25 Estimating the parameters of a random effects logistic model with the Nonparametric Maximum Likelihood Method (NPML)

1997 ◽  
Vol 18 (3) ◽  
pp. S56
Author(s):  
Florence Mesnil ◽  
France Mentré ◽  
Alain Mallet
2022 ◽  
Vol 12 (1) ◽  
pp. 168
Author(s):  
Eisa Abdul-Wahhab Al-Tarawnah ◽  
Mariam Al-Qahtani

This study aims to compare the effect of test length on the degree of ability parameter estimation in the two-parameter and three-parameter logistic models, using the Bayesian method of expected prior mode and maximum likelihood. The experimental approach is followed, using the Monte Carlo method of simulation. The study population consists of all subjects with the specified ability level. The study includes random samples of subjects and of items. Results reveal that estimation accuracy of the ability parameter in the two-parameter logistic model according to the maximum likelihood method and the Bayesian method increases with the increase in the number of test items. Results also show that with long and average length tests, the effectiveness is related to the maximum likelihood method and to all conditions of the sample size, whereas in short tests, the Bayesian method of prior mode outperformed in all conditions. Results indicate that the increase of the ability parameter in the three-parameter logistic model increases with the increase of test items number. The Bayesian method outperforms with respect to the accuracy of estimation at all conditions of the sample size, whereas in long tests the maximum likelihood method outperforms at all different conditions.   Received: 17 September 2021 / Accepted: 24 November 2021 / Published: 3 January 2022


2012 ◽  
Vol 33 (3-4) ◽  
pp. 393-400 ◽  
Author(s):  
Bálint Üveges ◽  
Bálint Halpern ◽  
Tamás Péchy ◽  
János Posta ◽  
István Komlósi

The objective of our research was to determine the heritability of head scale numbers of Vipera ursinii rakosiensis. 430 specimens (177 males and 253 females) were included in the analysis, most of which were born and raised in the Hungarian Meadow Viper Conservation Centre between 2004 and 2008. Due to the controlled breeding conditions, the dams of the offspring were known, and the sires were known in 51% of the cases. Only the ancestors of the wild caught specimens were unknown, but these animals were included as parents in the analysis. Photographic identification was used to identify and characterise the specimens, the majority over consecutive years. We counted the following scales: loreal-, circumocular-, apical-, and crown (intercanthal- and intersupraocular-) shields, as well as presence-absence data of other characteristics which are detailed further in the article. The variance and covariance components were determined via the restricted maximum likelihood method. The repeatability animal model consisted of the year of birth and the sex of the snakes as fixed effects, the dam as permanent environmental, and the animal as random effects. Heritability values varied between 0.32 and 0.70. We also report scale numbers and statistics of differences between scale numbers of sexes.


Author(s):  
Muhammad Ammar Malik ◽  
Tom Michoel

Abstract Random effects models are popular statistical models for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known, estimating simultaneously the contribution of known and latent variance components in random effects models is a challenge that has so far relied on numerical gradient-based optimizers to maximize the likelihood function. This is unsatisfactory because the resulting solution is poorly characterized and the efficiency of the method may be suboptimal. Here we prove analytically that maximum-likelihood latent variables can always be chosen orthogonal to the known confounding factors, in other words, that maximum-likelihood latent variables explain sample covariances not already explained by known factors. Based on this result we propose a restricted maximum-likelihood method which estimates the latent variables by maximizing the likelihood on the restricted subspace orthogonal to the known confounding factors, and show that this reduces to probabilistic PCA on that subspace. The method then estimates the variance-covariance parameters by maximizing the remaining terms in the likelihood function given the latent variables, using a newly derived analytic solution for this problem. Compared to gradient-based optimizers, our method attains greater or equal likelihood values, can be computed using standard matrix operations, results in latent factors that don’t overlap with any known factors, and has a runtime reduced by several orders of magnitude. Hence the restricted maximum-likelihood method facilitates the application of random effects modelling strategies for learning latent variance components to much larger gene expression datasets than possible with current methods.


Sign in / Sign up

Export Citation Format

Share Document