Conditional Maximum Likelihood Estimator Research Articles

Conditional Maximum Likelihood Estimation in Polytomous Rasch Models Using SAS

IRT models are widely used but often rely on distributional assumptions about the latent variable. For a simple class of IRT models, the Rasch models, conditional inference is feasible. This enables consistent estimation of item parameters without reference to the distribution of the latent variable in the population. Traditionally, specialized software has been needed for this, but conditional maximum likelihood estimation can be done using standard software for fitting generalized linear models. This paper describes an SAS macro %rasch_cml that fits polytomous Rasch models. The macro estimates item parameters using conditional maximum likelihood (CML) estimation and person locations using maximum likelihood estimator (MLE) and Warm's weighted likelihood estimation (WLE). Graphical presentations are included: plots of item characteristic curves (ICCs), and a graphical goodness-of-fit-test is also produced.

Content Sharing in a Social Broadcasting Environment: Evidence from Twitter

The rise of social broadcasting technologies has greatly facilitated open access to information worldwide, not only by powering decentralized information production and consumption, but also by expediting information diffusion through social interactions like content sharing. We study users’ voluntary information sharing in the context of Twitter, the predominant social broadcasting site, by modeling both the technology and user behavior. We collect a detailed dataset about the official content-sharing function on Twitter, called retweet, and document the statistical relationships between the users’ social network characteristics and their retweeting acts. We then estimate a more structural model using conditional Maximum Likelihood Estimation (MLE) method. The empirical results convincingly support our hypothesis that weak ties are more likely to engage in the social exchange process of content sharing. Specifically, we find that after an author posts a median quality tweet (as defined in the sample), the likelihood that a unidirectional follower will retweet is 3.1% higher than the likelihood that a bidirectional follower will.

HLA-B*44 Is Associated with Dengue Severity Caused by DENV-3 in a Brazilian Population

Human leukocyte antigen (HLA) alleles have been correlated with susceptibility or resistance to severe dengue; however, few immunogenetic studies have been performed in Latin American (LA) populations. We have conducted immunogenetic studies of HLA class I and II alleles in a cohort of 187 patients with DENV-3 infection and confirmed clinical diagnosis of either severe dengue, known as dengue hemorrhagic fever (DHF), or the less severe form, dengue fever (DF), in Recife, Pernambuco, Brazil. An association analysis was performed using Fisher's association test, with odds ratios (ORs) calculated using conditional maximum likelihood estimates. HLA-B∗44 (P = 0.047, OR = 2.025, 95% CI = 0.97–4.24) was found to be associated with increased susceptibility to DHF in response to DENV-3 infection. In addition, HLA-B∗07 (P = 0.048, OR = 0.501, one-sided 95% CI = 0–0.99) and HLA-DR∗13 (P = 0.028, OR = 0.511, one-sided 95% CI = 0–0.91) were found to be associated with resistance to secondary dengue infection by DENV-3. These results suggest that HLA-B∗44 supertype alleles and their respective T-cell responses might be involved in susceptibility to severe dengue infections, whereas the HLA-B∗07 supertype alleles and DR∗13 might be involved in cross-dengue serotype immunity.

Determinants of farmers’ participation in oyster mushroom production in Swaziland: Implications for promoting a non-conventional agricultural enterprise

ABSTRACT Despite receiving substantial support from the public and private sectors, the mushroom industry in Swaziland is still characterised by extremely low production volumes largely because few farmers have opted to include the mushroom enterprise in their farming systems. Considering the prevailing conditions that favour oyster mushroom production, there is a need to understand why many farmers are not engaged in this enterprise. This study uses cross-section data to identify factors that influence farmers’ decisions of whether or not to participate in oyster mushroom production. Using two-stage probit least squares and two-stage conditional maximum likelihood estimation procedures, the results indicate that apart from the level of farm diversification and farmers’ perceptions towards mushrooms, decisions of whether or not to produce are influenced mainly by institutional factors. Bearing in mind that mushrooms are not plants but fungi, farmers are bound to have mixed perceptions towards the enterprise and these perceptions are likely to have an influence on its acceptability. However, as established from the results, with improved awareness, training and mentoring, farmers are likely to develop positive attitudes as they would understand the circumstances associated with the production of edible mushrooms. Evidence drawn from this study suggests that policy interventions aimed at creating an enabling environment for the enterprise may remain ineffective unless they are paralleled by improvements in rural infrastructure and access to markets.

The covariance structure of cml-estimates in the Rasch model

Abstract In this paper we consider conditional maximum likelihood (cml) estimates for item parameters in the Rasch model under random subject parameters. We give a simple approximation for the asymptotic covariance matrix of the cml-estimates. The approximation is stated as a limit theorem when the number of item parameters goes to infinity. The results contain precise mathematical information on the order of approximation. The results enable the analysis of the covariance structure of cml-estimates when the number of items is large. Let us give a rough picture. The covariance matrix has a dominating main diagonal containing the asymptotic variances of the estimators. These variances are almost equal to the efficient variances under ml-estimation when the distribution of the subject parameter is known. Apart from very small numbers n of item parameters the variances are almost not affected by the number n. The covariances are more or less negligible when the number of item parameters is large. Although this picture intuitively is not surprising it has to be established in precise mathematical terms. This has been done in the present paper. The paper is based on previous results [6] of the author concerning conditional distributions of non-identical replications of Bernoulli trials. The mathematical background are Edgeworth expansions for the central limit theorem. These previous results are the basis of approximations for the Fisher information matrices of cml-estimates. The main results of the present paper are concerned with the approximation of the covariance matrices. Numerical illustrations of the results and numerical experiments based on the results are presented in Strasser [5].

Asymptotic expansions for conditional moments of Bernoulli trials

Abstract In this paper we study conditional distributions of independent, but not identically distributed Bernoulli random variables. The conditioning variable is the sum of the Bernoulli variables. We obtain Edgeworth expansions for the conditional expectations and the conditional variances and covariances. The results are of basic interest for several applications, e.g. for the study of conditional maximum likelihood estimation in Rasch models with many item parameters.

A comparison of least squares and conditional maximum likelihood estimators under volume endpoint censoring in tumor growth experiments

Measurements in tumor growth experiments are stopped once the tumor volume exceeds a preset threshold: a mechanism we term volume endpoint censoring. We argue that this type of censoring is informative. Further, least squares (LS) parameter estimates are shown to suffer a bias in a general parametric model for tumor growth with an independent and identically distributed measurement error, both theoretically and in simulation experiments. In a linear growth model, the magnitude of bias in the LS growth rate estimate increases with the growth rate and the standard deviation of measurement error. We propose a conditional maximum likelihood estimation procedure, which is shown both theoretically and in simulation experiments to yield approximately unbiased parameter estimates in linear and quadratic growth models. Both LS and maximum likelihood estimators have similar variance characteristics. In simulation studies, these properties appear to extend to the case of moderately dependent measurement error. The methodology is illustrated by application to a tumor growth study for an ovarian cancer cell line.

Likelihood-Based Inference for Weak Exogeneity in I(2) Cointegrated VAR Models

This article develops limit theory for likelihood analysis of weak exogeneity in I(2) cointegrated vector autoregressive (VAR) models incorporating deterministic terms. Conditions for weak exogeneity in I(2) VAR models are reviewed, and the asymptotic properties of conditional maximum likelihood estimators and a likelihood-based weak exogeneity test are then investigated. It is demonstrated that weak exogeneity in I(2) VAR models allows us to conduct asymptotic conditional inference based on mixed Gaussian distributions. It is then proved that a log-likelihood ratio test statistic for weak exogeneity in I(2) VAR models is asymptotically χ2 distributed. The article also presents an empirical illustration of the proposed test for weak exogeneity using Japan's macroeconomic data.

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.

Predicting the evolution of inflammatory arthritis in ACPA-positive individuals: can T cell subset help?

Backgroundand objectivesAnticitrullinated protein antibodies (ACPA)+ individuals with musculoskeletal pain are at high risk of developing rheumatoid arthritis (RA). The authors previously demonstrated dys-regulation of T cell subsets in early disease...

Flexible Rasch Mixture Models with Packagepsychomix

Measurement invariance is an important assumption in the Rasch model and mixture models constitute a flexible way of checking for a violation of this assumption by detecting unobserved heterogeneity in item response data. Here, a general class of Rasch mixture models is established and implemented in R, using conditional maximum likelihood estimation of the item parameters (given the raw scores) along with flexible specification of two model building blocks: (1) Mixture weights for the unobserved classes can be treated as model parameters or based on covariates in a concomitant variable model. (2) The distribution of raw score probabilities can be parametrized in two possible ways, either using a saturated model or a specification through mean and variance. The function raschmix() in the R package psychomix provides these models, leveraging the general infrastructure for fitting mixture models in the flexmix package. Usage of the function and its associated methods is illustrated on artificial data as well as empirical data from a study of verbally aggressive behavior.

Analysis of crash severities using nested logit model—Accounting for the underreporting of crashes

Recent studies in the area of highway safety have demonstrated the usefulness of logit models for modeling crash injury severities. Use of these models enables one to identify and quantify the effects of factors that contribute to certain levels of severity. Most often, these models are estimated assuming equal probability of the occurrence for each injury severity level in the data. However, traffic crash data are generally characterized by underreporting, especially when crashes result in lower injury severity. Thus, the sample used for an analysis is often outcome-based, which can result in a biased estimation of model parameters. This is more of a problem when a nested logit model specification is used instead of a multinomial logit model and when true shares of the outcomes-injury severity levels in the population are not known (which is almost always the case). This study demonstrates an application of a recently proposed weighted conditional maximum likelihood estimator in tackling the problem of underreporting of crashes when using a nested logit model for crash severity analyses.

EFFICIENT ESTIMATION OF FACTOR MODELS

This paper considers the factor model Xt = ΛFt + et. Assuming a normal distribution for the idiosyncratic error et conditional on the factors {Ft}, conditional maximum likelihood estimators of the factor and factor-loading spaces are derived. These estimators are called generalized principal component estimators (GPCEs) without the normality assumption. This paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces. It is shown that variance of the GPCE of the common component is smaller than that of the principal component estimator studied in Bai (2003, Econometrica 71, 135–172). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component estimator. The feasible GPCE (FGPCE) of the factor space is shown to be asymptotically equivalent to the GPCE. The GPCE and FGPCE are shown to be more efficient than the principal component estimator in finite samples.

Parameter recovery and model selection in mixed Rasch models

This study examines the precision of conditional maximum likelihood estimates and the quality of model selection methods based on information criteria (AIC and BIC) in mixed Rasch models. The design of the Monte Carlo simulation study included four test lengths (10, 15, 25, 40), three sample sizes (500, 1000, 2500), two simulated mixture conditions (one and two groups), and population homogeneity (equally sized subgroups) or heterogeneity (one subgroup three times larger than the other). The results show that both increasing sample size and increasing number of items lead to higher accuracy; medium-range parameters were estimated more precisely than extreme ones; and the accuracy was higher in homogeneous populations. The minimum-BIC method leads to almost perfect results and is more reliable than AIC-based model selection. The results are compared to findings by Li, Cohen, Kim, and Cho (2009) and practical guidelines are provided.

On uniqueness of the conditional maximum likelihood estimation for a binary panel model

This paper considers an estimation method for a binary panel model with incidental parameters as individual effects. The necessary condition for the conditional maximum likelihood approach proposed by Andersen (1970) is investigated and we show that unique sufficient statistics exist only for logit models in a two-wave panel.

Estimating financial distress with a dynamic model: Evidence from family owned enterprises in a small open economy

Employing earnings shortfall as a financial distress indicator, we formulate a dynamic nonlinear model, implementing Wooldridge's conditional maximum likelihood estimator and accounting for potentially endogenous covariates. Likewise, we not only achieve a significant improvement in consistency and classification accuracy over static approaches, but we also manage to understand better the evolution of the financial distress process. In our sample of Greek listed firms the higher the positive performance and the lower the leverage at the initial period the greater the chance that a company enters financial distress further down the road, possibly due to manager–owner overconfidence and debt-imposed discipline by company's creditors.

Conditional Maximum Likelihood and Interval Estimation for Two Weibull Populations under Joint Type-II Progressive Censoring

Comparative lifetime experiments are important when the object of a study is to determine the relative merits of two competing duration of life products. This study considers the interval estimation for two Weibull populations when joint Type-II progressive censoring is implemented. We obtain the conditional maximum likelihood estimators of the two Weibull parameters under this scheme. Moreover, simultaneous approximate confidence region based on the asymptotic normality of the maximum likelihood estimators are also discussed and compared with two Bootstrap confidence regions. We consider the behavior of probability of failure structure with different schemes. A simulation study is performed and an illustrative example is also given.

Dynamic Censored Regression and the Open Market Desk Reaction Function

The censored regression model and the Tobit model are standard tools in econometrics. This paper provides a formal asymptotic theory for dynamic time series censored regression when lags of the dependent variable have been included among the regressors. The central analytical challenge is to prove that the dynamic censored regression model satisfies stationarity and weak dependence properties if a condition on the lag polynomial holds. We show the formal asymptotic correctness of conditional maximum likelihood estimation of the dynamic Tobit model, and the correctness of Powell’s least absolute deviations procedure for the estimation of the dynamic censored regression model. The paper is concluded with an application of the dynamic censored regression methodology to temporary purchases of the Open Market Desk. This article has supplementary material online.

Eliciting Benefit–Risk Preferences and Probability-Weighted Utility Using Choice-Format Conjoint Analysis

This study applies conjoint analysis to estimate health-related benefit-risk tradeoffs in a non-expected-utility framework. We demonstrate how this method can be used to test for and estimate nonlinear weighting of adverse-event probabilities and we explore the implications of nonlinear weighting on maximum acceptable risk (MAR) measures of risk tolerance. We obtained preference data from 570 Crohn's disease patients using a web-enabled conjoint survey. Respondents were presented with choice tasks involving treatment options that involve different efficacy benefits and different mortality risks for 3 possible side effects. Using conditional logit maximum likelihood estimation, we estimate preference parameters using 3 models that allow for nonlinear preference weighting of risks--a categorical model, a simple-weighting model, and a rank dependent utility (RDU) model. For the second 2 models we specify and jointly estimate 1- and 2-parameter probability weighting functions. Although the 2-parameter functions are more flexible, estimation of the 1-parameter functions generally performed better. Despite well-known conceptual limitations, the simple-weighting model allows us to estimate weighting function parameters that vary across 3 risk types, and we find some evidence of statistically significant differences across risks. The parameter estimates from RDU model with the single-parameter weighting function provide the most robust estimates of MAR. For an improvement in Crohn's symptom severity from moderate and mild, we estimate maximum 10-year mortality risk tolerances ranging from 2.6% to 7.1%. Our results provide further the evidence that quantitative benefit-risk analysis used to evaluate medical interventions should account explicitly for the nonlinear probability weighting of preferences.

Analysis of accumulated rounding errors in autoregressive processes

In considering the rounding impact of an autoregressive (AR) process, there are two different models available to be considered. The first assumes that the dynamic system follows an underlying AR model and only the observations are rounded up to a certain precision. The second assumes that the updated observation is a rounded version of an autoregression on previous rounded observations. This article considers the second model and examines behaviour of rounding impacts to the statistical inferences. The conditional maximum-likelihood estimates for the model are proposed and their asymptotic properties are established, including strong consistency and asymptotic normality. Furthermore, both the classical AR model and the ordinary rounded AR model are no longer reliable when dealing with accumulated rounding errors. The three models are also applied to fit the Ocean Wave data. It turns out that the estimates under distinct models are significantly different. Based on our findings, we strongly recommend that models for dealing with rounded data should be in accordance with the actions of rounding errors.