Consistent Akaike Information Criterion Research Articles

Estimation and comparison of Weibull-Normal distribution with some other probability models using Bayesian method of estimation

In statistical applications the Normal distribution is adjudged to be the best. Recent studies Terna (2017) using classical method indicated that Weibull-Normal distribution outperformed the Normal distribution. In this study we used the non-classical Bayesian method of estimation to estimate and compare the Weibull-Normal distribution with some other distributions including Normal and Gamma-Normal distributions. This study derived explicit expressions for basic statistical properties such as moments, moment generating function, the characteristic function, reliability analysis and the distribution of order statistics. It looks at estimation of confidence intervals for the parameters of the Weibull-Normal distribution and estimated the parameters of the new distribution using a non-classical approach for the purpose of theoretical comparisons. The two other distributions whose parameters were also estimated by using Bayesian estimation are the normal distribution and gamma distribution as well as the combination Gamma-Normal distribution. Based on the analyses and interpretations of the results obtained it was found that the parameters and other general properties of Normal distribution gives a better fit than other distributions. R-software was used; the models were written as an R code in R program using the rjags library, the distribution parameters were obtained from a Gibbs sampling of a Bayesian Fit for data set I and data set II. The criteria used in R for comparisons were the negative log-likelihood, AIC (Akaike information criterion), CAIC (Consistent Akaike Information Criterion) and BIC (Bayesian information Criterion).

A new extension of linear failure rate distribution with estimation, simulation, and applications

In this article, we provide a new three-parameter model derived from the newly reduced Cauchy power-G family and linked to the linear failure rate model. The truncated Cauchy power linear failure rate (TCPLFR) is the name given to this distribution. The TCPLFR distribution also contains the truncated Cauchy power Rayleigh distribution and the truncated Cauchy power exponential distribution as sub-models. The TCPLFR distribution has rising, falling, and U-shaped hazard rate functions. The distribution characteristics of the TCPLFR are presented. To compute the population parameters’ point and estimated confidence intervals, the maximum likelihood approach is employed. We explore the behavior of the maximum likelihood estimates as well as the estimated confidence intervals for the model parameters using Monte Carlo simulation. To demonstrate the significance and flexibility of the TCPLFR distribution, the Akaike information criterion (D1), Bayesian information criterion (D2), consistent Akaike information criterion (D3), Hannan–Quinn information criterion (D4), and Kolmogorov–Smirnov (D5) statistic with its p-value (D6) were employed. According to a real-world data analysis, the truncated Cauchy power linear failure rate distribution outperforms alternative models with two, three, and four parameters.

SINE-LOMAX DISTRIBUTION: PROPERTIES AND APPLICATIONS TO REAL DATA SETS

In this study, a novel distribution called the two-parameter Sine Lomax distribution was introduced. The distribution was developed by combining the Sine generalized family of distributions with the Lomax distribution. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, quantile function, rth moment, entropy, moment generating function, and order statistics. The probability density function (PDF) plot indicated that the distribution is skewed to the right. Additionally, the hazard plot of the Sine Lomax distribution showed both monotonic increase and monotonic decrease. To estimate the parameters of the newly proposed distribution, the maximum likelihood approach was employed. A simulation study was conducted to evaluate the consistency of the estimators. The simulation results indicated that the estimators are consistent, as the bias and mean square error decrease with increasing sample sizes. The performance of the Sine Lomax distribution was compared to other extensions of Lomax distributions and the baseline distribution which is the Lomax distribution using various evaluation criteria, including the Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). The proposed distribution demonstrated the lowest scores among the competing models, indicating its potential for accurately modeling real-world data sets. Based on the results, the proposed Sine Lomax distribution is recommended as a superior alternative to the competing models for modeling certain real-world data sets.

A hybridized consistent Akaike type information criterion for regression models in the presence of multicollinearity

Consistent Akaike information criterion (CAIC) is an adjusted form of classical AIC. This criterion was developed by modifying the penalty. As a result, we propose a novel AIC type criterion, called CAIC The proposed criterion includes a dynamic parameter for controlling the penalty further. The distinctive feature of CAIC is to penalize multicollinearity level considering the information complexity measures. CAIC requires the parameter, and in addition, a procedure is proposed to estimate based on the information complexity of the regression model. Monte Carlo simulations and real data set examples demonstrate that CAIC performs better than classical information criteria for the potential multicollinearity problems.

Parametric Modeling Approach to Covid-19 Pandemic Data

The problem of skewness is common among clinical trials and survival data, which has been the research focus derivation and proposition of different flexible distributions. Thus, a new distribution called Extended Rayleigh Lomax distribution is constructed from Rayleigh Lomax distribution to capture the excessiveness of some survival data. We derive the new distribution by using beta logit function proposed by Jones (2004). Some statistical properties of the distribution such as density, cumulative density, reliability rate, hazard rate, reverse hazard rate, moment generating and likelihood functions; skewness, kurtosis and coefficient of variation are obtained. We also performed the expected estimation of model parameters by maximum likelihood; goodness of fit and model selection criteria, including Anderson Darling, CramerVon Misses, Kolmogorov Smirnov (KS), Akaike Information, Bayesian Information, and Consistent Akaike Information Criterion is employed to select the better distribution from those models considered in the work. The results from the statistics criteria show that the intended distribution performs well and has a good representation of the States in Nigeria’s Covid-19 death cases data than other competing models.

A Simulation Study on Latent Transition Analysis for Examining Profiles and Trajectories in Education: Recommendations for Fit Statistics

Latent transition analysis is an informative statistical tool for depicting heterogeneity in learning as latent profiles. We present a Monte Carlo simulation study to guide researchers in selecting fit indices for identifying the correct number of profiles. We simulated data representing profiles of learners within a typical pre- post- follow up-design with continuous indicators, varying sample size (N from 50 to 1,000), attrition rate (none/10% per wave), and profile separation (entropy; from .73 to .87). Results indicate that the most commonly used fit index, the Bayesian information criterion (BIC), and the consistent Akaike information criterion (CAIC) consistently underestimate the real number of profiles. A combination of the AIC or the AIC3 with the adjusted Bayesian Information Criterion (aBIC) provides the most precise choice for selecting the number of profiles and is accurate with sample sizes of at least N = 200. The AIC3 excels starting from N = 500. Results were mostly robust toward differing numbers of time points, profiles, indicator variables, and alternative profiles. We provide an online tool for computing these fit indices and discuss implications for research.

Is the Area Under Curve Appropriate for Evaluating the Fit of Psychometric Models?

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as χ2, M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian information criterion (BIC) for relative comparisons. Recent developments show a merging trend of psychometric and machine learnings, yet there remains a gap in the model fit evaluation, specifically the use of the area under curve (AUC). This study focuses on the behaviors of AUC in fitting IRT models. Rounds of simulations were conducted to investigate AUC's appropriateness (e.g., power and Type I error rate) under various conditions. The results show that AUC possessed certain advantages under certain conditions such as high-dimensional structure with two-parameter logistic (2PL) and some three-parameter logistic (3PL) models, while disadvantages were also obvious when the true model is unidimensional. It cautions researchers about the dangers of using AUC solely in evaluating psychometric models.

Fitted Copula Statistical Models for Four African and Four Major Stock Markets

The application of copula has become popular in recent years. The use of correlation as a dependence measure has several pitfalls and hence the application of regression prediction model using this correlation may not be an appropriate method. In financial markets, there is often a non-linear dependence between returns. Thus, alternative methods for capturing co-dependency should be considered, such as copula based ones. This paper studies the dependence structure between the four largest African stock markets in terms of market capitalization and other developed stock markets over the period 2003 to 2018 using copula models. The value at risk was used to determine the risk associated with the stock. The ten copula models were fitted to the log returns calculated from the data, two countries at a time of the twenty-eight pairs and examined. The Gumbel copula gives the best fit in terms of log-likelihood values, value of the Akaike information criterion, value of the Bayesian information criterion, value of the consistent Akaike information criterion, value of the corrected Akaike information criterion, value of the Hannan Quinn criterion and p-value of the information matrix equality of White. Estimates of value at risk with probability p for daily returns were computed using the best fitted copula model, from these value at risk, it is seen that SA/FTSE100 have the least risk while EGY/KEN has the highest risk. Prediction is given in terms of correlation and value at risk.

New compound probability distribution using biweight kernel function and exponential distribution

In this paper, a new continuous probability distribution is proposed for fitting real data using Biweight kernel function and the exponential distribution. The suggested distribution is named the Biweight-exponential distribution (BiEd). Some statistical properties of this distribution are derived and illustrated mathematically. The probability density function and the cumulative distribution function are derived. Some reliability analysis functions are defined. The moments and moment generating function are derived. Re’nyi entropy is derived. The maximum likelihood method of estimation is used to derive the parameter estimates. The Bonferroni and Lorenz curves and Gini index equations are derived. The distribution of the order statistic and the quantile function are derived as well. The mean and median absolute deviations of the new distribution are derived. A numerical study was conducted to the quantile equation. An application to real data set is conducted to investigate the usefulness of the suggested distribution. In the real data application, the values of Cramer-von misses (W), Anderson Darling statistic (A), Kolmogorov-Smirnov (D) statistic, the p-value, the maximum likelihood estimates (MLE), Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan Quinn information criterion (HQIC) and minimum value of the log-likelihood function are obtained. The distribution is compared with the exponential (base) distribution based on these criteria. The results showed that the BiED fits better than the exponential distribution. This means that the suggested distribution can replace the exponential distribution for analysis of some real data sets.

Novel model selection criteria for LMARS: MARS designed for biological networks

ABSTRACT In higher dimensions, the loop-based multivariate adaptive regression splines (LMARS) model is used to build sparse and complex gene structure nonparametrically by correctly defining its interactions in the network. Also, it prefers to apply the generalized cross-validation (GCV) value as its original model selection criterion in order to select the best model, in turn, represent the true network structure. In this study, we suggest to modify the model selection procedure of LMARS by changing GCV with our Kullback–Leibler information-based criteria, namely, consistent Akaike information criterion (CAIC), CAIC with Fisher information matrix and information complexity. Thereby, we aim to compare the performance of our proposal model selection criteria together with the state-of-art model selection criteria, namely, AIC and Bayesian information criterion by comparing their accuracy with GCV while modelling different dimensional and topological biological networks under both simulated and real datasets.

Model specification and data interpretation of climate in Pakistan

The issue of climate change has occurred very strongly during the last 2 decades on global scale in analysis of estimated inferences on the environment of vulnerable states. Pakistan is one of the states that has high vulnerability index to natural disaster. Currently, climate of Pakistan is growing warmer; and we are moving around different signals of change. Meanwhile, it is important to ascertain climate trend of temperature, rain, wind speed and humidity in Pakistan on sequential basis. Therefore, this study aims to ascertain the climate trend through model specification of Stretched distributions comprising Lindley Stretched Exponential distribution, Exponentiated Stretched Exponential distribution, Kumaraswamy Stretched Exponential distribution and Transmuted Stretched Exponential distribution. A sort of comparison among new proposed, classical and modern models is also put up to evaluate the relative quality of statistical models for Climate data through Maximized Log Likelihood, Akaike Information Criterion, Bayesian Information Criterion, Consistent Akaike Information Criterion, Hannan Quinn Information Criteria and Kolmogorov Smirnov test. Findings specify that Kumaraswamy Stretched Exponential distribution is the best fit for modeling mean minimum temperature (oC) data, Lindley Stretched Exponential distribution is the best fit for modeling total July’s rain (mm) data, Transmuted Stretched Exponential distribution is the best fit for modeling wind speed (knots) data, Exponentiated Stretched Exponential distribution is the best fit for modeling humidity (%) data according to model specification. Generally, the results demonstrate that and new proposed models are ascertained best models for specification of climate data in Pakistan. It is also observed that these models proved stretchy and flexible for modeling climate data in the state of Pakistan.

New compound probability distribution using biweight kernel function and exponential distribution

In this paper, a new continuous probability distribution is proposed for fitting real data using Biweight kernel function and the exponential distribution. The suggested distribution is named the Biweight-exponential distribution (BiEd). Some statistical properties of this distribution are derived and illustrated mathematically. The probability density function and the cumulative distribution function are derived. Some reliability analysis functions are defined. The moments and moment generating function are derived. Re’nyi entropy is derived. The maximum likelihood method of estimation is used to derive the parameter estimates. The Bonferroni and Lorenz curves and Gini index equations are derived. The distribution of the order statistic and the quantile function are derived as well. The mean and median absolute deviations of the new distribution are derived. A numerical study was conducted to the quantile equation. An application to real data set is conducted to investigate the usefulness of the suggested distribution. In the real data application, the values of Cramer-von misses (W), Anderson Darling statistic (A), Kolmogorov-Smirnov (D) statistic, the p-value, the maximum likelihood estimates (MLE), Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan Quinn information criterion (HQIC) and minimum value of the log-likelihood function are obtained. The distribution is compared with the exponential (base) distribution based on these criteria. The results showed that the BiED fits better than the exponential distribution. This means that the suggested distribution can replace the exponential distribution for analysis of some real data sets.

A Log-Dagum Weibull Distribution: Properties and Characterization

This article proposes a new family of continuous distributions generated from a log dagum random variable (named Log-Dagum Weibull Distribution) on the basis of T-X family technique. mathematical and statistical properties including survival function, hazard and reverse hazard function, Rth moments, L-moments, incomplete rth moments, quantile points, Order Statistics, Bonferroni and Lorenz curves as well as entropy measures for this class of distributions are presented also LDW distribution characterized by truncated moments order statistics and upper record values. Simulation study of the proposed family of distribution has been derived. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of four real data sets and the data sets show the new family of distributions is more appropriate as compared to Exponentiated exponential distribution (EED), Weibull distribution (WD), Gamma distribution (GD), NEED Nadarajah Exponentiated exponential distribution and Lomax distribution (LD). Moreover, perfection of competing models is also tested via the Kolmogrov-Simnorov (K S), the Anderson Darling (A*) and the Cramer-von Misses (W*). The measures of goodness of fit including the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan-Quinn information criterion (HQIC) are computed to compare the fitted models.

Population preferences for breast cancer screening policies: Discrete choice experiment in Belarus.

BackgroundReaching an acceptable participation rate in screening programs is challenging. With the objective of supporting the Belarus government to implement mammography screening as a single intervention, we analyse the main determinants of breast cancer screening participation.MethodsWe developed a discrete choice experiment using a mixed research approach, comprising a literature review, in-depth interviews with key informants (n = 23), “think aloud” pilots (n = 10) and quantitative measurement of stated preferences for a representative sample of Belarus women (n = 428, 89% response rate). The choice data were analysed using a latent class logit model with four classes selected based on statistical (consistent Akaike information criterion) and interpretational considerations.ResultsWomen in the sample were representative of all six geographic regions, mainly urban (81%), and high-education (31%) characteristics. Preferences of women in all four classes were primarily influenced by the perceived reliability of the test (sensitivity and screening method) and costs. Travel and waiting time were important components in the decision for 34% of women. Most women in Belarus preferred mammography screening to the existing clinical breast examination (90%). However, if the national screening program is restricted in capacity, this proportion of women will drop to 55%. Women in all four classes preferred combined screening (mammography with clinical breast examination) to single mammography. While this preference was stronger if lower test sensitivity was assumed, 28% of women consistently gave more importance to combined screening than to test sensitivity.ConclusionWomen in Belarus were favourable to mammography screening. Population should be informed that there are no benefits of combined screening compared to single mammography. The results of this study are directly relevant to policy makers and help them targeting the screening population.

Urinal Sperm Motility and Parasite Load in Anuran Amphibians (Anura)

Parasite load effect on the spermatozoa motility of the moor frog ( Rana arvalis Nilsson, 1842) native urinal sperm has been evaluated for the first time. Seven species of parasites were identified: Nematoda — Oswaldocruzia filiformis (Goeze, 1782), Neoraillietnema praeputiale (Skrjabin, 1916), Cosmocerca ornata (Dujardin, 1845), Rhabdias bufonis (Schrank, 1788); Trematoda — Dolichosaccus rastellus (Olsson, 1876), Haplometra cylindracea (Zeder, 1800); Opalinatea — Opalina ranarum (Dujardin, 1841). We found no impact of population specificity on sperm motility. The strong negative correlation between motile spermatozoa proportion and O. ranarum abundance was observed. For the purpose of selecting the optimal model of dependence pattern (linear-, logarithmic-, sigmoid- or threshold function), the Consistent Akaike Information Criterion (CAIC) was used. When the O. ranarum abundance was above the estimated threshold — 7.3 (95% CI 0.9 – 13.6) trophonts per probe, the expected probability to observe motile spermatozoa in the urinal sperm of moor frog decreased by 3.6 (95% CI for Risk Ratio: 1.9 – 6.8) times.

A new data adaptive elastic net predictive model using hybridized smoothed covariance estimators with information complexity

ABSTRACTWe develop a novel Adaptive Elastic Net (AEN) modelling using a new covariance-regularization approach via the Hybridized Smoothed Covariance Estimators (HSCEs) to identify and select the best subset of predictors in undersized high-dimensional data sets. We introduce and score the Consistent and Misspecification Resistant Information Measure of Complexity criterion, and the Extended Consistent Akaike's Information Criterion with Fisher Information in AEN models for the first time. We carry out a large Monte Carlo simulation study using the medianmean-squared-error (MMSE) to demonstrate and compare the performance of the MMSE prediction. This is done using Cross-validated Fit Adaptive Elastic Net (CV-AEN) to avoid double shrinkage by varying both the error variance and the correlation structure of the model. Later, the new proposed AEN model is applied to a real undersized benchmark data set to predict the Riboflavin (Vitamin B2) production to select the best subset of predictors to predict the production rate of vitamin B2 and provide the best predictive model. The proposed new approach enables a simple and reliable identification of the best subset of predictive genes of the production rate of Riboflavin (Vitamin B2) without an exhaustive search of all possible subset selection in undersized high-dimensional data. It is a new and novel approach that has generalizability to other regularized General Linear Regression (GLM) models to determine the best predictor space for undersized data.

Soil moisture from remote sensing to forecast desert locust presence

Abstract Preventive control of desert locusts is based on monitoring recession areas to detect outbreaks. Remote sensing has been increasingly used in the preventive control strategy. Soil moisture is a major ecological driver of desert locust populations but is still missing in the current imagery toolkit for preventive management. By means of statistical analyses, combining field observations of locust presence/absence and soil moisture estimates at 1 km resolution from a disaggregation algorithm, we assess the potential of soil moisture to help preventive management of desert locust. We observe that a soil moisture dynamics increase of above 0.09 cm3/cm3 for 20 days followed by a decrease of soil moisture may increase the chance to observe locusts 70 days later. We estimate the gains in early warning timing compared to using imagery from vegetation to be 3 weeks. We demonstrate that forecasting errors may be reduced by the combination of several types of indicators such as soil moisture and vegetation index in a common statistical model forecasting locust presence. Policy implications. Soil moisture estimates at 1 km resolution should be used to plan desert locust surveys in preventive management. When soil moisture increases in a dry area of potential habitat for the desert locust, field surveys should be conducted two months later to evaluate the need of further preventive actions. Remote sensing estimates of soil moisture could also be used for other applications of integrated pest management.

Random regression models with B-splines to estimate genetic parameters for body weight of young bulls in performance tests

ABSTRACT The objective of this study was to estimate genetic parameters for body weight of beef cattle in performance tests. Different random regression models with quadratic B-splines and heterogeneous residual variance were fitted to estimate covariance functions for body weights of Nellore and crossbred Charolais × Nellore bulls. The criteria −2 residual log-likelihood (−2RLL), Akaike Information Criterion (AIC), and consistent AIC (CAIC) were used to choose the most appropriate model. For Nellore bulls, residual variance was modeled with six classes [...]

Model Selection for Multilevel Mixture Rasch Models

Mixture item response theory (MixIRT) models can sometimes be used to model the heterogeneity among the individuals from different subpopulations, but these models do not account for the multilevel structure that is common in educational and psychological data. Multilevel extensions of the MixIRT models have been proposed to address this shortcoming. Successful applications of multilevel MixIRT models depend in part on detection of the best fitting model. In this study, performance of information indices, Akaike information criterion (AIC), Bayesian information criterion (BIC), consistent Akaike information criterion (CAIC), and sample-size adjusted Bayesian information criterion (SABIC), were compared for use in model selection with a two-level mixture Rasch model in the context of a real data example and a simulation study. Level 1 consisted of students and Level 2 consisted of schools. The performances of the model selection criteria under different sample sizes were investigated in a simulation study. Total sample size (number of students) and Level 2 sample size (number of schools) were studied for calculation of information criterion indices to examine the performance of these fit indices. Simulation study results indicated that CAIC and BIC performed better than the other indices at detection of the true (i.e., generating) model. Furthermore, information indices based on total sample size yielded more accurate detections than indices at Level 2.

Investigation of the Rosenbaum Concussion Knowledge and Attitudes Survey in Collegiate Athletes.

The purpose of this study is to determine whether the Rosenbaum Concussion Knowledge and Attitudes Survey (RoCKAS) is an appropriate outcome measure to assess knowledge and attitudes toward concussion in collegiate student-athletes as determined through validity and reliability testing. Convenience study. The researcher recruited all athletic teams at a Division III National Collegiate Athletic Association institution. Four hundred thirty-three collegiate student-athletes, 18 years of age or older, from a variety of sports took part in this study. As the validity of RoCKAS has never been established for the target population, this study randomly split respondents into 2 studies. Participants in this study completed the RoCKAS during preseason meetings before concussion education. The primary researcher was not present during the completion of the survey to allow participants to answer honestly without concern of coercion. A paper-based Rosenbaum Concussion Knowledge and Attitudes Survey. The Concussion Knowledge Index (CKI) was distributed in 2 cluster constructs and identified variables of low and high difficulty. Multivariate statistical analysis of the Concussion Attitude Index (CAI) explains 68.79% of the total variance. The Confirmatory Factor Analysis did not confirm the hypothesis that similar constructs can be found between data sets ((Equation is included in full-text article.)= 207.902; consistent akaike information criterion = 391.550; root mean square error of approximation = 0.125, and goodness of fit index = 0.868). The CKI is a valid and reliable measure in collegiate student-athletes. However, the results of the Confirmatory Factor Analysis indicated a poor model fit and improper correlations between attitude items. Therefore, the CAI may not be a sound outcome measure of collegiate student-athlete's attitudes toward concussions.