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Journal articles on the topic 'Binary model estimation'

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Author: Grafiati

Published: 10 March 2023

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1

Nishizawa, Kazutomo, and Iwaro Takahashi. "ESTIMATION METHODS BY STOCHASTIC MODEL IN BINARY AND TERNARY AHP." Journal of the Operations Research Society of Japan 50, no. 2 (2007): 101–22. http://dx.doi.org/10.15807/jorsj.50.101.

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2

Allman, Elizabeth, Hector Banos Cervantes, Serkan Hosten, Kaie Kubjas, Daniel Lemke, John Rhodes, and Piotr Zwiernik. "Maximum likelihood estimation of the Latent Class Model through model boundary decomposition." Journal of Algebraic Statistics 10, no. 1 (April 10, 2019): 51–84. http://dx.doi.org/10.18409/jas.v10i1.75.

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The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.

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3

Amin, Muhammad, Muhammad Nauman Akram, B. M. Golam Kibria, Huda M. Alshanbari, Nahid Fatima, and Ahmed Elhassanein. "On the Estimation of the Binary Response Model." Axioms 12, no. 2 (February 8, 2023): 175. http://dx.doi.org/10.3390/axioms12020175.

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The binary logistic regression model (LRM) is practical in situations when the response variable (RV) is dichotomous. The maximum likelihood estimator (MLE) is generally considered to estimate the LRM parameters. However, in the presence of multicollinearity (MC), the MLE is not the correct choice due to its inflated standard deviation (SD) and standard errors (SE) of the estimates. To combat MC, commonly used biased estimators, i.e., the Ridge estimators (RE) and Liu estimators (LEs), are preferred. However, most of the time, the traditional LE attains a negative value for its Liu parameter (LP), which is considered to be a major drawback. Therefore, to overcome this issue, we proposed a new adjusted LE for the binary LRM. Owing to numerical evaluation purposes, Monte Carlo simulation (MCS) study is performed under different conditions where bias and mean squared error are the performance criteria. Findings showed the superiority of our proposed estimator in comparison with the other estimation methods due to the existence of high but imperfect multicollinearity, which clearly means that it is consistent when the regressors are multicollinear. Furthermore, the findings demonstrated that whenever there is MC, the MLE is not the best choice. Finally, a real application is being considered to be evidence for the advantage of the intended estimator. The MCS and the application findings pointed out that the considered adjusted LE for the binary logistic regression model is a more efficient estimation method whenever the regressors are highly multicollinear.

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Assoudou, Souad, and Belkheir Essebbar. "A Bayesian model for binary Markov chains." International Journal of Mathematics and Mathematical Sciences 2004, no. 8 (2004): 421–29. http://dx.doi.org/10.1155/s0161171204202319.

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This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

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Yildiz, Neşe. "ESTIMATION OF BINARY CHOICE MODELS WITH LINEAR INDEX AND DUMMY ENDOGENOUS VARIABLES." Econometric Theory 29, no. 2 (March 28, 2013): 354–92. http://dx.doi.org/10.1017/s0266466612000436.

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This paper presents computationally simple estimators for the index coefficients in a binary choice model with a binary endogenous regressor without relying on distributional assumptions or on large support conditions and yields root-n consistent and asymptotically normal estimators. We develop a multistep method for estimating the parameters in a triangular, linear index, threshold-crossing model with two equations. Such an econometric model might be used in testing for moral hazard while allowing for asymmetric information in insurance markets. In outlining this new estimation method two contributions are made. The first one is proposing a novel “matching” estimator for the coefficient on the binary endogenous variable in the outcome equation. Second, in order to establish the asymptotic properties of the proposed estimators for the coefficients of the exogenous regressors in the outcome equation, the results of Powell, Stock, and Stoker (1989, Econometrica 75, 1403–1430) are extended to cover the case where the average derivative estimation requires a first-step semiparametric procedure.

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6

de Jong, Robert M., and Tiemen Woutersen. "DYNAMIC TIME SERIES BINARY CHOICE." Econometric Theory 27, no. 4 (March 3, 2011): 673–702. http://dx.doi.org/10.1017/s0266466610000472.

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This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

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Yanuar, Ferra, Rahmatika Fajriyah, and Dodi Devianto. "SMALL AREA ESTIMATION METHOD WITH EMPIRICAL BAYES BASED ON BETA BINOMIAL MODEL IN GENERATED DATA." MEDIA STATISTIKA 14, no. 1 (October 21, 2020): 1–9. http://dx.doi.org/10.14710/medstat.14.1.1-9.

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Small Area Estimation is one of the methods that can be used to estimate parameters in an area that has a small population. This study aims to estimate the value of the binary data parameter using the direct estimation method and an indirect estimation method by using the Empirical Bayes approach. To illustrate the method, we consider three conditions: direct estimator, empirical Bayes (EB) with auxiliary variables, and empirical Bayes without auxiliary variables. The smaller value of Mean Square Error is used to determine the better method. The results showed that the indirect estimation methods (EB method) gave the parameter value that was not much different from the direct estimation value. Then, the MSE values of indirect estimation with an auxiliary variable are smaller than the direct estimation method.

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8

Chen, Songnian, and Lung-Fei Lee. "EFFICIENT SEMIPARAMETRIC SCORING ESTIMATION OF SAMPLE SELECTION MODELS." Econometric Theory 14, no. 4 (August 1998): 423–62. http://dx.doi.org/10.1017/s026646669814402x.

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A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n-consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index restriction. For the binary choice sample selection model, it also attains the efficiency bound under the independence assumption. This method can be applied to the estimation of general sample selection models.

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9

Joebaedi, Khafsah, Iin Irianingsih, Badrulfalah Badrulfalah, Dwi Susanti, and Kankan Parmikanti. "Parameter Estimation STAR (1;1) Model Using Binary Weight." Eksakta : Berkala Ilmiah Bidang MIPA 20, no. 2 (August 31, 2019): 33–41. http://dx.doi.org/10.24036/eksakta/vol20-iss2/199.

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Space Time Auto Regressive(1;1) Model or STAR(1;1) model is a form of model that involves location and time. The STAR(1;1) model is a stationary space time model in mean and variance. The STAR model can be used to forecast future observations at these locations by involving the effects of observations at other nearby locations in spatial lag 1 and lag time 1 [2]. The STAR model can be written as a linear model assuming that error is normally distributed with zero mean and constant variance. In this research, the parameter estimation procedure for STAR model using binary weight, MKT method and STAR model for the estimation of petroleum production in 3 wells is assumed to be in a homogeneous reservoir.

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10

Benson, David, Matthew A. Masten, and Alexander Torgovitsky. "ivcrc: An instrumental-variables estimator for the correlated random-coefficients model." Stata Journal: Promoting communications on statistics and Stata 22, no. 3 (September 2022): 469–95. http://dx.doi.org/10.1177/1536867x221124449.

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We discuss the ivcrc command, which implements an instrumental-variables (IV) estimator for the linear correlated random-coefficients model. The correlated random-coefficients model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc command also allows for the estimation of varying-coefficient regressions, which are closely related in structure to the proposed IV estimator. We illustrate the use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men.

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Benson, David, Matthew A. Masten, and Alexander Torgovitsky. "ivcrc: An Instrumental Variables Estimator for the Correlated Random Coefficients Model." Finance and Economics Discussion Series 2020, no. 046r1 (April 4, 2022): 1–29. http://dx.doi.org/10.17016/feds.2020.046r1.

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We discuss the ivcrc module, which implements an instrumental variables (IV) estimator for the linear correlated random coefficients (CRC) model. The CRC model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc module also allows for the estimation of varying coefficients regressions, which are closely related in structure to the proposed IV estimator. We illustrate use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men.

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12

LI, R., J. ZHOU, and L. WANG. "ESTIMATION OF THE BINARY LOGISTIC REGRESSION MODEL PARAMETER USING BOOTSTRAP RE-SAMPLING." Latin American Applied Research - An international journal 48, no. 3 (July 31, 2018): 199–204. http://dx.doi.org/10.52292/j.laar.2018.228.

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In this paper, the non-parametric bootstrap and non-parametric Bayesian bootstrap methods are applied for parameter estimation in the binary logistic regression model. A real data study and a simulation study are conducted to compare the Nonparametric bootstrap, Non-parametric Bayesian bootstrap and the maximum likelihood methods. Study results shows that three methods are all effective ways for parameter estimation in the binary logistic regression model. In small sample case, the non-parametric Bayesian bootstrap method performs relatively better than the non-parametric bootstrap and the maximum likelihood method for parameter estimation in the binary logistic regression model.

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13

Westgate, Philip M. "A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE–type marginal model for binary outcomes." Clinical Trials 16, no. 1 (October 8, 2018): 41–51. http://dx.doi.org/10.1177/1740774518803635.

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Background/aims Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. Methods We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Results Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation–based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Conclusion Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation–based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation–based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

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14

Mey, Alexander, and Marco Loog. "Consistency and Finite Sample Behavior of Binary Class Probability Estimation." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8967–74. http://dx.doi.org/10.1609/aaai.v35i10.17084.

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We investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. We extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Following previous literature on excess risk bounds and proper scoring rules, we derive a class probability estimator based on empirical risk minimization. We then derive conditions under which this estimator will converge with high probability to the true class probabilities with respect to the L1-norm. One of our core contributions is a novel way to derive finite sample L1-convergence rates of this estimator for different surrogate loss functions. We also study in detail which commonly used loss functions are suitable for this estimation problem and briefly address the setting of model-misspecification.

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15

Kim, Gibak. "Eigenvoice Adaptation of Classification Model for Binary Mask Estimation." Journal of Broadcast Engineering 20, no. 1 (January 30, 2015): 164–70. http://dx.doi.org/10.5909/jbe.2015.20.1.164.

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16

Zhao, Lincheng, Chaofeng Kou, and Yaohua Wu. "Maximum Score Change-Point Estimation in Binary Response Model." Journal of Systems Science and Complexity 19, no. 3 (September 2006): 386–92. http://dx.doi.org/10.1007/s11424-006-0386-8.

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17

Neuhaus, J. "Estimation efficiency in a binary mixed-effects model setting." Biometrika 83, no. 2 (June 1, 1996): 441–46. http://dx.doi.org/10.1093/biomet/83.2.441.

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18

Moon, Hyungsik Roger. "Maximum score estimation of a nonstationary binary choice model." Journal of Econometrics 122, no. 2 (October 2004): 385–403. http://dx.doi.org/10.1016/j.jeconom.2003.10.027.

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19

Fatimata, Lo, Demba Bocar Ba, and Diop Aba. "Maximum likelihood estimation in the generalized extreme value regression model for binary data." Gulf Journal of Mathematics 12, no. 2 (March 15, 2022): 49–56. http://dx.doi.org/10.56947/gjom.v12i2.733.

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Generalized extreme value regression model is widely used when the dependent variable Y represents a rare event. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome Y and a set of potential predictors X. In this article we develop a maximum likelihood estimation procedure int he generalized extreme value regression model. We establish the asymptotic properties (existence, consistency and asymptotic normality) of the proposed maximum likelihood estimator.

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20

Ai, Chunrong, Oliver Linton, Kaiji Motegi, and Zheng Zhang. "A unified framework for efficient estimation of general treatment models." Quantitative Economics 12, no. 3 (2021): 779–816. http://dx.doi.org/10.3982/qe1494.

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This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment—as well as mixture of discrete and continuous treatment—under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile, and asymmetric least squares causal effect of treatment as special cases. For this general framework, we first derive the semiparametric efficiency bound for the causal effect of treatment, extending the existing bound results to a wider class of models. We then propose a generalized optimization estimator for the causal effect with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we establish the consistency and asymptotic normality of the proposed estimator of the causal effect and show that the estimator attains the semiparametric efficiency bound, thereby extending the existing literature on efficient estimation of causal effect to a wider class of applications. Finally, we discuss estimation of some causal effect functionals such as the treatment effect curve and the average outcome. To evaluate the finite sample performance of the proposed procedure, we conduct a small‐scale simulation study and find that the proposed estimation has practical value. In an empirical application, we detect a significant causal effect of political advertisements on campaign contributions in the binary treatment model, but not in the continuous treatment model.

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Jentsch, Carsten, and Lena Reichmann. "Generalized Binary Time Series Models." Econometrics 7, no. 4 (December 14, 2019): 47. http://dx.doi.org/10.3390/econometrics7040047.

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The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes.

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22

Horowitz, Joel L., and N. E. Savin. "Binary Response Models: Logits, Probits and Semiparametrics." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 43–56. http://dx.doi.org/10.1257/jep.15.4.43.

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A binary-response model is a mean-regression model in which the dependent variable takes only the values zero and one. This paper describes and illustrates the estimation of logit and probit binary-response models. The linear probability model is also discussed. Reasons for not using this model in applied research are explained and illustrated with data. Semiparametric and nonparametric models are also described. In contrast to logit and probit models, semi- and nonparametric models avoid the restrictive and unrealistic assumption that the analyst knows the functional form of the relation between the dependent variable and the explanatory variables.

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23

Filippou, Panagiota, Giampiero Marra, and Rosalba Radice. "Penalized likelihood estimation of a trivariate additive probit model." Biostatistics 18, no. 3 (March 4, 2017): 569–85. http://dx.doi.org/10.1093/biostatistics/kxx008.

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SUMMARY This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.

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24

Kawanabe, Motoaki, and Shun-ichi Amari. "Estimation of Network Parameters in Semiparametric Stochastic Perceptron." Neural Computation 6, no. 6 (November 1994): 1244–61. http://dx.doi.org/10.1162/neco.1994.6.6.1244.

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It was reported (Kabashima and Shinomoto 1992) that estimators of a binary decision boundary show asymptotically strange behaviors when the probability model is ill-posed or semiparametric. We give a rigorous analysis of this phenomenon in a stochastic perceptron by using the estimating function method. A stochastic perceptron consists of a neuron that is excited depending on the weighted sum of inputs but its probability distribution form is unknown here. It is shown that there exists no √n-consistent estimator of the threshold value h, that is, no estimator h that converges to h in the order of 1/ √n as the number n of observations increases. Therefore, the accuracy of estimation is much worse in this semiparametric case with an unspecified probability function than in the ordinary case. On the other hand, it is shown that there is a √n-consistent estimator ŵ of the synaptic weight vector. These results elucidate strange behaviors of learning curves in a semiparametric statistical model.

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25

Li, Chuan-Zhong. "Semiparametric Estimation of the Binary Choice Model for Contingent Valuation." Land Economics 72, no. 4 (November 1996): 462. http://dx.doi.org/10.2307/3146909.

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26

Weng, Haolei, and Yang Feng. "On the estimation of correlation in a binary sequence model." Journal of Statistical Planning and Inference 207 (July 2020): 123–37. http://dx.doi.org/10.1016/j.jspi.2019.09.016.

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27

Yuan, Min, Lin-cheng Zhao, and Yao-hua Wu. "Smoothed Maximum Score Change-point Estimation in Binary Response Model." Acta Mathematicae Applicatae Sinica, English Series 22, no. 4 (October 2006): 655–62. http://dx.doi.org/10.1007/s10255-006-0339-y.

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Kurkalova, Lyubov A., and Sergey S. Rabotyagov. "Estimation of a binary choice model with grouped choice data." Economics Letters 90, no. 2 (February 2006): 170–75. http://dx.doi.org/10.1016/j.econlet.2005.07.022.

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BADER, MARKUS, and JANA HÄUSSLER. "Toward a model of grammaticality judgments." Journal of Linguistics 46, no. 2 (November 30, 2009): 273–330. http://dx.doi.org/10.1017/s0022226709990260.

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This paper presents three experiments that investigate the relationship between gradient and binary judgments of grammaticality. In the first two experiments, two different groups of participants judged sentences by the method of magnitude estimation and by the method of speeded grammaticality judgments in a single session. The two experiments involved identical sentence materials but they differed in the order in which the two procedures were applied. The results show a high correlation between the magnitude estimation data and the speeded grammaticality judgments data, both within a session and across the two sessions. The third experiment was a questionnaire study in which participants judged the same sentences as either grammatical or ungrammatical without time pressure. This experiment yielded results quite similar to those of the other two experiments. Thus gradient and binary judgments both provide valuable and reliable sources for linguistic theory when assessed in an experimentally controlled way. We present a model based on Signal Detection Theory which specifies how gradient grammaticality scores are mapped to binary grammaticality judgments. Finally, we compare our experimental results to existing corpus data in order to inquire into the relationship between grammaticality and frequency of usage.

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Tan, Lili, and Yichong Zhang. "ROOT-N CONSISTENCY OF INTERCEPT ESTIMATORS IN A BINARY RESPONSE MODEL UNDER TAIL RESTRICTIONS." Econometric Theory 34, no. 6 (November 2, 2017): 1180–206. http://dx.doi.org/10.1017/s026646661700041x.

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The intercept of the binary response model is not regularly identified (i.e., $\sqrt n$ consistently estimable) when the support of both the special regressor V and the error term ε are the whole real line. The estimator of the intercept potentially has a slower than $\sqrt n$ convergence rate, which can result in a large estimation error in practice. This paper imposes additional tail restrictions which guarantee the regular identification of the intercept and thus the $\sqrt n$-consistency of its estimator. We then propose an estimator that achieves the $\sqrt n$ rate. Last, we extend our tail restrictions to a full-blown model with endogenous regressors.

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Skotarczak, E., M. Szyd, A. Dobek, K. Moli, and T. Szwaczkowski. "The algorithm of Bayesian estimation of maternal genetic and permanent maternal environmental variances in a two-trait binary threshold model." Czech Journal of Animal Science 49, No. 2 (December 12, 2011): 58–63. http://dx.doi.org/10.17221/4280-cjas.

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The paper presents an algorithm for the estimation and prediction of parameters in a two-trait binary threshold model. The model includes fixed effects and the following random effects: genetic direct additive, genetic maternal additive and permanent maternal environmental effects. The Gibbs sampling procedure was used to estimate the parameters. The algorithm was illustrated with a numerical example showing appropriateness of the proposed method.  

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YANG, MIIN-SHEN, and HWEI-MING CHEN. "FUZZY CLASS LOGISTIC REGRESSION ANALYSIS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 06 (December 2004): 761–80. http://dx.doi.org/10.1142/s0218488504003193.

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Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

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Bruckner, T., M. Schumacher, and M. Wolkewitz. "Accurate Variance Estimation for Prevalence Ratios." Methods of Information in Medicine 46, no. 05 (2007): 567–71. http://dx.doi.org/10.1160/me0416.

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Summary Objectives: The log-binomial model is recommended for calculating the prevalence ratio in cross-sectional studies with binary outcomes. However, convergence problems may occur as this model is numerically unstable. If this happens, the Poisson model should be used, but the Poisson model variance needsto be adjusted. Here, we compare different adjustments. Methods: Using simulation we evaluated the performance of Poisson models with i) a robust variance, ii) the scale parameter adjusted by Pearson’s chi-square, and iii) the scale parameter adjusted by the deviance. These models were compared with the log-binomial model with respectto hypothesis testing. Confounding and effect modification are considered. Results: All adjustment models improved the variance estimation. The Poisson model with a robust variance performed best. When the log-binomial model is numerically stable as well as unstable, this model yields reasonable power and type I error values. But the Poisson model with the scale parameter adjusted by Pearson’s chi-square also showed good results. Conclusions: When estimating prevalence ratios, if the log-binomial fails to converge, we recommend the Poisson modelwith a robust estimate of variance.

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ZOU, JIE. "ROSE CURVE MODEL AND AN ANALYTICAL SOLUTION FOR ESTIMATING ITS PARAMETERS." International Journal of Image and Graphics 08, no. 01 (January 2008): 99–108. http://dx.doi.org/10.1142/s021946780800299x.

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In this short paper, we introduce a parameterized shape model, rose curve model. An analytical solution for estimating rose curve parameters from a binary silhouette or a probability map is derived. This analytical method finds the global optimum directly and therefore is fast and reliable. Two similarity invariant shape features, which measures the concavity and circular frequency of the shape can be derived from the six parameters of the rose curve. We apply the rose curve model to approximately segmenting flower images, primarily for testing the analytic parameter estimation method. Experiments on a database of 180 flower images from 30 species show that the rose curve is an excellent shape model for many flower species and the analytical parameter estimation method locates the flower regions well.

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Horowitz, Joel L. "Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions." Econometric Theory 9, no. 1 (January 1993): 1–18. http://dx.doi.org/10.1017/s0266466600007301.

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The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and, after centering and suitable normalization, asymptotically normally distributed under weak assumptions [5]. Its rate of convergence in probability is N−h/(2h+1), where h ≥ 2 is an integer whose value depends on the strength of certain smoothness assumptions. This rate of convergence is faster than that of the maximum score estimator of Manski [11,12], which converges at the rate N−1/3 under assumptions that are somewhat weaker than those of the smoothed estimator. In this paper I prove that under the assumptions of smoothed maximum score estimation, N−h/(2h+1) is the fastest achievable rate of convergence of an estimator of the coefficient vector of a binary response model. Thus, the smoothed maximum score estimator has the fastest possible rate of convergence. The rate of convergence is defined in a minimax sense so as to exclude superefficient estimators.

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Purhadi, Purhadi, and M. Fathurahman. "A Logit Model for Bivariate Binary Responses." Symmetry 13, no. 2 (February 16, 2021): 326. http://dx.doi.org/10.3390/sym13020326.

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This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

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Wu, Nan, Lei Chen, Yongjun Lei, and Fankun Meng. "Adaptive estimation algorithm of boost-phase trajectory using binary asynchronous observation." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 230, no. 14 (February 24, 2016): 2661–72. http://dx.doi.org/10.1177/0954410016630000.

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A kind of adaptive filter algorithm based on the estimation of the unknown input is proposed for studying the adaptive adjustment of process noise variance of boost phase trajectory. Polynomial model is used as the motion model of the boost trajectory, truncation error is regarded as an equivalent to the process noise and the unknown input and process noise variance matrix is constructed from the estimation value of unknown input according to the quantitative relationship among the unknown input, the state estimation error, and optimal process noise variance. The simulation results show that in the absence of prior information, the unknown input is estimated effectively in terms of magnitude, a positive definite matrix of process noise covariance which is close to the optimal value is constructed real-timely, and the state estimation error approximates the error lower bound of the optimal estimation. The estimation accuracy of the proposed algorithm is similar to that of the current statistical model algorithm using accurate prior information.

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38

Xie, Yi. "Constraints on the standard model extension with binary pulsars." Proceedings of the International Astronomical Union 8, S291 (August 2012): 558–60. http://dx.doi.org/10.1017/s1743921312024866.

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AbstractUnder the standard model extension (SME) framework, Lorentz invariance is tested in five binary pulsars: PSR J0737-3039, PSR B1534+12, PSR J1756-2251, PSR B1913+16 and PSR B2127+11C. By analyzing the advance of periastron, we obtain the constraints on a dimensionless combination of SME parameters that is sensitive to timing observations. The results imply no evidence for the break of Lorentz invariance at 10−10 level, one order of magnitude larger than previous estimation.

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Chauhan, Vineet, Hemant K. Suman, and Nomesh B. Bolia. "Binary Logistic Model for Estimation of Mode Shift into Delhi Metro." Open Transportation Journal 10, no. 1 (October 7, 2016): 124–36. http://dx.doi.org/10.2174/1874447801610010124.

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This paper aims to study the public transport mode choice behaviour of commuters in Delhi so that appropriate strategies to incentivize the use of public transport can be developed. We examine the efficacy of a multivariate statistical modelling approach to predict the probability of non-metro commuters to shift to the Delhi metro. We also analyse the reasons for this shift from private motor vehicles (PMVs) and buses. Data is collected through a survey of the metro commuters over various metro lines. A binomial logistic regression model is formulated to predict whether existing metro users have shifted from buses or are new additions to public transport shifting from PMVs. The model is validated well through several methods. The model analysis reveals that 57% of the metro users have shifted from buses and 28.8% from PMVs. The shift is more amongst females than males.

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Glindemann, A., R. G. Lane, and J. C. Dainty. "Estimation of binary star parameters by model fitting the bispectrum phase." Journal of the Optical Society of America A 9, no. 4 (April 1, 1992): 543. http://dx.doi.org/10.1364/josaa.9.000543.

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Feddag, M. L. "Pairwise likelihood estimation for the normal ogive model with binary data." AStA Advances in Statistical Analysis 100, no. 2 (November 18, 2015): 223–37. http://dx.doi.org/10.1007/s10182-015-0263-7.

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Chen, Songnian. "Rank estimation of a location parameter in the binary choice model." Journal of Econometrics 98, no. 2 (October 2000): 317–34. http://dx.doi.org/10.1016/s0304-4076(00)00021-x.

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Chen, Tianshi, Yanlong Zhao, and Lennart Ljung. "Impulse response estimation with binary measurements: a regularized FIR model approach." IFAC Proceedings Volumes 45, no. 16 (July 2012): 113–18. http://dx.doi.org/10.3182/20120711-3-be-2027.00219.

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Ikeda, Shiro. "Combining binary machines for multi-class: Statistical model and parameter estimation." Journal of Physics: Conference Series 233 (June 1, 2010): 012006. http://dx.doi.org/10.1088/1742-6596/233/1/012006.

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Hu, Tao, and Heng Jian Cui. "Efficient estimation of a varying-coefficient partially linear binary regression model." Acta Mathematica Sinica, English Series 26, no. 11 (October 15, 2010): 2179–90. http://dx.doi.org/10.1007/s10114-010-8043-5.

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Hoderlein, Stefan, and Robert Sherman. "Identification and estimation in a correlated random coefficients binary response model." Journal of Econometrics 188, no. 1 (September 2015): 135–49. http://dx.doi.org/10.1016/j.jeconom.2015.03.044.

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Seurat, Jérémy, Thu Thuy Nguyen, and France Mentré. "Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes." Statistical Methods in Medical Research 29, no. 3 (May 27, 2019): 934–52. http://dx.doi.org/10.1177/0962280219850588.

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To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.

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Hasebe, Takuya. "Endogenous models of binary choice outcomes: Copula-based maximum-likelihood estimation and treatment effects." Stata Journal: Promoting communications on statistics and Stata 22, no. 4 (December 2022): 734–71. http://dx.doi.org/10.1177/1536867x221140943.

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In this article, I describe the commands that implement the estimation of three endogenous models of binary choice outcome. The command esbinary fits the endogenously switching model, where a potential outcome differs across two treatment states. The command edbinary fits the endogenous dummy model, which includes a dummy variable indicating the treatment state as one of the explanatory variables. After one estimates the parameters of these models, various treatment effects can be estimated as postestimation statistics. The command ssbinary fits the sample-selection model, where an outcome is observed in only one of the states. The commands fit these models using copula-based maximumlikelihood estimation.

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Li, Lie, and Xinlei Wang. "Meta-analysis of rare binary events in treatment groups with unequal variability." Statistical Methods in Medical Research 28, no. 1 (July 31, 2017): 263–74. http://dx.doi.org/10.1177/0962280217721246.

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Meta-analysis has been widely used to synthesize information from related studies to achieve reliable findings. However, in studies of rare events, the event counts are often low or even zero, and so standard meta-analysis methods such as fixed-effect models with continuity correction may cause substantial bias in estimation. Recently, Bhaumik et al. developed a simple average estimator for the overall treatment effect based on a random effects model. They proved that the simple average method with the continuity correction factor 0.5 (SA_0.5) is the least biased for large samples and showed via simulation that it has superior performance when compared with other commonly used estimators. However, the random effects models used in previous work are restrictive because they all assume that the variability in the treatment group is equal to or always greater than that in the control group. Under a general framework that explicitly allows treatment groups with unequal variability but assumes no direction, we prove that SA_0.5 is still the least biased for large samples. Meanwhile, to account for a trade-off between the bias and variance in estimation, we consider the mean squared error to assess estimation efficiency and show that SA_0.5 fails to minimize the mean squared error. Under a new random effects model that accommodates groups with unequal variability, we thoroughly compare the performance of various methods for both large and small samples via simulation and draw conclusions about when to use which method in terms of bias, mean squared error, type I error, and confidence interval coverage. A data example of rosiglitazone meta-analysis is used to provide further comparison.

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Gallego, Ángeles M., and Amelia Simó. "RANDOM CLOSED SET MODELS: ESTIMATING AND SIMULATING BINARY IMAGES." Image Analysis & Stereology 22, no. 1 (May 3, 2011): 133. http://dx.doi.org/10.5566/ias.v22.p133-145.

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In this paper we show the use of the Boolean model and a class of RACS models that is a generalization of it to obtain simulations of random binary images able to imitate natural textures such as marble or wood. The different tasks required, parameter estimation, goodness-of-fit test and simulation, are reviewed. In addition to a brief review of the theory, simulation studies of each model are included.

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