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Threshold Models (threshold + models)
Selected AbstractsSample Splitting and Threshold EstimationECONOMETRICA, Issue 3 2000Bruce E. Hansen Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously-distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super-consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross-section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson (1995). [source] QUANTITATIVE GENETICS OF SEXUAL PLASTICITY: THE ENVIRONMENTAL THRESHOLD MODEL AND GENOTYPE-BY-ENVIRONMENT INTERACTION FOR PHALLUS DEVELOPMENT IN THE SNAIL BULINUS TRUNCATUSEVOLUTION, Issue 5 2000Marie-France Ostrowski Abstract Sexual polymorphisms are model systems for analyzing the evolution of reproductive strategies. However, their plasticity and other binary traits have rarely been studied, with respect to environmental variables. A possible reason is that, although threshold models offer an adequate quantitative genetics framework for binary traits in a single environment, analyzing their plasticity requires more refined empirical and theoretical approaches. The statistical framework proposed here, based on the environmental threshold model (ETM), should partially fill this gap. This methodology is applied to an empirical dataset on a plastic sexual polymorphism, aphally, in the snail Bulinus truncatus. Aphally is characterized by the co-occurrence of regular hermaphrodites (euphallics) together with hermaphrodites deprived of the male copulatory organ (aphallics). Reaction norms were determined for 40 inbred lines, distributed at three temperatures, in a first experiment. A second experiment allowed us to rule out maternal effects. We confirmed the existence of high broad-sense heritabilities as well as a positive effect of high temperatures on aphally. However a significant genotype-by-environment interaction was detected for the first time, suggesting that sexual plasticity itself can respond to selection. A nested series of four ETM-like models was developed for estimating genetical effects on both mean aphally rate and plasticity. These models were tested using a maximum-likelihood procedure and fitted to aphally data. Although no perfect fit of models to data was observed, the refined versions of ETM models conveniently reduce the analysis of complex reaction norms of binary traits into standard quantitative genetics parameters, such as genetic values and environmental variances. [source] Multiple stressors and regime shifts in shallow aquatic ecosystems in antipodean landscapesFRESHWATER BIOLOGY, Issue 2010JENNY DAVIS Summary 1. Changes in land management (land use and land cover) and water management (including extraction of ground water and diversion of surface waters for irrigation) driven by increases in agricultural production and urban expansion (and fundamentally by population growth) have created multiple stressors on global freshwater ecosystems that we can no longer ignore. 2. The development and testing of conceptual ecological models that examine the impact of stressors on aquatic ecosystems, and recognise that responses may be nonlinear, is now essential for identifying critical processes and predicting changes, particularly the possibility of catastrophic regime shifts or ,ecological surprises'. 3. Models depicting gradual ecological change and three types of regime shift (simple thresholds, hysteresis and irreversible changes) were examined in the context of shallow inland aquatic ecosystems (wetlands, shallow lakes and temporary river pools) in southwestern Australia subject to multiple anthropogenic impacts (hydrological change, eutrophication, salinisation and acidification). 4. Changes in hydrological processes, particularly the balance between groundwater-dominated versus surface water-dominated inputs and a change from seasonal to permanent water regimes appeared to be the major drivers influencing ecological regime change and the impacts of eutrophication and acidification (in urban systems) and salinisation and acidification (in agricultural systems). 5. In the absence of hydrological change, urban wetlands undergoing eutrophication and agricultural wetlands experiencing salinisation appeared to fit threshold models. Models encompassing alternative regimes and hysteresis appeared to be applicable where a change from a seasonal to permanent hydrological regime had occurred. 6. Irreversible ecological change has potentially occurred in agricultural landscapes because the external economic driver, agricultural productivity, persists independently of the impact on aquatic ecosystems. 7. Thematic implications: multiple stressors can create multiple thresholds that may act in a hierarchical fashion in shallow, lentic systems. The resulting regime shifts may follow different models and trajectories of recovery. Challenges for ecosystem managers and researchers include determining how close a system may be to critical thresholds and which processes are essential to maintaining or restoring the system. This requires an understanding of both external drivers and internal ecosystem dynamics, and the interactions between them, at appropriate spatial and temporal scales. [source] Comparison of repeatability and multiple trait threshold models for litter size in sheep using observed and simulated data in Bayesian analysesJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 4 2010W. Mekkawy Summary Bayesian analyses were used to estimate genetic parameters on 5580 records of litter size in the first four parities from 1758 Mule ewes. To examine the appropriateness of fitting repeatability (RM) or multiple trait threshold models (MTM) to litter size of different parities, both models were used to estimate genetic parameters on the observed data and were thereafter compared in a simulation study. Posterior means of the heritabilities of litter size in different parities using a MTM ranged from 0.12 to 0.18 and were higher than the heritability based on the RM (0.08). Posterior means of the genetic correlations between litter sizes of different parities were positive and ranged from 0.24 to 0.71. Data sets were simulated based on the same pedigree structure and genetic parameters of the Mule ewe population obtained from both models. The simulation showed that the relative loss in accuracy and increase in mean squared error (MSE) was substantially higher when using the RM, given that the parameters estimated from the observed data using the opposite model are the true parameters. In contrast, Bayesian information criterion (BIC) selected the RM as most appropriate model given the data because of substantial penalty for the higher number of parameters to be estimated in the MTM model. In conclusion, when the relative change in accuracy and MSE is of main interest for estimation of breeding values of litter size of different parities, the MTM is recommended for the given population. When reduction in risk of using the wrong model is the main aim, the BIC suggest that the RM is the most appropriate model. [source] Predictive ability of models for calving difficulty in US HolsteinsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 3 2009E.L. De Maturana Summary The performance of alternative threshold models for analyzing calving difficulty (CD) in Holstein cows was evaluated in terms of predictive ability. Four models were considered, with CD classified into either three or four categories and analysed either as a single trait or jointly with gestation length (GL). The data contained GL and CD records from 90 393 primiparous cows, sired by 1122 bulls and distributed over 935 herd-calving year classes. Predictive ability of each model was evaluated using four criteria: mean squared error of the difference between observed and predicted CD scores; a Kullback-Leibler divergence measure between the observed and predicted distributions of CD scores; Pearson's correlation between observed and predicted CD scores and ability to correctly classify bulls as above or below average for incidence of CD. In general, the four models had similar predictive abilities. The joint analysis of CD with GL produced little, if any, improvement in predictive ability over univariate models. In light of the small difference in predictive ability between models treating CD with three or four categories and considering that a greater number of categories can provide more information, analysis of CD classified into four categories seems warranted. [source] A comparison between multivariate Slash, Student's t and probit threshold models for analysis of clinical mastitis in first lactation cowsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 5 2006Y-M. Chang Summary Robust threshold models with multivariate Student's t or multivariate Slash link functions were employed to infer genetic parameters of clinical mastitis at different stages of lactation, with each cow defining a cluster of records. The robust fits were compared with that from a multivariate probit model via a pseudo-Bayes factor and an analysis of residuals. Clinical mastitis records on 36 178 first-lactation Norwegian Red cows from 5286 herds, daughters of 245 sires, were analysed. The opportunity for infection interval, going from 30 days pre-calving to 300 days postpartum, was divided into four periods: (i) ,30 to 0 days pre-calving; (ii) 1,30 days; (iii) 31,120 days; and (iv) 121,300 days of lactation. Within each period, absence or presence of clinical mastitis was scored as 0 or 1 respectively. Markov chain Monte Carlo methods were used to draw samples from posterior distributions of interest. Pseudo-Bayes factors strongly favoured the multivariate Slash and Student's t models over the probit model. The posterior mean of the degrees of freedom parameter for the Slash model was 2.2, indicating heavy tails of the liability distribution. The posterior mean of the degrees of freedom for the Student's t model was 8.5, also pointing away from a normal liability for clinical mastitis. A residual was the observed phenotype (0 or 1) minus the posterior mean of the probability of mastitis. The Slash and Student's t models tended to have smaller residuals than the probit model in cows that contracted mastitis. Heritability of liability to clinical mastitis was 0.13,0.14 before calving, and ranged from 0.05 to 0.08 after calving in the robust models. Genetic correlations were between 0.50 and 0.73, suggesting that clinical mastitis resistance is not the same trait across periods, corroborating earlier findings with probit models. [source] Bayesian inference strategies for the prediction of genetic merit using threshold models with an application to calving ease scores in Italian Piemontese cattleJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 4 2002K. Kizilkaya Summary First parity calving difficulty scores from Italian Piemontese cattle were analysed using a threshold mixed effects model. The model included the fixed effects of age of dam and sex of calf and their interaction and the random effects of sire, maternal grandsire, and herd-year-season. Covariances between sire and maternal grandsire effects were modelled using a numerator relationship matrix based on male ancestors. Field data consisted of 23 953 records collected between 1989 and 1998 from 4741 herd-year-seasons. Variance and covariance components were estimated using two alternative approximate marginal maximum likelihood (MML) methods, one based on expectation-maximization (EM) and the other based on Laplacian integration. Inferences were compared to those based on three separate runs or sequences of Markov Chain Monte Carlo (MCMC) sampling in order to assess the validity of approximate MML estimates derived from data with similar size and design structure. Point estimates of direct heritability were 0.24, 0.25 and 0.26 for EM, Laplacian and MCMC (posterior mean), respectively, whereas corresponding maternal heritability estimates were 0.10, 0.11 and 0.12, respectively. The covariance between additive direct and maternal effects was found to be not different from zero based on MCMC-derived confidence sets. The conventional joint modal estimates of sire effects and associated standard errors based on MML estimates of variance and covariance components differed little from the respective posterior means and standard deviations derived from MCMC. Therefore, there may be little need to pursue computation-intensive MCMC methods for inference on genetic parameters and genetic merits using conventional threshold sire and maternal grandsire models for large datasets on calving ease. Zusammenfassung Die Kalbeschwierigkeiten bei italienischen Piemonteser Erstkalbskühen wurden mittels eines gemischten Threshold Modells untersucht. Im Modell wurden die fixen Einflüsse vom Alter der Kuh und dem Geschlecht des Kalbes, der Interaktion zwischen beiden und die zufälligen Effekte des Großvaters der Mutter und der Herden-Jahr-Saisonklasse berücksichtigt. Die Kovarianz zwischen dem Vater der Kuh und dem Großvater der Mutter wurde über die nur auf väterlicher Verwandtschaft basierenden Verwandtschaftsmatrix berücksichtigt. Es wurden insgesamt 23953 Datensätze aus den Jahren 1989 bis 1998 von 4741 Herden-Jahr-Saisonklassen ausgewertet. Die Varianz- und Kovarianzkomponenten wurden mittels zweier verschiedener approximativer marginal Maximum Likelihood (MML) Methoden geschätzt, die erste basierend auf Expectation-Maximierung (EM) und die zweite auf Laplacian Integration. Rückschlüsse wurden verglichen mit solchen, basierend auf drei einzelne Läufe oder Sequenzen von Markov Chain Monte Carlo (MCMC) Stichproben, um die Gültigkeit der approximativen MML Schätzer aus Daten mit ähnlicher Größe und Struktur zu prüfen. Die Punktschätzer der direkten Heritabilität lagen bei 0,24; 0,25 und 0,26 für EM, Laplacian und MCMC (Posterior Mean), während die entsprechenden maternalen Heritabilitäten bei 0,10, 0,11 und 0,12 lagen. Die Kovarianz zwischen dem direkten additiven und dem maternalen Effekt wurden als nicht von Null verschieden geschätzt, basierend auf MCMC abgeleiteten Konfidenzintervallen. Die konventionellen Schätzer der Vatereffekte und deren Standardfehler aus den MML-Schätzungen der Varianz- und Kovarianzkomponenten differieren leicht von denen aus der MCMC Analyse. Daraus folgend besteht wenig Bedarf die rechenintensiven MCMC-Methoden anzuwenden, um genetische Parameter und den genetischen Erfolg zu schätzen, wenn konventionelle Threshold Modelle für große Datensätze mit Vätern und mütterlichen Großvätern mit Kalbeschwierigkeiten genutzt werden. [source] Generalized marker regression and interval QTL mapping methods for binary traits in half-sib family designsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 5 2001H. N. Kadarmideen A Generalized Marker Regression Mapping (GMR) approach was developed for mapping Quantitative Trait Loci (QTL) affecting binary polygenic traits in a single-family half-sib design. The GMR is based on threshold-liability model theory and regression of offspring phenotype on expected marker genotypes at flanking marker loci. Using simulation, statistical power and bias of QTL mapping for binary traits by GMR was compared with full QTL interval mapping based on a threshold model (GIM) and with a linear marker regression mapping method (LMR). Empirical significance threshold values, power and estimates of QTL location and effect were identical for GIM and GMR when QTL mapping was restricted to within the marker interval. These results show that the theory of the marker regression method for QTL mapping is also applicable to binary traits and possibly for traits with other non-normal distributions. The linear and threshold models based on marker regression (LMR and GMR) also resulted in similar estimates and power for large progeny group sizes, indicating that LMR can be used for binary data for balanced designs with large families, as this method is computationally simpler than GMR. GMR may have a greater potential than LMR for QTL mapping for binary traits in complex situations such as QTL mapping with complex pedigrees, random models and models with interactions. Generalisierte Marker Regression und Intervall QTL Kartierungsmethoden für binäre Merkmale in einem Halbgeschwisterdesign Es wurde ein Ansatz zur generalisierten Marker Regressions Kartierung (GMR) entwickelt, um quantitative Merkmalsloci (QTL) zu kartieren, die binäre polygenetische Merkmale in einem Einfamilien-Halbgeschwisterdesign beeinflussen. Das GMR basiert auf der Theorie eines Schwellenwertmodells und auf der Regression des Nachkommenphänotyps auf den erwarteten Markergenotyp der flankierenden Markerloci. Mittels Simulation wurde die statistische Power und Schiefe der QTL Kartierung für binäre Merkmale nach GMR verglichen mit vollständiger QTL Intervallkartierung, die auf einem Schwellenmodell (GIM) basiert, und mit einer Methode zur linearen Marker Regressions Kartierung (LMR). Empirische Signifikanzschwellenwerte, Power und Schätzer für die QTL Lokation und der Effekt waren für GIM und GMR identisch, so lange die QTL Kartierung innerhalb des Markerintervalls definiert war. Diese Ergebnisse zeigen, dass die Theorie der Marker Regressions-Methode zur QTL Kartierung auch für binäre Merkmale und möglicherweise auch für Merkmale, die keiner Normalverteilung folgen, geeignet ist. Die linearen und Schwellenmodelle, die auf Marker Regression (LMR und GMR) basieren, ergaben ebenfalls ähnliche Schätzer und Power bei großen Nachkommengruppen, was schlussfolgern lässt, dass LMR für binäre Daten in einem balancierten Design mit großen Familien genutzt werden kann. Schließlich ist diese Methode computertechnisch einfacher als GMR. GMR mag für die QTL Kartierung bei binären Merkmalen in komplexen Situationen ein größeres Potential haben als LMR. Ein Beispiel dafür ist die QTL Kartierung mit komplexen Pedigrees, zufälligen Modellen und Interaktionsmodellen. [source] The non-linear dynamics of output and unemployment in the U.S.JOURNAL OF APPLIED ECONOMETRICS, Issue 4 2001Filippo Altissimo This paper studies the joint dynamics of U.S. output and unemployment rate in a non-linear VAR model. The non-linearity is introduced through a feedback variable that endogenously augments the output lags of the VAR in recessionary phases. Sufficient conditions for the ergodicity of the model, potentially applying to a larger class of threshold models, are provided. The linear specification is rejected in favour of our threshold VAR. However, in the estimation the feedback is found to be statistically significant only on unemployment, while it transmits to output through its cross-correlation. This feedback effect from recessions generates important asymmetries in the propagation of shocks, a possible key to interpret the divergence in the measures of persistence in the literature. The regime-dependent persistence also explains the finding that the feedback from recession exerts a positive effect on the long-run growth rate of the economy, an empirical validation of the Schumpeterian macroeconomic theories. Copyright © 2001 John Wiley & Sons, Ltd. [source] Forecasting volatility by means of threshold modelsJOURNAL OF FORECASTING, Issue 5 2007M. Pilar Muñoz Abstract The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out-of-sample forecasting ability of the SETAR-Threshold GARCH (SETAR-TGARCH) and the SETAR-Threshold Stochastic Volatility (SETAR-THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ,true' underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR-THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd. [source] A cautionary note on outlier robust estimation of threshold modelsJOURNAL OF FORECASTING, Issue 1 2006Paolo GiordaniArticle first published online: 28 DEC 200 Abstract Chan and Cheung (1994) propose a GM approach to outlier robust estimation of threshold models. We show that their estimator can be inconsistent and extremely inefficient even when the model is correctly specified and the disturbances are normally distributed, and outline situations in which the problem is likely to be more severe. Copyright © 2006 John Wiley & Sons, Ltd. [source] Testing for Temporal Asymmetry in the Price-Volume RelationshipBULLETIN OF ECONOMIC RESEARCH, Issue 4 2003Imad A. Moosa G14; C22 Abstract This paper presents some evidence for the presence of temporal asymmetry in the price-volume relationship in the crude oil futures market. By using threshold models we show that there is bidirectional causality between volume and prices, whereas the conventional model that assumes symmetry can only detect unidirectional causality. The results also show that the price-volume relationship is asymmetric, in the sense that negative price and volume changes have stronger effects (on each other) than positive changes. Some explanations for asymmetry in the price-volume relationship are suggested. [source] | |||||||||||||||||||||||||