Conditional Likelihood Function Research Articles

Using the Conditional Maximum Likelihood function with the genetic algorithm to estimate STARIMA models (pλ, d, qm)

Strategic planning for a specific phenomenon depends mainly on accurate prediction by developing a model to represent that phenomenon. Therefore, this research dealt with spatiotemporal series models such as the STARIMA model (pλ, d, qm) model when there is a spatial correlation for neighbouring sites and a spatial correlation for the same geographical location. The methods for estimating the parameters are the Conditional Maximum Likelihood method and the method of estimating the parameters using the genetic algorithm (MLEGA). These models were compared using the statistical comparison metrics (RMSE). The data represents the daily infections with the COVID-19 epidemic for (10) sectors on the Rusafa side of the city of Baghdad from 29/2/2020 until 25/4/2023; it was found that spatiotemporal series data consider the analysis of spatial relationships between geographic points, which allows for a better understanding of the development of phenomena across time and space. The applied results reached the superiority of the spatiotemporal model STARIMA (11,1,31) with the presence of spatial correlation of neighbouring sites using the genetic algorithm because it has a lower (RMSE), so it was used to predict the daily infections of the Covid-19 epidemic for (10) sectors on the Rusafa side of the city of Baghdad For the period from 26/2/2020 until 5/5/2023. Paper type :Research paper.

Joint Variational Inference Network for domain generalization

Domain generalization is a machine learning task that involves training a model on a set of domains with the goal of achieving high performance on unseen domains. While most domain generalization methods focus on extracting domain-invariant features, they may ignore domain-specific information beyond object styles which is label-relevant for classification. In this paper, we first propose a two-step data generation process in which the domain label and observed data are sampled from two distributions sequentially, and accordingly develop an end-to-end Joint Variational Inference Network (JVINet) for domain generalization. JVINet is a framework that admits a variational-based discriminative structure, which the domain-specific latent variable is learned and integrated to enhance the feature for classification. When testing on unseen target domains, the potential beneficial domain information is hence utilized to improve generalization ability. The overall objective is to optimize the variational lower bound of the conditional joint likelihood functions for both class and domain labels. We provide theoretical proof that JVINet can achieve an optimal lower bound using a variational-based discriminative approach. To evaluate the effectiveness of our method, we compare it with state-of-the-art methods on both simulated and real-world datasets.

Crack localization in glass fiber composite beams by experimental modal analysis and multi variable Gaussian process regression method

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.

Local likelihood of quantile difference under left-truncated, right-censored and dependent assumptions

We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods.

A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP): Modelling framework for episode-level activity participation and time-use analysis

This paper formulates a novel, multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP) to analyze multiple discrete-continuous (MDC) choices at a disaggregate level, including the number of instances different alternatives are chosen and the amount of consumption at each instance of choice. In doing so, the proposed model ensures a logically consistent prediction of multiple choice instances of an alternative. Specifically, the model prevents the prediction of positive allocation to the jth instance (i.e., a frequency of j episodes) of a good while predicting zero allocation to the (j-1)th or lower-numbered instances of that alternative. This is achieved by imposing a non-increasing order on the baseline-preference parameters of different choice instances of an alternative. The model results in a conditional likelihood function, where the likelihood arising from the optimality conditions of the utility maximization problem is conditioned on the ordering of baseline marginal utilities. Combining this strategy with independent and identically distributed (IID) Gumbel stochastic terms in the utility functions results in a closed-form likelihood expression that is not much more difficult than that of the MDCEV model. The proposed framework is applied for an empirical analysis of disaggregate, episode-level activity participation and time allocation behavior of non-working adults in Los Angeles, California. The empirical MDCEV-OP model provided better fit and predictive accuracy (in both estimation and validation datasets) for analyzing episode-level activity participation than a disaggregate MDCEV model that does not recognize the logical ordering of episodes. At the same time, the activity-level predictions aggregated from the episode-level predictions of the MDCEV-OP model do not deviate significantly from the predictions of an aggregate MDCEV model. These results highlight the efficacy of the proposed model for analyzing episode-level activity generation and time allocation.

Integrative Bayesian models using Post-selective inference: A case study in radiogenomics.

Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates for uncertainty in the resulting integrative models are however unreliable unless inference accounts for the selection of these associations with accuracy. In this paper, we develop selection-aware Bayesian methods, which (1) counteract the impact of model selection bias through a "selection-aware posterior" in a flexible class of integrative Bayesian models post a selection of promising variables via ℓ1 -regularized algorithms; (2) strike an inevitable trade-off between the quality of model selection and inferential power when the same data set is used for both selection and uncertainty estimation. Central to our methodological development, a carefully constructed conditional likelihood function deployed with a reparameterization mapping provides tractable updates when gradient-based Markov chain Monte Carlo (MCMC) sampling is used for estimating uncertainties from the selection-aware posterior. Applying our methods to a radiogenomic analysis, we successfully recover several important gene pathways and estimate uncertainties for their associations with patient survivaltimes.

The Basket-Based Choice Experiment: A Method for Food Demand Policy Analysis

Although economic research on food consumer demand has exploded in recent years, most survey demand elicitation approaches have substantial limitations for food policy evaluations as they involve consumers choosing only one item out of a bundle. There is a need to design a more flexible approach capturing more realistic consumption patterns. This study introduces such an approach – a basket-based choice experiment – where consumers select their preferred food item or combination thereof. Our basket-based choice experiment includes 21 food items that can be freely combined to construct over 2 million possible baskets. Our results show that when given the opportunity, consumers select multiple items for their basket, most commonly three or four items. A composite conditional likelihood function approach is used to reduce the computational burden associated with modeling the choice of over 2 million possible baskets, and estimates are utilized in a multivariate logit model to calculate the probability of bundle selection and individual food price elasticities. Unlike typical choice experiments utilizing multinomial logit model variants, which forces products to be demand substitutes, our basket-based approach is able to capture a rich set of substitution and complementary patterns, and we find that most of the 21 food items studied are demand complements. The BBCE is used to explore policy questions related to the impacts of changing prices on the healthfulness of consumer dietary choices and the welfare effects of product bans, such as Meatless Monday.

Score-Driven Modeling of Spatio-Temporal Data

A simultaneous autoregressive score-driven model with autoregressive disturbances is developed for spatio-temporal data that may exhibit heavy tails. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a nonlinear function of the past variables and a set of explanatory variables, while the noise follows a multivariate Student-t distribution. The key feature of the model is that the dynamics of the space-time varying signal are driven by the score of the conditional likelihood function. When the distribution is heavy-tailed, the score provides a robust update of the space-time varying location. Consistency and asymptotic normality of maximum likelihood estimators are derived along with the stochastic properties of the model. The motivating application of the proposed model comes from brain scans recorded through functional magnetic resonance imaging when subjects are at rest and not expected to react to any controlled stimulus. We identify spontaneous activations in brain regions as extreme values of a possibly heavy-tailed distribution, by accounting for spatial and temporal dependence.

Maximum likelihood estimation for score-driven models

We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student’s t distribution.

Maximum likelihood estimation for multivariate normal with auxiliary information

Closed forms are obtained for the maximum likelihood estimators (MLE) of the mean vectors and the covariance matrix of a multivariate normal samples using known means of auxiliary variables. The likelihood function is decomposed as product of several independent normal and conditional normal likelihood functions. The parameters are transformed into a new set of parameters of which the MLEs are easy to derive. Since the MLE are invariant, the MLE of the original parameters are derived using the inverse transformation.MSC2000 subject classi cations: 62H12; 62H15.

Maximum likelihood estimation for multivariate normal distribution with hierarchical missing data

Closed forms are obtained for the maximum likelihood estimators (MLE) of the mean vector and the covariance matrix of a multivariate normal model with a hierarchical missing pattern. According to the missing pattern, the likelihood function is decomposed as product of several independent normal and conditional normal likelihood functions. The original parameters are transformed into a new set of parameters whose MLE are easy to derive. Since the MLE are invariant, the MLE of the original parameters are derived using the inverse transformation.

Semiparametric Multinomial Logistic Regression for Multivariate Point Pattern Data

We propose a new method for analysis of multivariate point pattern data observed in a heterogeneous environment and with complex intensity functions. We suggest semiparametric models for the intensity functions that depend on an unspecified factor common to all types of points. This is for example well suited for analyzing spatial covariate effects on events such as street crime activities that occur in a complex urban environment. A multinomial conditional composite likelihood function is introduced for estimation of intensity function regression parameters and the asymptotic joint distribution of the resulting estimators is derived under mild conditions. Crucially, the asymptotic covariance matrix depends on ratios of cross pair correlation functions of the multivariate point process. To make valid statistical inference without restrictive assumptions, we construct consistent nonparametric estimators for these ratios. Finally, we construct standardized residual plots, predictive probability plots, and semiparametric intensity plots to validate and to visualize the findings of the model. The effectiveness of the proposed methodology is demonstrated through extensive simulation studies and an application to analyzing the effects of socio-economic and demographical variables on occurrences of street crimes in Washington DC. Supplementary materials for this article are available online.

Survival analysis under the Cox proportional hazards model with pooled covariates.

For a continuous time-to-event outcome and an expensive-to-measure exposure, we develop a pooling design and propose a likelihood-based approach to estimate the hazard ratios (HRs) of a Cox proportional hazards (PH) model. Our proposed approach fits a PH model based on pooled exposures with individually observed time-to-event outcomes. The design and estimation exploits the equivalence of the conditional logistic likelihood functions arising from a matched case-control study and the partial likelihood function of a riskset-matched, nested case-control (NCC) subset of a cohort study. To create the pools, we first focus on an NCC subcohort. Pools are formed at random while keeping the matching intact. Pool-level exposure and confounders are then evaluated and used in the likelihood to estimate the HR and the standard error of the estimates. The estimators are MLEs, provide consistent estimates of the individual-level HRs, and are asymptotically normal. Our simulation results indicate that the pooled estimates are comparable to the estimates obtained from the NCC subcohort. The units of analysis for the pooled design are the pools and not the individual participants. Hence the effective sample size is reduced. Therefore, the variance of the HR estimate increases with increasing poolsize. However, this variance inflation in small samples can be offset by including more matched controls per case within the NCC subcohort. An application is demonstrated with the Second Manifestations of ARTerial disease (SMART) study.

General regression model for the subdistribution of a competing risk under left-truncation and right-censoring.

Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function. We compare different weights from recent literature and develop a heuristic interpretation from a cure model perspective that is based on pseudo risk sets. Our approach accommodates external time-dependent covariate effects on the subdistribution hazard. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate solid performance of the proposed method. Comparing the sandwich estimator with the inverse Fisher information matrix, we observe a bias for the inverse Fisher information matrix and diminished coverage probabilities in settings with a higher percentage of left-truncation. To illustrate the practical utility of the proposed method, we study its application to a large HIV vaccine efficacy trial dataset.

A novel robust Student’s t-based Gaussian approximate filter with one-step randomly delayed measurements

In this paper, a novel robust Student’s t-based Gaussian approximate filter (RSTGAF) is proposed to solve the filtering problem of the nonlinear system with one-step randomly delayed measurements (ORDM) and heavy-tailed measurement noise. The conditional likelihood function is transformed into an exponential multiplication form after using state augmentation approach and introducing a Bernoulli random variable, and then the augmentation state vector, the auxiliary random variables and the Bernoulli random variable are jointly estimated based on the variational Bayesian (VB) approach. The simulation results demonstrate the superiority of the proposed filter, as compared with the existing filters, to address the ORDM and heavy-tailed measurement noise.

Semiparametric regression analysis for left-truncated and interval-censored data without or with a cure fraction

Interval censoring and truncation arise often in cohort studies, longitudinal and sociological research. In this article, we formulate the effects of covariates on left-truncated and mixed case interval-censored (LTIC) data without or with a cure fraction through a general class of semiparametric transformation models. We propose the conditional likelihood approach for statistical inference. For data without a cure fraction, we propose a computationally efficient EM algorithm, facilitated by a novel data augmentation method, to obtain the conditional maximum likelihood estimator (cMLE). For data with a cure fraction, we consider a semiparametric mixture cure model, which combines a logistic regression formula for the uncured probability with the class of transformation models for the failure time of uncured individuals. To overcome the computational complexity due to the presence of a cure fraction, by reparameterization of cure rate in the conditional likelihood function, we propose a computationally stable EM algorithm for obtaining the cMLE. We show that the cMLEs for the regression parameters are consistent and asymptotically normal. Based on the profile likelihood, we apply an EM-aided numerical differentiation method to compute the asymptotic variance estimates. We demonstrate the performance of our procedures through intensive simulation studies and application to the datasets from the Cardiovascular Disease Risk Factors Two-Township Study.

Design of the flexibly-reconfigurable roll forming process by a progressively-improving goal seeking approach

In order to design the flexibly-reconfigurable roll forming (FRRF) process, i.e., to find the set of process parameters that lead to the target 3D surface, an efficient approach is suggested in the present study that can significantly improve the production rate by FRRF where each process design is usually applied for a few or a single forming. According to this approach, the results of the already performed simulations and experiments are used as the sample data for constructing a surrogate model that receives a set of process parameters and returns the longitudinal radius. Then, the genetic algorithm (GA) is hired to explore the surrogate model to predict a set of process parameters that would lead to the target longitudinal radius. This is accomplished by a goal seeking approach and maximization of a conditional likelihood function. The predicted set of the process parameters is given to an efficient finite element method (FEM) to evaluate the corresponding longitudinal radius, and the new input-output pair is added to the sample data to improve the subsequent modeling and predictions. Then, the sequential modeling-prediction-evaluation (MPE) steps are repeated until the output is close enough to the target value. Since the results of all the simulations and experiments are saved in a database to be used for the next designs, the efficiency of the procedure is progressively improved because the surrogate model becomes more informative that in turn enables more exact predictions. However, constructing the surrogate model becomes slower as the number of sample points increases. For preventing this phenomenon, a modified version of the Morris-Mitchel criterion is utilized for subset sampling that selects a desired number of sample points with maximum space-filling property. In order to examine the suggested procedure, an initial database containing 54 sample points collected from experimental study is constructed. Then, the suggested approach is hired to reproduce 3 of the samples which are randomly selected from the database. The results show that this method can be used for design of FRRF process with a few or even one MPE that can significantly improve the production rate in this process.

Analysis of Error Structure for Additive Biomass Equations on the Use of Multivariate Likelihood Function

Research Highlights: this study developed additive biomass equations respectively from nonlinear regression (NLR) on original data and linear regression (LR) on a log-transformed scale by nonlinear seemingly unrelated regression (NSUR). To choose appropriate regression form, the error structures (additive vs. multiplicative) of compatible biomass equations were determined on the use of the multivariate likelihood function which extended the method of likelihood analysis to the general occasion of a contemporaneously correlated set of equations. Background and Objectives: both NLR and LR could yield the expected predictions for allometric scaling relationship. In recent studies, there are vigorous debates on which regression (NLR or LR) should apply. The main aim of this paper is to analyze the error structure of a compatible system of biomass equations to choose more appropriate regression. Materials and Methods: based on biomass data of 270 trees for three tree species, additive biomass equations were developed respectively for NLR and LR by NSUR. Multivariate likelihood functions were computed to determine the error structure based on the multivariate probability density function. The anti-log correction factor which kept the additive property was obtained separately using the arithmetic and weighted average of basic correction factors from each equation to assess two model specifications on the comparably original scale. Results: the assumption of additive error structure was well favored for an additive system of three species based on the joint likelihood function. However, the error structure of each component equation calculated from the conditional likelihood function for compatible equations might be different. The performance of additive equations corrected by a weighted average of basic correction factor from each component equation performed better than that of the arithmetic average and held good property of compatibility after corrected. Conclusions: NLR provided a better fit for additive biomass equations of three tree species. Additive equations which confirmed the responding assumption of error structure performed better. The joint likelihood function on the use of the multivariate likelihood function could be used to analyze the error structure of the additive system which was a result of a tradeoff for each component equation. Based on the average of correction factors from each component equation to correct the bias of additive equations was feasible for the hold of additive property, which might lead to a poor correction effect for some component equation.

On semiparametric transformation model with LTRC data: pseudo likelihood approach

When the distribution of the truncation time is known up to a finite-dimensional parameter vector, many researches have been conducted with the objective to improve the efficiency of estimation for nonparametric or semiparametric model with left-truncated and right-censored (LTRC) data. When the distribution of truncation times is unspecified, one approach is to use the conditional maximum likelihood estimators (cMLE) (Chen and Shen in Lifetime Data Anal https://doi.org/10.1007/s10985-016-9385-9, 2017). Although the cMLE has nice asymptotic properties, it is not efficient since the conditional likelihood function does not incorporate information on the distribution of truncation time. In this article, we aim to develop a more efficient estimator by considering the full likelihood function. Following Turnbull (J R Stat Soc B 38:290–295, 1976) and Qin et al. (J Am Stat Assoc 106:1434–1449, 2011), we treat the unobserved (left-truncated) subpopulation as missing data and propose a two-stage approach for obtaining the pseudo maximum likelihood estimators (PMLE) of regression parameters. In the first stage, the distribution of left truncation time is estimated by the inverse-probability-weighted (IPW) estimator (Wang in J Am Stat Assoc 86:130–143, 1991). In the second stage, we obtain the pseudo complete-data likelihood function by replacing the distribution of truncation time with the IPW estimator in the full likelihood. We propose an expectation–maximization algorithm for obtaining the PMLE and establish the consistency of the PMLE. Simulation results show that the PMLE outperforms the cMLE in terms of mean squared error. The PMLE can also be used to analyze the length-biased data, where the truncation time is uniformly distributed. We demonstrate that the PMLE works more robust against the support assumption of truncation time for length-biased data compared with the MLE proposed by Qin et al. (2011). We apply our proposed method to the channing house data. While the PMLE is quite appealing under specific cases with independent censoring and time-invariant covariates, its applicability, as shown in simulation study, can be rather restricted for more general settings.