostics factors need to be systematically analyzed in the context of these new therapeutic strategies. The aim of this study was to analyze prognostic factors related to clinical outcome following thrombectomy in ischemic stroke. Methods: This single - center prospective study included 84 patients with large vessel occlusion stroke, in the anterior and the posterior circulation. Sexes, age, time to recanalization were prospectively collected. Clinical outcome was assessed post treatment, day one and discharge by means of a NIHSS. Three months mRS evaluation was performed by an independent neurologist. The probability of good outcome at 3 months was assessed by forward stepwise logistic regression using baseline NIHSS score, Glasgow score (GCS) at entrance, hyperglycemia, dyslipidemia, NIHSS at discharge, ASPECT score, collateral scale, TICI scale and time to recanalization. All variables significantly associated with the outcome in the univariate analysis were entered in the model. The significance of adding or removing a variable from the logistic model was determined by the maximum likelihood ratio test. Odds - ratio (OR) and their 95% confidence intervals were calculated. Results: At 3 months 55.2% of patients had a mRS 0 - 2. Baseline NIHSS score (p = 0.001), hyperglycemia (p = 0.024), dyslipidemia (p = 0.016), ASPECT score at entrance (p = 0.005), Good collateral status (p = 0.046) were all factors significantly associated with 3 month clinical outcome. Collateral scale, TICI scale and time to final TICI were not correlated to 3 months outcome. Baseline NIHSS score (OR, 2.539; 95% CI, 1.278 - 5.049; p = 0.008), hyperglycemia (OR, 29.841; 95% CI, 1.050 - 848.183; p = 0.047), emerged as independent predictors of outcome at 3 months. Overall embolic complication rate was 5%, and symptomatic intracranial hemorrhage was 3.5%. Conclusions: There are multiple factors that determine the predictors of clinical outcome in patients who undenwent endovascular treatment. High NIHSS and hyperglycemia at admission were the two factor independently associated with a bad outcome at 90 days.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Gamma regression model

Geographically Weighted Regression (GWR) study potential relationships in regression models that distinguish geographic spaces using non-stationary parameters to overcome spatial effects. The use of gamma regression, namely regression with the dependent variable with a gamma distribution, can be an alternative if the data do not follow a normal distribution. Gamma distribution is a continuous set of non-negative values, generally skewed to the right or positive skewness. Gamma regression is developed to be Bivariate Gamma Regression (BGR) when there are two dependent variables with gamma distribution. If the observation units are location points, spatial effects may occur. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model can be a solution for spatial heterogeneity. However, during its development, many cases require information from panel data. Using panel data can provide complete information because it covers several periods, but it allows for temporal effects. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to handle spatial and temporal heterogeneity simultaneously. The estimation of the GTWBGR model parameters uses the Maximum Likelihood Estimation (MLE) method that followed by the numerical iteration of Berndt Hall Hall Hausman (BHHH). The simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT) method to get a test statistic. With a large sample size, the distribution of the test statistic approaches chi-square. Meanwhile, partial testing uses the Z test statistic.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate generalized Poisson regression

Poisson regression is used to model the data with the response variable in the form of count data. This modeling must meet the equidispersion assumption. That is, the average value is the same as the variance. However, this assumption is often violated. Violation of the equidispersion assumption in Poisson regression modeling will result in invalid conclusions. These violations are an overdispersion and an underdispersion of the response variable. Generalized Poisson Regression (GPR) is an alternative if there is a violation of the equidispersion assumption. If there are two correlated response variables, modeling will use the Bivariate Generalized Poisson Regression (BGPR). However, in the panel data with the observation unit in the form of an area, BGPR is not quite right because there is spatial and temporal heterogeneity in the data. Geographically and Temporally Weighted Bivariate Generalized Poisson Regression (GTWBGPR) is a method for modeling spatial and temporal heterogeneity data. GTWBGPR is a development of GWBGPR. In GTWBGPR, besides accommodating spatial effects, it also accommodates temporal effects. This research will discuss the parameter estimation and test statistics for the GTWBGPR model. Parameter estimation uses Maximum Likelihood Estimation (MLE), but the result is not closed-form, so it is solved by numerical iteration. The numerical iteration used is Newton-Raphson. The test statistic for simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT). With large samples, then this test statistic has a chi-square distribution approximation. So the test statistic for the partial test uses the Z test statistic.

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.

Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

In both Tweedie and geometric Tweedie models, the common power parameter works as an automatic distribution selection. It separates two subclasses of semicontinuous (1<p<2) and positive continuous () distributions. Our paper centres around exploring diagnostic tools based on the maximum likelihood ratio test and minimum Kolmogorov-Smirnov distance methods to discriminate very close distributions within each subclass of these two models according to values of p. Grounded on the unique equality of variation indices, we also discriminate the gamma and geometric gamma distributions with p = 2 in Tweedie and geometric Tweedie families, respectively. Probabilities of correct selection for several parameters combination and sample sizes are examined by simulations. We thus perform a numerical comparison study to assess the discrimination procedures in these subclasses of two families. Finally, semicontinuous () distributions in the broad sense are significantly more distinguishable than the over-varied continuous (p>2) ones; and two datasets for illustration purposes are investigated.