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Growth mixture models (GMMs) are applied to intervention studies with repeated measures to explore heterogeneity in the intervention effect. However, traditional GMMs are known to be difficult to estimate, especially at sample sizes common in single-center interventions. Common strategies to coerce GMMs to converge involve post hoc adjustments to the model, particularly constraining covariance parameters to equality across classes. Methodological studies have shown that although convergence is improved with post hoc adjustments, they embed additional tenuous assumptions into the model that can adversely impact key aspects of the model such as number of classes extracted and the estimated growth trajectories in each class. To facilitate convergence without post hoc adjustments, this paper reviews the recent literature on covariance pattern mixture models, which approach GMMs from a marginal modeling tradition rather than the random effect modeling tradition used by traditional GMMs. We discuss how the marginal modeling tradition can avoid complexities in estimation encountered by GMMs that feature random effects, and we use data from a lifestyle intervention for increasing insulin sensitivity (a risk factor for type 2 diabetes) among 90 Latino adolescents with obesity to demonstrate our point. Specifically, GMMs featuring random effects—even with post hoc adjustments—fail to converge due to estimation errors, whereas covariance pattern mixture models following the marginal model tradition encounter no issues with estimation while maintaining the ability to answer all the research questions.

In a mean-variance framework with a representative agent, any linear model for the cross section of expected returns can be supported as an equilibrium as long as the market portfolio is spanned by the factor mimicking portfolios. Any set of factors is admissible as long as the spanning condition is satisfied. Factors based on size, book-to-market, momentum, investment, profitability, behavioral biases, principal components, or any combination of these can be used as equilibrium factors. An equilibrium model with M risk factors can be reduced to a collection of M models where each model has a single risk factor, which is covariance with the market portfolio.

Multi-state model (MSM) is a useful tool to analyze longitudinal data for modeling disease progression at multiple time points. While the regularization approaches to variable selection have been widely used, extending them to MSM remains largely unexplored. In this paper, we have developed the L1-regularized multi-state model (L1MSTATE) framework that enables parameter estimation and variable selection simultaneously. The regularized optimization problem was solved by deriving a one-step coordinate descent algorithm with great computational efficiency. The L1MSTATE approach was evaluated using extensive simulation studies, and it showed that L1MSTATE outperformed existing regularized multi-state models in terms of the accurate identification of risk factors. It also outperformed the un-regularized multi-state models (MSTATE) in terms of identifying the important risk factors in situations with small sample sizes. The power of L1MSTATE in predicting the transition probabilities comparing with MSTATE was demonstrated using the Europe Blood and Marrow Transplantation (EBMT) dataset. The L1MSTATE was implemented in the open-access R package ‘L1mstate’.

In insurance and finance it is often important to have a satisfactory estimate for an extreme quantile, like the one underlying capital requirements in Solvency II and Basel III. If credibility techniques on means are used for the determination of such quantiles, this can lead to quite unsatisfactory results, in particular in the presence of outliers in the data. Quantile credibility models themselves, however, cannot perform effectively when the set of data has a nested (hierarchical) structure. This paper develops multi-stage nested classification hierarchical credibility models for quantiles as an alternative to Jewell’s (G Ist Ital Attuari 38:1–16, 1975) approach, where more than one risk factor divides the portfolio into different sectors or classes. We establish hierarchical quantile credibility estimators and illustrate their performance in two numerical illustrations.

Using features extracted from StockTwits messages between July 2009 and September 2012, we show through simulations that: (1) message volume and sentiment can be used as a risk factor in an asset pricing model framework; (2) message volume and sentiment help explain the diffusion of price information over several days, and (3) message volume and sentiment can be used as features to predict asset price directional moves. Our findings suggest statistics derived from message volume and sentiment can improve asset price forecasts and leads to a profitable trading strategy.

Bitcoin is a digital currency started in early 2009 by its inventor under the pseudonym of Satoshi Nakamoto. In the last few years, Bitcoin has received much attention and has shown a surprising price increase. Bitcoin is currently traded on many web-exchanges making it a rare example of a good for which different prices are readily available; this feature implies important issues about arbitrage opportunities since prices on different exchanges are shown to be driven by the same risk factor. In this paper, we show that simple strategies of strong arbitrage arise by trading across different Bitcoin exchanges taking advantage of the common risk factor. The suggested arbitrage strategies are based on two alternative model specifications. Precisely, we consider the multivariate versions of Black and Scholes model and of an attention-based dynamics recently introduced in the literature.

It is difficult sometimes to estimate the confidence intervals for the particular statistics, because there is no so far for some of them mathematical expression for their variance. That is true for availability factor—complex characteristic of restorable items reliability. Statistical bootstrap, as one of resampling methods, has been applied to this problem. Availability of subsystems of rotary excavator has been considered using the proposed method. The data of reliability were collected in Serbia, at open coal development. The proposed model is based on statistical bootstrap method. On the basis of proposed method, the availability factor confidence intervals and histograms for excavator subsystems were built. The availability factor of the system in a whole was also evaluated. The results, as well as comparison with existing approaches, are presented. The attempt has been made to estimate the risk factor of subsystems using the data of availability.

In this paper, we have formulated quantum beetle antennae search (QBAS), a meta-heuristic optimization algorithm, and a variant of beetle antennae search (BAS). We apply it to portfolio selection, a well-known finance problem. Quantum computing is gaining immense popularity among the scientific community as it outsmarts the conventional computing in efficiency and speed. All the traditional computing algorithms are not directly compatible with quantum computers, for that we need to formulate their variants using the principles of quantum mechanics. In the portfolio optimization problem, we need to find the set of optimal stock such that it minimizes the risk factor and maximizes the mean-return of the portfolio. To the best of our knowledge, no quantum meta-heuristic algorithm has been applied to address this problem yet. We apply QBAS on real-world stock market data and compare the results with other meta-heuristic optimization algorithms. The results obtained show that the QBAS outperforms swarm algorithms such as the particle swarm optimization (PSO) and the genetic algorithm (GA).

This study investigates whether local gambling norms are associated with audit pricing. Using a religion-based measure of local social gambling norms, we find strong evidence that public firms located in U.S. counties with more liberal gambling norms exhibit higher levels of audit fees. This result is consistent with our view that, as an important external risk factor, clients’ local gambling norms influence audit pricing decisions. Our findings are robust to a battery of sensitivity tests, including non-religion based measures of liberal gambling norms and a natural experiment.

Recent literature has investigated the risk aggregation of a portfolio $X=(X_{i})_{1\leq i\leq n}$ under the sole assumption that the marginal distributions of the risks $X_{i} $ are specified, but not their dependence structure. There exists a range of possible values for any risk measure of $S=\sum_{i=1}^{n}X_{i}$ , and the dependence uncertainty spread, as measured by the difference between the upper and the lower bound on these values, is typically very wide. Obtaining bounds that are more practically useful requires additional information on dependence. Here, we study a partially specified factor model in which each risk $X_{i}$ has a known joint distribution with the common risk factor $Z$ , but we dispense with the conditional independence assumption that is typically made in fully specified factor models. We derive easy-to-compute bounds on risk measures such as Value-at-Risk ( $\mathrm{VaR}$ ) and law-invariant convex risk measures (e.g. Tail Value-at-Risk ( $\mathrm{TVaR}$ )) and demonstrate their asymptotic sharpness. We show that the dependence uncertainty spread is typically reduced substantially and that, contrary to the case in which only marginal information is used, it is not necessarily larger for $\mathrm{VaR}$ than for $\mathrm{TVaR}$ .

Motivated by the problem of sharp risk bounds in partially specified risk factor models and by the method of cost-efficient payoffs with given payoff structure we introduce and describe some stochastic odering problems for conditionally comonotonic resp. antimonotonic random variables. The aim is to describe the influence of the specified dependence of the components of the random vector X with a benchmark Z on the risk bounds in a risk portfolio resp. on the gain of cost efficiency of the optimal payoffs. We obtain in particular explicit results in dependence on distributional parameters for elliptical models in the case of risk bounds and for the multivariate Samuelson model in the case of cost efficient payoffs.

Background:Gait impairment is a risk factor for falls in patients with Parkinson's disease (PD). Gait can be conveniently assessed by electronic walkways, but there is need to select which spatiotemporal gait variables are useful for assessing gait in PD. Existing models for gait variables developed in healthy subjects and patients with PD show some methodological shortcomings in their validation through exploratory factor analysis (EFA), and were never confirmed by confirmatory factor analysis (CFA). The aims of this study were (1) to create a new model of gait for PD through EFA, (2) to analyze the factorial structure of our new model and compare it with existing models through CFA. Results:From the 37 variables initially considered in 250 patients with PD, 10 did not show good-to-excellent reliability and were eliminated, while further 19 were eliminated after correlation matrix and Kaiser-Meyer-Olkin measure. The remaining eight variables underwent EFA and three factors emerged: pace/rhythm, variability, and asymmetry. Structural validity of our new model was then examined with CFA, using the structural equation modeling. After some modifications, suggested by the Modification Indices, we obtained a final model that showed an excellent fit. In contrast, when the structure of previous models of gait was analyzed, no model achieved convergence with our sample of patients. Conclusions:Our model for spatiotemporal gait variables of patients with PD is the first to be developed through an accurate EFA and confirmed by CFA. It contains eight gait variables divided into three factors and shows an excellent fit. Reasons for the non-convergence of other models could be their inclusion of highly inter-correlated or low-reliability variables or could be possibly due to the fact that they did not use more recent methods for determining the number of factors to extract.

Software Cost Estimation (SCE) is the emerging concern of the software companies during the development phase of the software, as it requires effort and cost factors for modelling the software. These factors are modelled using the Artificial Intelligence models, which seem to be less accurate and non-reliable by increasing the risk factor of the software projects. Thus, for estimating the software cost, meta-heuristics are employed. This paper proposes an algorithm, termed as whale–crow optimization (WCO) algorithm, which is the integration of the whale optimization algorithm (WOA) and the crow search algorithm (CSA). The main function of the WCO algorithm is to determine the Optimal Regression coefficients for the regression models, such as the Linear Regression model and the Kernel Logistic Regression model, to develop an Optimal Regression model to estimate the software cost. The experimentation is carried out using four datasets taken from the Promise software engineering repository to perform effective performance analysis. Analysis is carried out regarding the mean magnitude of relative error (MMRE) that proves that the proposed method of SCE is effective, attaining the average MMRE at a rate of 0.2442 for the proposed Linear Regression model and 0.2692 for the proposed Kernel Regression model.

Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternative to multifactor risk models but one out of myriad possible regularization schemes. We give an example of a scheme designed to be less prone to said instabilities. We contextualize this within multifactor models.

Most mortality models to date in life insurance have inconsistent modeling assumptions between past and future survival probabilities. This paper aims at correcting this inconsistency by introducing a Bayesian framework for the joint modeling of past survival probabilities and the forecasting of future survival probabilities. To that end, the Bayesian modeling framework introduced considers both the uncertainty in the populations counts (random effects) as well as the uncertainty in the survival probability surface (systemic effects). In particular, the model uses an n-dimensional latent risk factor process to encode the survival probability surface, taking into account its intrinsic dependencies. We use the model for a case study of Swiss mortality. The case study shows that the model fits well to Swiss data and systemic events in the Swiss survival probability surface are captured by the model. The Swiss case study also exhibits the different rate of improvements in mortality for different age groups of the Swiss population.

The main results of this paper are monotonicity statements about the risk measures value-at-risk (VaR) and tail value-at-risk (TVaR) with respect to the parameters of single and multi risk factor models, which are standard models for the quantification of credit and insurance risk. In the context of single risk factor models, non-Gaussian distributed latent risk factors are allowed. It is shown that the TVaR increases with increasing claim amounts, probabilities of claims and correlations, whereas the VaR is in general not monotone in the correlation parameters. To compare the aggregated risks arising from single and multi risk factor models, the usual stochastic order and the increasing convex order are used in this paper, since these stochastic orders can be interpreted as being induced by the VaR-concept and the TVaR-concept, respectively. To derive monotonicity statements about these risk measures, properties of several further stochastic orders are used and their relation to the usual stochastic order and to the increasing convex order are applied.

Financial assessment in forestry is characterized by considerable impacts of risk factors due to large time horizons. Accounting for the risk of timber price fluctuation mixtures of Rauli (Nothofagus alpina, P. et E., OERST.) and Douglas fir (Pseudotsuga menziesii, Mirb.) have been evaluated by different approaches. The data were taken from plantations in Southern Chile between 39°10' and 39°50' south latitude. Increments have been modelled in order to calculate possible financial returns and changed volume growth has been taken into consideration for mixtures of large blocks and single-tree mixtures of both species. The optimum proportions of both species varied depending on the different perspectives of the financial assessment: first, the effects of diversification shown by classical portfolio approach were low; second, the integration of moderate risk aversion of the decision maker resulted in predominance of stands with high proportions of Douglas fir, but optimum proportions of Rauli increased with higher degrees of risk aversion. The maximization of the expected surplus in relation to the fluctuation of net present values (NPVs) (Sharpe ratio) resulted in even higher optimum proportions of Rauli. However, mixed stands proved more advantageous in contrast to the financial assessment without consideration of the risk factor timber price fluctuation (maximization of NPV). Finally, the integration of further risk factors can have impacts on the results as well as the integration of further effects of single-tree mixtures. Both lacks of information should be investigated for more extensive assessments in the future.

Investors who are more willing to accept risks when evaluating their investments less\ud frequently are said to exhibit myopic loss aversion (MLA). Several recent experimental\ud studies found that, on average, subjects bet significantly higher amounts on a risky lottery\ud when they observe only a cumulative outcome of several realizations of the lottery (long\ud evaluation period). In this paper we reexamine these empirical findings by analyzing\ud individual rather than aggregate choice patterns. The behavior of the majority of subjects\ud is inconsistent with the hypothesis of MLA: they bet an intermediate fraction of their\ud initial endowment and these bets, on average, are not significantly different across two\ud treatments with short and long evaluation period. We discuss several alternative\ud explanations of this finding, including the Fechner model of random errors and the\ud financial asset pricing model.

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing.

This paper uses duality to elaborate Slutzky equations of risks in quasi-linear decision models extended by independent background risks. Wealth, substitution and total effects are characterized in terms of mean-variance preferences. It is shown that both Pratt and Zeckhauser’s proper risk aversion and Kimball’s standard risk aversion are sufficient for negative substitution effects.

International audience; This paper studies the entry strategies of firms on risky markets. We focus on markets where demand is affine and cost is linear, moreover, the demand includes a normally distributed random variable. In such a model, we show that the leader's strategy changes with the level of market risk even when firms are risk neutral. Therefore, the availability of future information for a Stackelberg follower has a feedback effect on the leader's strategy. We also show that compared with traditional markets with no risk, the basic trade-off between flexibility and pre-commitment is only slightly changed in the qualitative game where firms are free to choose when to enter the market.

Existing biomathematical models of human fatigue and performance are reviewed with the aim of identifying open questions and ways of improving models. Most fatigue and alertness models are based on the twoprocess model of sleep regulation. They present a mathematical formulation of the two-process model targeted on different metrics including alertness, fatigue, sleepiness, performance measures and accident risk. One of the reviewed fatigue models is completely empirical without reference to sleep regulation. Differences between the models result from the specific data set on which a model is based. These data sets determine the possible application areas for the models ranging from airline operations, car and truck drivers to industrial shift work. It is generally accepted that fatigue models are useful also for educating people about fatigue in non-standard work situations and for generating scientific hypotheses that can be tested by experiments. Important points for the improvement of models include the consideration of cumulative fatigue, interindividual differences, effects of external factors such as light on fatigue, and task-related effects. Very few models consider the task-related fatiguing effect of different activities.

Background Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. Methods A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. Results A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Conclusion Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models. Electronic supplementary material The online version of this article (doi:10.1186/s12936-015-0966-y) contains supplementary material, which is available to authorized users.

A return policy is one of the major issues in supply chain management, particularly for managing single-period products that are characterized with short sales period and little salvage value. The value of the buyback price is important to ensure a stable supply chain. The role of the risk attitude of the retailer and supplier is also known as an essential factor to the decision in determining a return policy. In this paper, we present the result of our investigation into this problem. The aim of our work is to develop a model to determine optimal return policies for single-period products based on uncertain market demands and in the presence of risk preferences. The impact of the wholesale price and selling price is also investigated to determine the optimal order quantities and optimal buyback price for different types of risk attitudes.

The Value-at-Risk calculation reduces the dimensionality of the risk factor space. The main reasons for such simplifications are, e. g., technical efficiency, the logic and statistical appropriateness of the model. In Chapter 2 we present three simple mappings: the mapping on the market index, the principal components models and the model with equally correlated risk factors. The comparison of these models in Chapter 3 is based on the literature on the verification of weather forecasts (Murphy and Winkler, 1992; Murphy, 1997). Some considerations on the quantitative analysis are presented in the fourth chapter. In the last chapter, we present empirical analysis of the DAX data using XploRe.

When assessing the association between a factor X and a subsequent outcome Y in observational studies, the question that arises is what are the variables to adjust for to reduce bias due to confounding for causal inference on the effect of X on Y. Disregarding such factors is often a source of overestimation because these variables may affect both X and Y. On the other hand, adjustment for such variables can also be a source of underestimation because such variables may be the causal consequence of X and part of the mechanism that leads from X to Y.In this paper, we present a simple method to compute control variables in the presence of age at onset data on both X and a set of other variables. Using these age at onset data, control variables are computed that adjust only for conditions that occur prior to X. This strategy can be used in prospective as well as in survival analysis. Our method is motivated by an argument based on the counterfactual model of a causal effect.The procedure is exemplified by examining of the relation between panic attack and the subsequent incidence of MDD.The results reveal that the adjustment for all other variables, irrespective of their temporal relation to X, can yield a false negative result (despite unconsidered confounders and other sources of bias).

This study compares and contrasts the single factor, three factor, macrovariable and APT models, using industry portfolios of all available firms on CRSP from 1980 to 1992. Comparatively, the APT is best, macrovariable second best and single factor model worse in pricing securities. Consistently, the market variable is cross sectionally priced in all models, and two of four APT factors capture the majority of variance in industry returns. In the latter case, factor three is ***DIRECT SUPPORT *** A00DH002 00002 consistently related to market returns, and factors two and three are also associated with risk premiums and exchange rates after 1987. Factor four is not related to any macrovariable, and term structure and production are never related to any risk factor.

Background Alcohol consumption is a major risk factor in the global burden of disease, with overall volume of exposure as the principal underlying dimension. Two main sources of data on volume of alcohol exposure are available: surveys and per capita consumption derived from routine statistics such as taxation. As both sources have significant problems, this paper presents an approach that triangulates information from both sources into disaggregated estimates in line with the overall level of per capita consumption. Methods A modeling approach was applied to the US using data from a large and representative survey, the National Epidemiologic Survey on Alcohol and Related Conditions. Different distributions (log-normal, gamma, Weibull) were used to model consumption among drinkers in subgroups defined by sex, age, and ethnicity. The gamma distribution was used to shift the fitted distributions in line with the overall volume as derived from per capita estimates. Implications for alcohol-attributable fractions were presented, using liver cirrhosis as an example. Results The triangulation of survey data with aggregated per capita consumption data proved feasible and allowed for modeling of alcohol exposure disaggregated by sex, age, and ethnicity. These models can be used in combination with risk relations for burden of disease calculations. Sensitivity analyses showed that the gamma distribution chosen yielded very similar results in terms of fit and alcohol-attributable mortality as the other tested distributions. Conclusions Modeling alcohol consumption via the gamma distribution was feasible. To further refine this approach, research should focus on the main assumptions underlying the approach to explore differences between volume estimates derived from surveys and per capita consumption figures.

This paper considers two fundamental aspects of the analysis of dynamic choices under risk: the issue of the dynamic consistency of the strategies of a non EU maximizer, and the issue that an individual whose preferences are nonlinear in probabilities may choose a strategy which is in some appropriate sense dominated by other strategies. A proposed way of dealing with these problems, due to Karni and Safra and called ‘behavioral consistency’, is described. The implications of this notion of ‘behavioral consistency’ are explored, and it is shown that while the Karni and Safra approach obtains dynamically consistent behavior under nonlinear preferences, it may imply the choice of ‘dominated’ strategies even in very simple decision trees.

Ding et al. [1] recently published a paper on GEIRA, a gene-environment and gene–gene interaction research application. The authors developed a program in SAS and R to calculate interactions on an additive and multiplicative scale. We want to compliment the authors on providing such a useful tool, which may accommodate more frequent calculation of interaction on an additive scale. However, there is one flaw in the program, which the authors only partly acknowledge, that we would like to address. Measures of interaction on an additive scale, such as the proportion attributable to interaction (AP), cannot be validly calculated if any of the odds ratios of the independent and joint effects is smaller than 1, i.e. preventive [2]. The authors state in the discussion section that: “[] the OR associated with the genetic factor might still be less than 1 among subjects unexposed to the environmental factor. In this case, the interpretation for interaction should be cautious”. We think that ‘caution’ is not enough; in this case, the calculations should just not be performed. Fortunately, there is an easy solution to get valid estimates for measures of interaction on an additive scale when having preventive exposures by appropriately recoding one or both of the exposures. We have described this in detail elsewhere for general measures of additive interaction [2]. Tests for specific forms of antagonism may, however, require different forms of recoding [3]. The reason why using odds ratios smaller than 1 gives wrong results in the measures of interaction on an additive scale is because an odds ratio is restricted between 0 and 1 for a preventive factor while it can go from 1 to infinity for a risk factor. For example, an odds ratio of 0.60 means a relative risk reduction of 40%, whereas the inverse (1/0.60 = 1.67) means a relative increase in risk of 67%. If 0.60 is used in calculating a measure of additive interaction this leads to different results than if 1.67 is used in calculating the interaction. Moreover, with preventive exposures, measures such as the relative excess risk due to interaction or the attributable proportion can give results that are in the opposite direction of other additive interaction measures such as the synergy index [2]. A simple solution for the problem is recoding the variables in such a way that the stratum with the lowest risk when both factors are considered jointly becomes the reference category. The result of this recoding is that for one or both factors the absence of the exposure (rather than the presence) becomes the risk factor for the outcome. If factors are recoded one at a time, rather than jointly as we suggest, this can again result in invalid measures of interaction on an additive scale [2]. The authors of GEIRA might consider incorporating a recoding scheme in their program to prevent mistakes from being made when calculating measures of interaction on an additive scale with odds ratios smaller than 1. Alternatively, users of GEIRA could carry out this recoding themselves and apply GEIRA subsequently. Caution is always needed in interpreting the interaction after recoding as the exposure is changed to its opposite.