Likelihood-based approaches to modeling demand for medical care

We review recent likelihood-based approaches to modeling demand for medical care. A semi-nonparametric model along the lines of Cameron and Johansson's Poisson polynomial model, but using a negative binomial baseline model, is introduced. We apply these models, as well a semiparametric Poisson, hurdle semiparametric Poisson, and finite mixtures of negative binomial models to six measures of health care usage taken from the Medical Expenditure Panel survey. We conclude that most of the models lead to statistically similar results, both in terms of information criteria and conditional and unconditional prediction. This suggests that applied researchers may not need to be overly concerned with the choice of which of these models they use to analyze data on health care demand.

BadiRate: Estimating Family Turnover Rates by Likelihood-Based Methods

Motivation: The comparative analysis of gene gain and loss rates is critical for understanding the role of natural selection and adaptation in shaping gene family sizes. Studying complete genome data from closely related species allows accurate estimation of gene family turnover rates. Current methods and software tools, however, are not well designed for dealing with certain kinds of functional elements, such as microRNAs or transcription factor binding sites. Results: Here, we describe BadiRate, a new software tool to estimate family turnover rates, as well as the number of elements in internal phylogenetic nodes, by likelihood-based methods and parsimony. It implements two stochastic population models, which provide the appropriate statistical framework for testing hypothesis, such as lineage-specific gene family expansions or contractions. We have assessed the accuracy of BadiRate by computer simulations, and have also illustrated its functionality by analyzing a representative empirical dataset.

BadiRate: estimating family turnover rates by likelihood-based methods

Motivation: The comparative analysis of gene gain and loss rates is critical for understanding the role of natural selection and adaptation in shaping gene family sizes. Studying complete genome data from closely related species allows accurate estimation of gene family turnover rates. Current methods and software tools, however, are not well designed for dealing with certain kinds of functional elements, such as microRNAs or transcription factor binding sites. Results: Here, we describe BadiRate, a new software tool to estimate family turnover rates, as well as the number of elements in internal phylogenetic nodes, by likelihood-based methods and parsimony. It implements two stochastic population models, which provide the appropriate statistical framework for testing hypothesis, such as lineage-specific gene family expansions or contractions. We have assessed the accuracy of BadiRate by computer simulations, and have also illustrated its functionality by analyzing a representative empirical dataset.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Indirect likelihood inference

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two-step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Business Cycle Regimes in CEECs Production: A Threshold SURE Approach

We use a threshold seemingly unrelated regressions specification to assess whether the Central and East European countries (CEECs) are synchronized in their business cycles to the Euro-area. This specification is useful in two ways: First, it takes into account the common institutional factors and the similarities across CEECs in their process of economic transition. Second, it captures business cycle asymmetries by allowing for the presence of two distinct regimes for the CEECs. As the CEECs are strongly affected by the Euro-area these regimes may be associated with Euro-area expansions and contractions. We discuss representation, estimation by maximum likelihood and inference. The methodology is illustrated by using monthly industrial production in 8 CEECs. The results show that apart from Lithuania the rest of the CEECs experience “normal” growth when the Euro-area contracts and “high” growth when the Euro-area expands. Given that the CEECs are “catching up” with the Euro-area this result shows that most CEECs seem synchronized to the Euro-area cycle. Keywords: Threshold SURE; asymmetry; business cycles; CEECs. JEL classification: C33; C50; E32.

Does money matter in shaping domestic business cycles? An international investigation (with appendices)

We study the contribution of money to business cycle fluctuations in the US,the UK, Japan, and the Euro area using a small scale structural monetary business cycle model. Constrained likelihood-based estimates of the parameters areprovided and time instabilities analyzed. Real balances are statistically importantfor output and inflation fluctuations. Their contribution changes over time. Models giving money no role provide a distorted representation of the sources of cyclicalfluctuations, of the transmission of shocks and of the events of the last 40 years.

Man-bites-dog business cycles

The newsworthiness of an event is partly determined by how unusual it isand this paper investigates the business cycle implications of this fact. In particular, weanalyze the consequences of information structures in which some types of signals are morelikely to be observed after unusual events. Such signals may increase both uncertainty anddisagreement among agents and when embedded in a simple business cycle model, can helpus understand why we observe (i) occasional large changes in macro economic aggregatevariables without a correspondingly large change in underlying fundamentals (ii) persistentperiods of high macroeconomic volatility and (iii) a positive correlation between absolutechanges in macro variables and the cross-sectional dispersion of expectations as measuredby survey data. These results are consequences of optimal updating by agents when theavailability of some signals is positively correlated with tail-events. The model is estimatedby likelihood based methods using individual survey responses and a quarterly time seriesof total factor productivity along with standard aggregate time series. The estimated modelsuggests that there have been episodes in recent US history when the impact on outputof innovations to productivity of a given magnitude was more than eight times as largecompared to other times.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

Student modeling based on fuzzy inference mechanisms

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for each student, suggesting the competences the student is more prepared to study. We use fuzzy set theory for dealing with uncertainty. The marks of the assessment tests are transformed into linguistic terms and used for assigning values to linguistic variables. For each competence, the level of difficulty and the level of knowing its prerequisites are calculated based on the assessment marks. Using these linguistic variables and approximate reasoning (fuzzy IF-THEN rules), a crisp category is assigned to each competence regarding its level of recommendation.

eggNOG v4.0: nested orthology inference across 3686 organisms

With the increasing availability of various 'omics data, high-quality orthology assignment is crucial for evolutionary and functional genomics studies. We here present the fourth version of the eggNOG database (available at http://eggnog.embl.de) that derives nonsupervised orthologous groups (NOGs) from complete genomes, and then applies a comprehensive characterization and analysis pipeline to the resulting gene families. Compared with the previous version, we have more than tripled the underlying species set to cover 3686 organisms, keeping track with genome project completions while prioritizing the inclusion of high-quality genomes to minimize error propagation from incomplete proteome sets. Major technological advances include (i) a robust and scalable procedure for the identification and inclusion of high-quality genomes, (ii) provision of orthologous groups for 107 different taxonomic levels compared with 41 in eggNOGv3, (iii) identification and annotation of particularly closely related orthologous groups, facilitating analysis of related gene families, (iv) improvements of the clustering and functional annotation approach, (v) adoption of a revised tree building procedure based on the multiple alignments generated during the process and (vi) implementation of quality control procedures throughout the entire pipeline. As in previous versions, eggNOGv4 provides multiple sequence alignments and maximum-likelihood trees, as well as broad functional annotation. Users can access the complete database of orthologous groups via a web interface, as well as through bulk download.

Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.

Protocol of the COSMIN study: consensus-based standards for the selection of health measurement instruments

Background: Choosing an adequate measurement instrument depends on the proposed use of the instrument, the concept to be measured, the measurement properties (e.g. internal consistency, reproducibility, content and construct validity, responsiveness, and interpretability), the requirements, the burden for subjects, and costs of the available instruments. As far as measurement properties are concerned, there are no sufficiently specific standards for the evaluation of measurement properties of instruments to measure health status, and also no explicit criteria for what constitutes good measurement properties. In this paper we describe the protocol for the COSMIN study, the objective of which is to develop a checklist that contains COnsensus-based Standards for the selection of health Measurement INstruments, including explicit criteria for satisfying these standards. We will focus on evaluative health related patient-reported outcomes (HR-PROs), i.e. patient-reported health measurement instruments used in a longitudinal design as an outcome measure, excluding health care related PROs, such as satisfaction with care or adherence. The COSMIN standards will be made available in the form of an easily applicable checklist.Method: An international Delphi study will be performed to reach consensus on which and how measurement properties should be assessed, and on criteria for good measurement properties. Two sources of input will be used for the Delphi study: (1) a systematic review of properties, standards and criteria of measurement properties found in systematic reviews of measurement instruments, and (2) an additional literature search of methodological articles presenting a comprehensive checklist of standards and criteria. The Delphi study will consist of four (written) Delphi rounds, with approximately 30 expert panel members with different backgrounds in clinical medicine, biostatistics, psychology, and epidemiology. The final checklist will subsequently be field-tested by assessing the inter-rater reproducibility of the checklist.Discussion: Since the study will mainly be anonymous, problems that are commonly encountered in face-to-face group meetings, such as the dominance of certain persons in the communication process, will be avoided. By performing a Delphi study and involving many experts, the likelihood that the checklist will have sufficient credibility to be accepted and implemented will increase.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.