Penalized Joint Maximum Likelihood Estimation Applied to Two Parameter Logistic Item Response Models

Item response theory (IRT) models are a conventional tool for analyzing both small scale and large scale educational data sets, and they are also used for the development of high-stakes tests such as the Scholastic Aptitude Test (SAT) and the Graduate Record Exam (GRE). When estimating these models it is imperative that the data set includes many more examinees than items, which is a similar requirement in regression modeling where many more observations than variables are needed. If this requirement has not been met the analysis will yield meaningless results. Recently, penalized estimation methods have been developed to analyze data sets that may include more variables than observations. The main focus of this study was to apply LASSO and ridge regression penalization techniques to IRT models in order to better estimate model parameters. The results of our simulations showed that this new estimation procedure called penalized joint maximum likelihood estimation provided meaningful estimates when IRT data sets included more items than examinees when traditional Bayesian estimation and marginal maximum likelihood methods were not appropriate. However, when the IRT datasets contained more examinees than items Bayesian estimation clearly outperformed both penalized joint maximum likelihood estimation and marginal maximum likelihood

A HYPERBOLIC TANGENT YIELD FUNCTION OF FLORIDA CITRUS

This study models Florida citrus production as a function of the age profile of a given tree stock. The age relationship is estimated using a modified hyperbolic tangent function and the parameters is solved by Spatial Process Models and Maximum Likelihood approach. The estimation is based on the production data of four citrus varieties in 25 regions of Florida from 1992 to 2005. The results show smooth S-shaped yield curves of Florida citrus. This analysis offers yield function of citrus as the first step for statistical modeling of the risks associated with citrus cancers aimed at pricing insurance rates.yield function, citrus, hyperbolic tangent, insurance, spatial autoregressive, Demand and Price Analysis,

Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified case

In parametric estimation of covariance function of Gaussian processes, it is often the case that the true covariance function does not belong to the parametric set used for estimation. This situation is called the misspecified case. In this case, it has been shown that, for irregular spatial sampling of observation points, Cross Validation can yield smaller prediction errors than Maximum Likelihood. Motivated by this observation, we provide a general asymptotic analysis of the misspecified case, for independent and uniformly distributed observation points. We prove that the Maximum Likelihood estimator asymptotically minimizes a Kullback-Leibler divergence, within the misspecified parametric set, while Cross Validation asymptotically minimizes the integrated square prediction error. In a Monte Carlo simulation, we show that the covariance parameters estimated by Maximum Likelihood and Cross Validation, and the corresponding Kullback-Leibler divergences and integrated square prediction errors, can be strongly contrasting. On a more technical level, we provide new increasing-domain asymptotic results for independent and uniformly distributed observation points.Comment: A supplementary material (pdf) is available in the arXiv source

Lateral stability and control derivatives of a jet fighter airplane extracted from flight test data by utilizing maximum likelihood estimation

A method of parameter extraction for stability and control derivatives of aircraft from flight test data, implementing maximum likelihood estimation, has been developed and successfully applied to actual lateral flight test data from a modern sophisticated jet fighter. This application demonstrates the important role played by the analyst in combining engineering judgment and estimator statistics to yield meaningful results. During the analysis, the problems of uniqueness of the extracted set of parameters and of longitudinal coupling effects were encountered and resolved. The results for all flight runs are presented in tabular form and as time history comparisons between the estimated states and the actual flight test data

Estimation of Heterogeneous Treatment Effects on Hazard Rates

Consider a setting where a treatment that starts at some point during a spell (e.g. in unemployment) may impact on the hazard rate of the spell duration, and where the impact may be heterogeneous across subjects. We provide Monte Carlo evidence on the feasibility of estimating the distribution of treatment effects from duration data with selectivity, by means of a nonparametric maximum likelihood estimator with unrestricted numbers of mass points for the heterogeneity distribution. We find that specifying the treatment effect as homogenous may yield misleading average results if the true effects are heterogeneous, even when the sorting into treatment is appropriately accounted for. Specifying the treatment effect as a random coefficient allows for precise estimation of informative average treatment effects including the program’s overall impact on the mean duration.duration analysis, unobserved heterogeneity, program evaluation, nonparametric estimation, Monte Carlo simulation, timing of events, random effects

A general statistical framework for dissecting parent-of-origin effects underlying endosperm traits in flowering plants

Genomic imprinting has been thought to play an important role in seed development in flowering plants. Seed in a flowering plant normally contains diploid embryo and triploid endosperm. Empirical studies have shown that some economically important endosperm traits are genetically controlled by imprinted genes. However, the exact number and location of the imprinted genes are largely unknown due to the lack of efficient statistical mapping methods. Here we propose a general statistical variance components framework by utilizing the natural information of sex-specific allelic sharing among sibpairs in line crosses, to map imprinted quantitative trait loci (iQTL) underlying endosperm traits. We propose a new variance components partition method considering the unique characteristic of the triploid endosperm genome, and develop a restricted maximum likelihood estimation method in an interval scan for estimating and testing genome-wide iQTL effects. Cytoplasmic maternal effect which is thought to have primary influences on yield and grain quality is also considered when testing for genomic imprinting. Extension to multiple iQTL analysis is proposed. Asymptotic distribution of the likelihood ratio test for testing the variance components under irregular conditions are studied. Both simulation study and real data analysis indicate good performance and powerfulness of the developed approach.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS323 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org