Monotonicity Assumption Research Articles

Causal Inference Under Outcome-Based Sampling with Monotonicity Assumptions

We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the potential outcome framework. It is shown that strong ignorability is not always as powerful as it is under random sampling and that certain monotonicity assumptions yield comparable results in terms of sharp identified intervals. Specifically, the usual odds ratio is shown to be a sharp identified upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions. We offer algorithms for inference on the causal parameters that are aggregated over the true population distribution of the covariates. We show the usefulness of our approach by studying three empirical examples: the benefit of attending private school for entering a prestigious university in Pakistan; the relationship between staying in school and getting involved with drug-trafficking gangs in Brazil; and the link between physicians’ hours and size of the group practice in the United States.

On Stein’s method for stochastically monotone single-birth chains

We discuss Stein’s method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson’s equation for such a process. Applications include rates of convergence to stationarity, and bounding the total variation distance between the stationary distributions of two Markov chains in the case where one transition matrix dominates the other.

Identification of multi-valued treatment effects with unobserved heterogeneity

In this paper, we establish sufficient conditions for identifying treatment effects on continuous outcomes in endogenous and multi-valued discrete treatment settings with unobserved heterogeneity. We employ the monotonicity assumption for multi-valued discrete treatments and instruments, and our identification condition has a clear economic interpretation. In addition, we identify the local treatment effects in multi-valued treatment settings and derive closed-form expressions of the identified treatment effects. We provide examples to illustrate the usefulness of our result.

Characteristics of the switch process and geometric divisibility

AbstractThe switch process alternates independently between 1 and $-1$ , with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of some switch process. We derive an explicit relation under the assumption of monotonicity of the expected value function. It is shown that geometric divisible switching time distributions correspond to a non-negative decreasing expected value function. Moreover, an explicit relation between the expected value of a switch process and the autocovariance function of the switch process stationary counterpart is obtained, leading to a new interpretation of the classical Pólya criterion for positive-definiteness.

Overcoming floor and ceiling effects in knee arthroplasty outcome measurement.

To map the Oxford Knee Score (OKS) and High Activity Arthroplasty Score (HAAS) items to a common scale, and to investigate the psychometric properties of this new scale for the measurement of knee health. Patient-reported outcome measure (PROM) data measuring knee health were obtained from the NHS PROMs dataset and Total or Partial Knee Arthroplasty Trial (TOPKAT). Assumptions for common scale modelling were tested. A graded response model (fitted to OKS item responses in the NHS PROMs dataset) was used as an anchor to calibrate paired HAAS items from the TOPKAT dataset. Information curves for the combined OKS-HAAS model were plotted. Bland-Altman analysis was used to compare common scale scores derived from OKS and HAAS items. A conversion table was developed to map between HAAS, OKS, and the common scale. We included 3,329 response sets from 528 patients undergoing knee arthroplasty. These generally met the assumptions of unidimensionality, monotonicity, local independence, and measurement invariance. The HAAS items provided more information than OKS items at high levels of knee health. Combining both instruments resulted in higher test-level information than either instrument alone. The mean error between common scale scores derived from the OKS and HAAS was 0.29 logits. The common scale allowed more precise measurement of knee health than use of either the OKS or HAAS individually. These techniques for mapping PROM instruments may be useful for the standardization of outcome reporting, and pooling results across studies that use either PROM in individual-patient meta-analysis.

Psychometric properties of the Chinese version of the PROMIS-Cancer-Anxiety item bank assessed using a graded response model

ObjectiveThis study aimed to examine the psychometric properties of the Chinese version of the Patient-Reported Outcome Measurement Information System (PROMIS)-Cancer-Anxiety item bank using a graded response model in a sample of patients with cancer. MethodsA cross-sectional study was conducted and the Chinese version of the PROMIS-Cancer-Anxiety item bank was used to measure anxiety in patients with cancer. The unidimensional structure of the item bank was evaluated using principal component analysis. Residual correlations and the graphs of item mean scores conditional on the rest scores were examined to evaluate the local independence and monotonicity of the items, respectively. Item characteristics were described using item parameter estimates and item information. Operating characteristic curves (OCCs) and test information curve (TIC) were also plotted. Measurement invariance across age, gender, and education level was assessed to identify possible differential item functioning (DIF). ResultsA total of 1075 patients with cancer were enrolled. Under the assumptions of unidimensionality, local independence, and monotonicity, the discrimination parameters a ranged from 2.30 to 5.47, and the threshold parameters b ranged from b1 = −2.87 to b4 = 3.21 with proper intervals. Completely overlapped category curves were not observed among the OCCs of any items. Item information and TIC showed that the item bank had a wide measurement range. The DIFs for age, gender, and education level for all items were not remarkable. ConclusionsThe results supported using the Chinese version of the PROMIS-Cancer-Anxiety item bank to measure anxiety and develop a computerized adaptive testing (CAT) system for anxiety in patients with cancer.

A Localized Progressive Hedging Algorithm for Solving Nonmonotone Stochastic Variational Inequalities

The progressive hedging algorithm (PHA) is an effective solution method for solving monotone stochastic variational inequalities (SVIs). However, this validity is based on the assumption of global maximal monotonicity. In this paper, we propose a localized PHA for solving nonmonotone SVIs and show that its validity is based on the weaker assumption of locally elicitable maximal monotonicity. Furthermore, we prove that such assumption holds when the mapping involved in the SVI is locally elicitable monotone or locally monotone. The local convergence of the proposed algorithm is established, and it is shown that the localized PHA has the rate of linear convergence under some mild assumptions. Some numerical experiments, including a two-stage orange market problem and randomly generated two-stage piecewise stochastic linear complementarity problems, indicate that the proposed algorithm is efficient. Funding: This work was supported by the National Natural Science Foundation of China [Grant 12171271].

Causal effects of mental health on food security

Although mental health conditions are known to be associated with socioeconomic hardships, their causal effects remain largely unexplored. Using a sample of low-income families in the National Health Interview Survey (NHIS), we assess causal effects of serious mental illness (SMI) and related mental health conditions on family food security. We apply partial identification methods to account for fundamental endogeneity and measurement identification problems in a unified framework. To implement these methods, we combine a proxy measure of SMI in the NHIS with an estimate of the true rate of SMI from the Substance Abuse and Mental Health Services Administration. We also develop an innovative approach to approximate true prevalence rates when only self-reported prevalence rates are available. Applying relatively weak monotonicity assumptions on latent food security outcomes, we find that alleviating SMI would improve the food security rate by at least 9.5 percentage points, or 15 %.JEL codes: C21, I10, I38

REGULARIZED JACOBI-TYPE ADMM-METHOD FOR FINDING SOLUTIONS TO GENERALIZED NASH EQUILIBRIUM PROBLEM

In this paper, we extended the well-known alternating direction method of multipliers (ADMM) for optimization problems to generalized Nash equilibrium problems (GNEP) with shared constraints. We developed an ADMM-type algorithm with fixed regularization to tackle the problem (GNEP) where an upper estimate for the operator norm is not known and then we apply a multiplier-penalty in order to get rid of the joint constraints. We equipped the Hilbert space with an appropriate weighted scalar product and it turns out to be weakly convergent under a lipschitz and monotonicity assumption. A proximal term is then added to improve the convergence properties. Furthermore, a comparative analysis of quasi-variational inequality method, interior point method, penalty method and the proposed method are discussed.

Modeling item revisiting behavior in computer-based testing: Exploring the effect of item revisitations as collateral information.

Item revisiting behavior is one of the most frequently occurring test-taking strategies, and it can decrease test anxiety and improve test validity. Examinees either confirm the initial answers due to persistence of their beliefs or change to different answers after careful rethought on each part of the questions. Item revisiting sequences as collateral information reveal the examinees' underlying psychological processes, such as motivation, effort, and engagement, which supports policy makers in taking further steps to facilitate instructions for the examinees. Item revisiting behavior is commonly correlated with the latent traits of examinees, and it needs to be properly analyzed in order to make valid statistical inference. In this paper, we proposed a novel item revisiting model, in which a monotonicity assumption is considered based on the observation that examinees are more likely to revisit the current item if more revisiting behavior occurs previously. Three simulation studies were conducted: (1) to evaluate the performance of the proposed Bayesian estimation algorithm for the new model; (2) to show that ignoring item revisiting sequences induces biased parameter estimates; (3) to assess the model fit of the proposed model with the ignorable and nonignorable item revisiting behavior assumptions. The results indicate that item revisiting behavior can be effectively utilized in conjunction with responses and response times to improve parameter estimation precision. A real data example is provided to illustrate the application of the proposed model.

Fixed-Time Stable Proximal Dynamical System for Solving MVIPs

In this paper, a novel modified proximal dynamical system is proposed to compute the solution of a mixed variational inequality problem (MVIP) within a fixed time, where the time of convergence is finite and is uniformly bounded for all initial conditions. Under the assumptions of strong monotonicity and Lipschitz continuity, it is shown that a solution of the modified proximal dynamical system exists, is uniquely determined, and converges to the unique solution of the associated MVIP within a fixed time. Furthermore, the fixed-time stability of the modified projected dynamical system continues to hold, even if the assumption of strong monotonicity is relaxed to that of strong pseudomonotonicity. Finally, it is shown that the solution obtained using the forward-Euler discretization of the proposed modified proximal dynamical system converges to an arbitrarily small neighborhood of the solution of the associated MVIP within a fixed number of time steps, independent of the initial conditions.

NeuralCD: A General Framework for Cognitive Diagnosis

Recent decades have witnessed a rapid growth of intelligent educational systems as well as an increasing demand for computer-aided educational technologies. One of the fundamental issues in intelligent education is cognitive diagnosis, which aims to discover the proficiency level of students on specific knowledge concepts. Existing approaches usually mine linear interactions of student exercising process by manually designed function (e.g., logistic function). However, the cognitive interactions between students and exercises is a complex process, and excessive simplifications would lead to under fitting and thus get inaccurate diagnostic results. Besides, the manually designed interaction functions are relatively inflexible and limits their extensibility. This consequently causes lack of consideration about useful non-numerical information in the cognitive process besides response logs. In this paper, we propose a general Neural Cognitive Diagnosis (NeuralCD) framework as well as several implemented models (a basic implementation NeuralCDM and three extensions), where we project students and exercises to factor vectors and incorporates neural networks to learn the complex exercising interactions. To ensure the interpretability of diagnostic results, which is essential for cognitive diagnosis, we apply an monotonicity assumption to our NeuralCD framework. Moreover, NeuralCD is a general framework and has good extensibility. We show the generality of NeuralCD through proving how it can cover some traditional models. Then, we demonstrate the extensibility of NeuralCD, which benefits future developments. On one hand, we demonstrate content-based extensions where we provide examples of exploring the rich contents of exercise texts (CNCD-Q and CNCD-F). On the other hand, we demonstrate a knowledge-association based extension to show that NeuralCD is flexible for structural adjustments so as to solve specific problems. For instance, we improve the diagnostic results on uncovered knowledge concepts of a student by extending NeuralCD with the knowledge associations consideration (KaNCD). Extensive experimental results on real-world datasets show the effectiveness of NeuralCD framework with both accuracy and interpretability.

Generalized backward stochastic differential equations with jumps in a general filtration

Abstract In this paper, we analyze multidimensional generalized backward stochastic differential equations with jumps in a filtration that supports a Brownian motion and an independent integer-valued random measure. Under monotonicity and linear growth assumptions on the coefficients, we give the existence and uniqueness of 𝕃 2 {\mathbb{L}^{2}} -solutions provided that the generators and the terminal condition satisfy some suitable integrability conditions.

Psychometric properties and general population reference values for PROMIS Global Health in Hungary

ObjectivesPatient-Reported Outcomes Measurement Information System–Global Health (PROMIS-GH) is a widely used generic measure of health status. This study aimed to (1) assess the psychometric properties of the Hungarian PROMIS-GH and to (2) develop general population reference values in Hungary.MethodsAn online cross-sectional survey was conducted among the Hungarian adult general population (n = 1700). Respondents completed the PROMIS-GH v1.2. Unidimensionality (confirmatory factor analysis and bifactor model), local independence, monotonicity (Mokken scaling), graded response model fit, item characteristic curves and measurement invariance were examined. Spearman’s correlations were used to analyse convergent validity of PROMIS-GH subscales with SF-36v1 composites and subscales. Age- and gender-weighted T-scores were computed for the Global Physical Health (GPH) and Global Mental Health (GMH) subscales using the US item calibrations.ResultsThe item response theory assumptions of unidimensionality, local independence and monotonicity were met for both subscales. The graded response model showed acceptable fit indices for both subscales. No differential item functioning was detected for any sociodemographic characteristics. GMH T-scores showed a strong correlation with SF-36 mental health composite score (rs = 0.71) and GPH T-scores with SF-36 physical health composite score (rs = 0.83). Mean GPH and GMH T-scores of females were lower (47.8 and 46.4) compared to males (50.5 and 49.3) (p < 0.001), and both mean GPH and GMH T-scores decreased with age, suggesting worse health status (p < 0.05).ConclusionThis study established the validity and developed general population reference values for the PROMIS-GH in Hungary. Population reference values facilitate the interpretation of patients’ scores and allow inter-country comparisons.

On the Continuity of Optimal Stopping Surfaces for Jump-Diffusions

We show that optimal stopping surfaces arising from time-inhomogeneous optimal stopping problems on two-dimensional jump-diffusions are continuous (jointly in time and space) under mild monotonicity and regularity assumptions of local nature.

Dinlediğini Anlama Testinin Türk Kültürüne Uyarlanması

Introduction: Listening, the first language skill developed by many children, serves as the basis of subsequent language skills. In addition, listening comprehension skills affect reading success in many different groups such as typically developing readers, children with learning disabilities and children with specific language disorders. The purpose of this research is to adapt the listening comprehension measurement tool to Turkish culture. Method: The purpose of this study is to examine the psychometric properties of the measurement tool within the framework of item response theory (IRT) through two-parameter logistic model (2PLM). Among model assumptions, confirmatory factor analysis (CFA) for unidimensionality Q3 statistics and item characteristic curv for the monotonic increase assumption showing the response probabilities conditional to the ability continuum were examined, respectively. The results for the assumptions were satisfactory. Then, general model-data fit, item-based model-data fit, discrimination parameters, difficulty parameters and information functions were examined with factor loadings. Findings: The results showed that item parameters were in the expected ranges in practical applications, and test information function peaked at lower ability level similar to the original measurement tool. Examining factor loadings, it was shown that they were higher than generally acceptable limit except for 23rd item. When contribution of this item to the model was tested statistically, it was concluded that it would be appropriate to include it in the measurement tool to keep the other items of associated with story block. Moreover, marginal reliability coefficient shows that the measurement results were highly reliable. Discussion: It was concluded that sufficient evidence of validity and reliability was obtained for one-dimensional structure of 36-item form of the measurement tool.

An analysis of reproductive outcomes for conceptions of participants of the Air Force Health Study

Analyses were conducted of reproductive outcomes for conceptions of participants of the Air Force Heath Study. Participants were male Air Force veterans of the Vietnam War. Conceptions were categorized into conceived before and after the start of the participant's Vietnam War service. Analyses accounted for correlation between outcomes for multiple conceptions for each participant. For each of three non-sparsely occurring outcomes, including not live born, miscarriage, and preterm, the probability of occurrence increased substantially when conceived after compared to before the start of Vietnam War service. These results support the conclusion of an adverse effect due to Vietnam War service on these reproductive outcomes. Data for conceptions after the start of Vietnam War service for participants with measured dioxin values were used to estimate dose-response curves for the effect of dioxin exposure on the occurrence of each of the three non-sparsely occurring outcomes. These curves were assumed to be constant up to a threshold and then monotonic after that threshold. For each of the three non-sparsely occurring outcomes, the estimated dose-response curves increased nonlinearly after associated thresholds. These results support the conclusion that the adverse effect due to conception after the start of Vietnam War service is attributable to high enough exposures to dioxin, a toxic contaminant of Agent Orange used for herbicide spraying in the Vietnam War. Sensitivity analyses supported the conclusion that dioxin results were not substantially affected by the assumption of monotonicity, decay due to elapsed time from exposure to measurement, and available covariates.

The ideal test for the divergence of a series

We generalize the classical Olivier’s theorem which says that for any convergent series sum _n a_n with positive nonincreasing real terms the sequence (n a_n) tends to zero. Our results encompass many known generalizations of Olivier’s theorem and give some new instances. The generalizations are done in two directions: we either drop the monotonicity assumption completely or we relax it to the monotonicity on a large set of indices. In both cases, the convergence of (na_n) is replaced by ideal convergence. In the second part of the paper, we examine families of sequences for which the assertions of our generalizations of Olivier’s theorem fail. Here, we are interested in finding large linear and algebraic substructures in these families.

On the study of multistage stochastic vector quasi-variational problems

This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model.

A Spatial Pareto Exchange Economy Problem

We use convex duality techniques to study a spatial Pareto problem with transport costs and derive a spatial second welfare theorem. The existence of an integrable equilibrium distribution of quantities is nontrivial and established under general monotonicity assumptions. Our variational approach also enables us to give a numerical algorithm à la Sinkhorn and present simulations for equilibrium prices and quantities in one-dimensional domains and a network of French cities.