Conditional Likelihood Research Articles

Relative humidity prediction across the Indian subcontinent using Kumaraswamy distribution based non-Gaussian model.

Relative humidity (RH) significantly influences various aspects of human life, including agriculture, weather prediction, indoor air quality, and energy consumption. Its intricate non-linear behavior poses a significant challenge for accurate estimation. In the context of Indian climate change, precise forecasting of RH is vital for agriculture and weather prediction. This study proposes a new non-Gaussian approach, the Kumaraswamy seasonal autoregressive moving average (KSARMA) model, for RH prediction across India's five climatic zones (hot-dry, warm-humid, moderate, cold, and composite). Analyzing monthly RH data from 1981 to 2021, model selection was based on diagnostic analysis and Akaike's information criterion (AIC), with parameter estimation utilizing conditional maximum likelihood estimators (CMLE). The KSARMA model demonstrated superior predictive accuracy compared to other models (e.g., multilayer perceptron, SARIMA, Holt-Winter, and SARMA) across all climatic zones, except the hot-dry zone, as supported by error metrics including RMSE (0.04-0.12), MAE (0.03-0.1), SMAPE (0.04-0.2), and MASE (0.5-.08).

A Spatial–Temporal Bayesian Model for a Case-Crossover Design with Application to Extreme Heat and Claims Data

Epidemiological approaches for examining human health responses to environmental exposures in observational studies frequently address confounding by employing advanced matching techniques and statistical methods grounded in conditional likelihood. This study incorporates a recently developed Bayesian hierarchical spatiotemporal model within a conditional logistic regression framework to capture the heterogeneous effects of environmental exposures in a case-crossover (CCO) design. Spatial and temporal dependencies are modeled through random effects incorporating multivariate conditional autoregressive priors. Flexible frailty structures are introduced to explore strategies for managing temporal variables. Parameter estimation and inference are conducted using a Monte Carlo Markov chain method within a Bayesian framework. Model fit and optimal model selection are evaluated using the deviance information criterion. Simulations assess and compare model performance across various scenarios. Finally, the approach is illustrated with workers’ compensation claims data from New York and Florida to examine spatiotemporal heterogeneity in hospitalization rates related to heat prostration.

Signed integer-valued autoregressive model with time-varying coefficients

An integer time series is a sequence of discrete integers arranged chronologically to represent a specific event or phenomenon. It may include negative integers, and its behavior can be influenced by variations in covariates. To address these complexities, this paper introduces a p-order signed integer-valued autoregressive model with time-varying coefficients. Considering the presence of zero-inflated phenomena, we specifically employ the zero-inflated Skellam distribution. To estimate the unknown parameters and nonparametric functions in our proposed model, we adopt a two-step iterative process that combines local linear estimation with either conditional least squares or conditional maximum likelihood. Through a comprehensive simulation study, we evaluate the performance of our estimation method and demonstrate the usefulness of the proposed model using a real-life dataset.

Modeling and testing for endpoint-inflated count time series with bounded support

Count time series with bounded support frequently exhibit binomial overdispersion, zero inflation and right-endpoint inflation in practical scenarios. Numerous models have been proposed for the analysis of bounded count time series with binomial overdispersion and zero inflation, yet right-endpoint inflation has received comparatively less attention. To better capture these features, this article introduces three versions of extended first-order binomial autoregressive (BAR(1)) models with endpoint inflation. Corresponding stochastic properties of the new models are investigated and model parameters are estimated by the conditional maximum likelihood and quasi-maximum likelihood methods. A binomial right-endpoint inflation index is also constructed and further used to test whether the data set has endpoint-inflated characteristic with respect to a BAR(1) process. Finally, the proposed models are applied to two real data examples. Firstly, we illustrate the usefulness of the proposed models through an application to the voting data on supporting interest rate changes during consecutive monthly meetings of the Monetary Policy Council at the National Bank of Poland. Then, we apply the proposed models to the number of police stations that received at least one drunk driving report per month. The results of the two real data examples indicate that the new models have significant advantages in terms of fitting performance for the bounded count time series with endpoint inflation.

A novel bounded ℤ-valued autoregressive model with its application on crime data

This paper tackles the challenge of autoregressive modelling for bounded Z -valued count time series, a topic that has been largely overlooked in the existing literature. To bridge this gap, we introduce the trinomial difference bounded Z -valued autoregressive (TDBZAR) model utilizing the trinomial difference thinning operator, and we explore its stochastic properties in detail. Two notable advantages of the TDBZAR model are that the incorporated trinomial difference thinning operator ensures the conditional expectation takes a linear form and allows its 1-step transition probability to be expressed as the convolution of two independent trinomial difference distributions. This significantly simplifies the computation of both the conditional least squares (CLS) and conditional maximum likelihood (CML) estimates, making them more practical and straightforward. Second, we examine the two-step CLS and CML estimates, establishing their asymptotic properties. Third, we compare the performance of these estimators through simulation studies. Finally, we apply the proposed model to a real dataset to investigate which type of crime (rape or sex offense) was more prevalent in police reports from January 1990 to December 1998.

Cox regression model with doubly truncated and interval-censored data

Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.

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.

Impact of Imputation on Performance of Goodness-of-Fit Tests for the Logistic Panel Data Model

Goodness-of-fit tests aim at discerning model misspecification and identifying a model which is poorly fitting a given data set. They are methods used to determine the suitability of the fitted model. The subject of assessment of goodness-of-fit in logistic regression model has attracted the attention of many scientists and researchers. Several methods for assessing how well observed data can fit into logistic regression models have been proposed and discussed where test statistics are functions of the observed data values and their corresponding estimated values after parameter estimation. Considering a correctly specified panel data model with balanced data set, the conditional maximum likelihood estimates of the parameters are less biased and the estimated response variable values are actually in the neighborhood of the observed values. Relative to the induced biases of the parameter estimates resulting from imputation of missing covariates, the performances of the goodness-of-fit tests may be misjudged. This study looks at the susceptibility of the goodness-of-fit tests for logistic panel data models with imputed covariates. Simulation results show that Bayesian imputation impacts less on the goodness-of-fit test statistics and therefore stands out as the better technique against other classical imputation methods. An increased proportion of missingness however appeared to reduce the confidence interval of the test statistics which in turn reduces the chances of adopting the model under study.

An extension of ℤ-valued time series with Poisson difference innovation via logistic regression

ℤ-valued time series are a type of models that are extremely significant and widely utilized. The Poisson difference distribution is a crucial element in this kind of time series. This paper considers an extension of ℤ-valued autoregressive models with Poisson difference innovation by introducing the random coefficient composed of logistic regression. The estimation process is examined using conditional maximum likelihood and conditional least squares methods. A two-step approach is suggested to further optimize the estimation results. The likelihood ratio test is utilized to ascertain the presence of the random coefficient. Both simulation studies and analysis of real data demonstrate that the suggested model and method demonstrate outstanding performance.

A non-linear integer-valued autoregressive model with zero-inflated data series

A new non-linear stationary process for time series of counts is introduced. The process is composed of the survival and innovation component. The survival component is based on the generalized zero-modified geometric thinning operator, where the innovation process figures in the survival component as well. A few probability distributions for the innovation process have been discussed, in order to adjust the model for observed series with the excess number of zeros. The conditional maximum likelihood and the conditional least squares methods are investigated for the estimation of the model parameters. The practical aspect of the model is presented on some real-life data sets, where we observe data with inflation as well as deflation of zeroes so we can notice how the model can be adjusted with the proper parameter selection.

Reliability analysis based on doubly-truncated and interval-censored data

Field data provide important information on product reliability. Interval sampling is widely used for collection of field data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated (DT) data if the exact failure time is known. In many situations, the exact failure date is known only to fall within an interval, leading to doubly truncated and interval censored (DTIC) data. This article considers analysis of DTIC data under parametric failure time models. We consider a conditional likelihood approach and propose interval estimation for parameters and the cumulative distribution functions. Simulation studies show that the proposed method performs well for finite sample size.

Robust Permutation Tests in Linear Instrumental Variables Regression

This paper develops permutation versions of identification-robust tests in linear instrumental variables regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson-Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroskedasticity under standard exclusion restriction i.e. the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Numerical illustrations corroborate the theoretical results.

Earthquake Predictability and Forecast Evaluation Using Likelihood-Based Marginal and Conditional Scores

Abstract Earthquake probability forecasts are typically based on simulations of seismicity generated by statistical (point process) models or direct calculation when feasible. To systematically assess various aspects of such forecasts, the Collaborative Studies on Earthquake Predictability testing center has utilized N- (number), M- (magnitude), S- (space), conditional likelihood-, and T- (Student’s t) tests to evaluate earthquake forecasts in a gridded space–time range. This article demonstrates the correct use of point process likelihood to evaluate forecast performance covering marginal and conditional scores, such as numbers, occurrence times, locations, magnitudes, and correlations among space–time–magnitude cells. The results suggest that for models that only rely on the internal history but not on external observation to do simulation, such as the epidemic-type aftershock sequence model, test and scoring can be rigorously implemented via the likelihood function. Specifically, gridding the space domain unnecessarily complicates testing, and evaluating spatial forecasting directly via marginal likelihood might be more promising.

Primary care experiences of adults reporting learning disability: a probability sample survey.

Background Adults with learning disability face multiple adversities, but evidence on their needs and primary care experiences is limited. Aim To compare the characteristics and primary care experiences of adults reporting learning disability with those who did not. Design and setting An analysis of the 2022 General Practice Patient Survey, a national probability sample survey conducted in 2022 with people registered with NHS primary care in England. Method This analysis reports descriptive profiles, weighted and with 95% confidence intervals. Logistic regression models adjusting for gender, age, ethnicity, and area-level deprivation compared experiences of adults reporting learning disability with those who did not. Results Survey participants comprised 623,157 people aged 16 or older, including 6,711 reporting learning disability. Adults reporting learning disability were more likely to be male, younger, of mixed or multiple ethnicities, and live in more deprived areas. All chronic conditions included in the survey were more common in adults reporting learning disability, especially reported sensory, neurodevelopmental, neurological, and mental health conditions. Adults reporting learning disability were twice as likely to have a preferred GP, and less likely to find their practice's website easy to navigate. They were also less likely to have confidence and trust in their healthcare professional, or feel their needs were met. Conclusion Adults reporting a learning disability had a higher likelihood of chronic health conditions. Their reported experiences of primary care indicate that despite recent initiatives to improve services offered, further adaptations to the consistency and ease of access to primary care is needed.

Threshold integer-valued autoregressive model with serially dependent innovation

ABSTRACT Nonlinearity in count time series is commonly encountered in practice. To better explain the nonlinear phenomena in count time series, this article introduces a new threshold INAR(1) model using the idea of serially dependent innovation. The proposed model contains some existing INAR(1) models as special cases and establishes a connection between the threshold INAR(1) model and the threshold INARCH(1) model. The basic probabilistic and statistical properties of the new model are investigated. Model parameters, including the threshold variable, are estimated by the conditional least squares, modified quasi-likelihood and conditional maximum likelihood methods. Asymptotic properties and numerical results of the estimates are also studied. An application to the monthly trading volume of stock B in Shanghai Stock Exchange is conducted to show the practicability of the proposed model.

Periodic INAR(1) model with Bell innovations distribution

Abstract In this paper, we introduce a class of periodic integer-valued autoregressive BL-PINAR(1) models with Bell innovations distribution based on the binomial thinning operator. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed forms of these moments are, under the obtained conditions, derived. Furthermore, the periodic autocovariance structure is also considered while providing the closed form of the periodic autocorrelation function. The conditional least squares (CLS), Yule–Walker (YW), weighted conditional least squares (WCLS), and conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The asymptotic properties of the CLS and the YW estimators are obtained. The performances of these methods are compared through a simulation study. An application on a real data set is provided.

Hypoglycaemia in screening oral glucose tolerance test in pregnancy with low birth weight fetus.

Maternal hypoglycemia, a condition characterized by lower than normal blood glucose levels in pregnant women, has been increasingly associated with adverse pregnancy outcomes, including low birth weight (LBW) in neonates. LBW, defined as a birth weight of less than 2500 g, can result from various factors, including maternal nutrition, health status, and metabolic conditions like hypoglycemia. Maternal hypoglycemia may affect fetal growth by altering the supply of essential nutrients and oxygen to the fetus, leading to restricted fetal development and growth. This condition poses significant risks not only during pregnancy but also for the long-term health of the child, increasing the likelihood of developmental delays, health issues, and chronic conditions later in life. Research in this area has focused on understanding the mechanisms through which maternal hypoglycemia influences fetal development, with studies suggesting that alterations in placental blood flow and nutrient transport, as well as direct effects on fetal insulin levels and metabolism, may play a role. Given the potential impact of maternal hypoglycemia on neonatal health outcomes, early detection and management are crucial to minimize risks for LBW and its associated complications. Further investigations are needed to fully elucidate the complex interactions between maternal glucose levels and fetal growth, as well as to develop targeted interventions to support the health of both mother and child. Understanding these relationships is vital for improving prenatal care and outcomes for pregnancies complicated by hypoglycemia.

Clinical and functional outcomes of locked plating vs. cerclage compression wiring for AO type C patellar fractures– a retrospective single-center cohort study

Abstract Purpose Although “tension-band wiring” is still commonly used to stabilize patellar fractures, the technique has recently been scrutinized due to biomechanical insufficiency. Consequently, the AO Foundation renamed the principle to compression cerclage wiring (CCW). Several studies propose favorable outcomes when utilizing locked plating (LP). This study aims to compare outcome of CCW and LP for complex patellar fractures. Methods A retrospective, single-center cohort study was performed on patients who underwent operative treatment for (AO 34 C-Type) patellar fractures between April 2013 and March 2023. Patients with a 12 month follow up were included. We grouped and compared patients based on the applied treatment strategy: group LP vs. group CCW. Primary outcome parameters included implant-related complications and revision surgeries. Secondary outcomes were length of stay, return to work and 12 months functional outcome (Lysholm score). Odd ratios for complications and revisions were calculated using the conditional Maximum Likelihood Estimate. The threshold for statistical significance was set at p < 0.05. Results Of 145 patients, 63 could be included (group LP: n = 23 and group CCW: n = 40). Fractures in group LP were significantly more complex in regard to AO Classification (p < 0.001), number of fragments (p < 0.001) and degree of comminution (p < 0.001), yet odds of complications were significantly lower in group LP (OR: 0.147; 95%CI: 0.015–0.742; p = 0.009). K-wire migration was the most common complication in group CCW (20%). Odds of revision surgery were significantly lower in group LP (OR: 0.000; 95%CI: 0.000-1.120; p = 0.041). The average Lysholm score at one year was favorable in both groups (89.8; SD: 11.9 in group LP and 90.6; SD: 9.3 in group CCW; n.s.). Conclusion In our study cohort, LP was routinely chosen for more complex fracture morphologies; nevertheless the data implies that LP may be considered as the superior fixation technique in regard to complications and revision operations. Especially, K-wire migration occurs frequently after CCW. The one year functional outcome was comparable between the groups, with both demonstrating good results. Prospective randomized studies are indicated to validate our findings.

The moderating effect of access to food facilities and recreational activity space on mHealth multiple health behavior change intervention.

To evaluate whether the neighborhood social and built environment moderates response to a mobile health multiple health behavior change intervention targeting fruit/vegetable intake, sedentary behavior, and physical activity. Participants were 156 Chicago-residing adults with unhealthy lifestyle behaviors. Using linear mixed models, we evaluated whether access to food facilities (fast food restaurants and grocery stores) and recreational activity spaces (gyms and parks) moderated the difference in behavior change between the active intervention condition relative to control. Using spatial data analysis (cross K functions), we also assessed whether participants who achieved goal levels of behaviors ("responders") were more or less likely than those who did not achieve intervention goals ("non-responders") to reside near fast food restaurants, grocery stores, gyms, or parks. According to linear mixed models, none of the neighborhood social and built environment factors moderated the difference in behavior change between the active intervention condition and the control condition (Likelihood Ratio (χ²[1] = 0.02-2.33, P-values > 0.05). Cross K functions showed that diet behavior change responders were more likely than non-responders to reside near fast food restaurants, but not grocery stores. The results for activity behavior change were more variable. Sedentary screen time responders were more likely to reside around recreational activity spaces than non-responders. Moderate-vigorous physical activity responders had greater and lesser clustering than non-responders around parks, dependent upon distance from the park to participant residence. A complex relationship was observed between residential proximity to Chicago facilities and response to multiple health behavior change intervention. Replication across diverse geographic settings and samples is necessary.

Estimasi Parameter Model Regresi Logistik Biner dengan Conditional Maximum Likelihood Estimation pada Data Panel

Binary logistic regression models can be used on panel data with categorical responses that experience repeated measurements based on time. This study aims to determine the factors that influence the Human Development Index in South Sulawesi Province in 2015-2019. Data were analyzed through binary logistic regression with fixed effect model approach through Conditional Maximum Likelihood Estimation (CMLE) for panel data. The results of this study indicate that the variables that have a significant effect are life expectancy (X1), school length expectancy (X2) and the average length of schooling (X3). Obtained the probability value of districts/cities that have a medium low and medium high human development index with a classification accuracy of 56.25%.