Constrained Regression Model Research Articles

Distorted correlations among censored data: causes, effects, and correction.

Data censoring occurs when researchers do not know precise values of data points (e.g., age is 55+ or concentration ≤ .001). Censoring is frequent within psychology but typically unrecognized outside of longitudinal studies. We describe five circumstances when censoring may occur, demonstrate censoring distorts correlations, and discuss how censoring can create spurious factors. Next, we explain how to use R package lava to calculate maximum likelihood estimates (Holst and Budtz-JørgensenComputational Statistics, 28(4), 1385-1452,2013) of correlations between uncensored variables based upon censored variables. Previous research demonstrated these estimates were more accurate than Muthén's (1984) estimate for one particular model, but no research has systematically examined their accuracy. We therefore conducted a simulation study exploring the effects of the correlation, sample size, and censoring on point and interval estimates of correlations. Based upon 80 cells in which low values of normally distributed variables were censored, we recommend the constrained regression model with Wald confidence intervals. These methods were precise and unbiased unless both variables had 70% censoring and the correlation was large and negative (e.g., -.9), in which case estimates were closer to -1 than they should be. Opposite results would occur if low values of one variable and high values of the other were censored: Estimates would be precise and unbiased unless censoring was extreme and correlations were large and positive. To estimate large correlations accurately, we recommend researchers reduce censoring by using longer longitudinal studies, using scales with more response options, and matching measures to populations to reduce floor and ceiling effects.

Discriminative Projected Clustering via Unsupervised LDA.

This work focuses on the projected clustering problem. Specifically, an efficient and parameter-free clustering model, named discriminative projected clustering (DPC), is proposed for simultaneously low-dimensional and discriminative projection learning and clustering, from the perspective of least squares regression. The proposed DPC, a constrained regression model, aims at finding both a transformation matrix and a binary indicator matrix to minimize the sum-of-squares error. Theoretically, a significant conclusion is drawn and used to reveal the connection between DPC and linear discriminant analysis (LDA). Experimentally, experiments are conducted on both toy and real-world data to validate the effectiveness and efficiency of DPC; experiments are also conducted on hyperspectral images to further verify its practicability in real-world applications. Experimental results demonstrate that DPC achieves comparable or superior results to some state-of-the-art clustering methods.

B - 82 Relations between Subjective and Objective Memory Functioning: Investigating Psychometric Equivalence across Race Using Structural Equation Models.

We assessed the relations between the Subjective Memory Complaints Questionnaire (SMCQ) and the Spanish English Verbal Learning Test (SEVLT) for equivalence across race. Secondary objectives include evaluating the SMCQ for measurement invariance across race. The current study accessed data from the University of North Texas Health Science Center's Health and Aging Brain Study - Health Disparities (HABS-HD). We used structural equation modeling (SEM) to test the SMCQ for measurement invariance across Black (n = 515), Hispanic (n = 1104), and White (n = 1096) Americans. We first specified a configural model to assess the fit of the underlying structure across groups, followed by a scalar model to determine whether scores reflect comparable levels of the latent construct. Next, we regressed the SEVLT on the SMCQ to test the relation between subjective and objective memory functioning. Lastly, we specified a multigroup SEM to compare unconstrained and constrained regression models across race. Full scalar invariance was tenable for the SMCQ (ΔCFI = 0.007, NCI = 0.023). There were significant negative relations between the SMCQ and the SEVLT for each group (Black: b = -2.31; Hispanic: b = -1.63; White: b = -2.72), but the relations were not equivalent across groups [χ2 diff (df) = 20.2.45 (2), p < 0.001]. Results suggest that the SMCQ can be administered to screen Black, Hispanic, and White individuals for memory functioning and that mean comparisons can be made. Differential regression coefficients suggest that clinical thresholds may need to be set independently across groups to promote clinical utility.

Estimation of cell lineages in tumors from spatial transcriptomics data

Spatial transcriptomics (ST) technology through in situ capturing has enabled topographical gene expression profiling of tumor tissues. However, each capturing spot may contain diverse immune and malignant cells, with different cell densities across tissue regions. Cell type deconvolution in tumor ST data remains challenging for existing methods designed to decompose general ST or bulk tumor data. We develop the Spatial Cellular Estimator for Tumors (SpaCET) to infer cell identities from tumor ST data. SpaCET first estimates cancer cell abundance by integrating a gene pattern dictionary of copy number alterations and expression changes in common malignancies. A constrained regression model then calibrates local cell densities and determines immune and stromal cell lineage fractions. SpaCET provides higher accuracy than existing methods based on simulation and real ST data with matched double-blind histopathology annotations as ground truth. Further, coupling cell fractions with ligand-receptor coexpression analysis, SpaCET reveals how intercellular interactions at the tumor-immune interface promote cancer progression.

Modeling Hot Deformation of 5005 Aluminum Alloy through Locally Constrained Regression Models with Logarithmic Transformations

This study presents the adoption of locally constrained regression models (LCRMs) with logarithmic transformations in order to model the flow stress behavior of the high-temperature deformation of 5005 aluminum alloy. Hot tensile tests for 5005 aluminum alloy were conducted under the temperatures of 290 °C, 360 °C, 430 °C, and 500 °C, and the strain rates of 0.0003/s, 0.003/s, and 0.03/s. The flow stress behavior was analyzed based on variations in temperature and strain rate. The flow stress during the hot deformation was modeled using the traditional Arrhenius type constitutive equation and the neural network approach. Then, for improved prediction accuracy, the flow stress was modeled using LCRMs. The prediction accuracies of the models were compared by calculating the MAE (Maximum Absolute Error) and RMSE (Root-Mean-Squared Errors) values. The MAE and RMSE of the LCRMs were lower than the errors of the Arrhenius equation and the neural network model. The results show that LCRMs can be useful in modeling the flow stress of 5005 aluminum alloy, and that the developed model can accurately predict the flow stress.

Political and Social Consequences of Qualification Mismatches: A Bounding Approach to Status Inconsistency

Abstract Many employees work in jobs that do not match their level of formal education. Status inconsistency theory (SIT) argues that such mismatches result in stress, dissatisfaction, political alienation, and social withdrawal. Status inconsistency may, therefore, pose a threat to social cohesion. However, extant SIT scholarship does not fully appreciate the consequences of an identification problem due to the perfect collinearity among the effects of occupation, education, and their mismatch. I review the literature and show that prior findings depend on implicit theoretical assumptions that are often implausible once spelled out. To overcome this problem, I propose a new approach to the study of mismatches that builds on recent advances in the modeling of age, period, and cohort effects. I demonstrate how a set of relatively weak assumptions that are transparently grounded in sociological theory allows for (partial) identification of mismatch effects. The empirical analysis draws on comparable large-scale survey data from the United Kingdom (UKLHS) and Germany (GSOEP), two countries with a very different institutional organization of education to job matching. Compared with previous research, I use theoretically justified identifying assumptions and provide more rigorous evidence by addressing non-random selection into mismatch. Constrained regression models show mismatch effects on work-related identities, satisfaction, and organizational integration. Contra SIT, my results suggest that the effects of mismatches do not arise from cognitive dissonance but from an expectation formation mechanism. I find only weak evidence that mismatch effects spill over into the political domain. Despite large institutional differences, the results are similar across countries.

Exploiting Incomplete Information in Risk Adjustment Using Constrained Regression

Health insurance markets with regulated premiums typically include risk adjustment (RA) to mitigate selection incentives. Even the most sophisticated RA models, however, tend to undercompensate (overcompensate) insurers for people in poor (good) health. One reason RA models are imperfect is that some predictors cannot serve as risk adjustor because they are not available for the entire population. This paper applies an indirect method to exploit such predictive information: constrained regression. Our focus is on the Netherlands where morbidity data from general practitioners (GPs) are available for only around 10 percent of the population. We combine this incomplete sample with complete data (N=16.7 million) on spending and risk adjustors. In a first step, we find that GP morbidity data are predictive net of the Dutch RA model. In a second step, we use the GP morbidity data to impose constraints on the coefficients of the RA model. This results in more RA funds being sent to undercompensated groups. Using a split-sample approach, we simulate two constrained regression models and compare the outcomes to those of an unconstrained model. Our findings indicate that constrained regression can be a useful tool to exploit predictive information that is available for only a sample of the population.

Robust mixed-norm constrained regression with application to face recognitions

Most existing regression-based classification methods cope with pixelwise noise via $$\ell _1$$ -norm or $$\ell _2$$ -norm, but neglect the structural information between pixels. To the best of our knowledge, nuclear norm-based matrix regression approaches have achieved great success for addressing imagewise noise, but may result in unreasonable regression and incorrect classification, especially when test images are extremely corrupted by larger occlusions and severe illumination variations, since they apply the corrupted test images to reconstruction process directly, and the influence of noise will be unavoidable. To overcome this limitation, this paper presents a robust mixed-norm constrained regression model to deal with the structural noise corruption. To be more specific, nuclear norm of the error between corrupted test image and its corresponding recovered image is exploited as a regular term for characterizing the low rank noise structure, and Frobenius norm is utilized to depict the difference between the recovered image and restructured image on account of the less noise of recovered image. Then, we adopt the alternating direction method of multipliers to settle our proposed approaches efficiently. Furthermore, the theoretical convergence proof and detailed analysis of computational complexity are provided to assess our algorithms. Eventually, extensive experiments on five well-known face databases have manifested that the proposed methods outperform some state-of-the-art regression-based approaches for primarily addressing noise caused by occlusion and illumination changes.

Integer constraints for enhancing interpretability in linear regression

One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated features. In this paper we aim to enhance interpretability in linear regression in presence of multicollinearity by: (i) forcing the sign of the estimated coefficients to be consistent with the sign of the correlations between predictors, and (ii) avoiding spurious coefficients so that only significant features are represented in the model. This will be addressed by modelling constraints and adding them to an optimization problem expressing some estimation procedure such as ordinary least squares or the lasso. The so-obtained constrained regression models will become Mixed Integer Quadratic Problems. The numerical experiments carried out on real and simulated datasets show that tightening the search space of some standard linear regression models by adding the constraints modelling (i) and/or (ii) help to improve the sparsity and interpretability of the solutions with competitive predictive quality.

Valuation of EQ-5D-3l Health States in Slovenia: VAS Based and TTO Based Value Sets.

IntroductionThe two primary objectives of this paper were (a) to develop first logically consistent TTO based EQ-5D-3L value sets for Slovenia and (b) to revisit earlier developed VAS based EQ-5D-3L value sets.MethodsBetween September 2005 and April 2006, face-to-face interviews with 225 individuals in Slovenia were conducted. Protocols from the Measurement and Value of Health study were followed closely. Each respondent valued 15 health states out of a total of 23. Model selection was informed by the criteria monotonicity/logical consistency. Predictive accuracy was assessed in terms of mean square difference between out-of-sample predictions and corresponding observed means, as well as Lin’s Concordance Correlation Coefficient.ResultsModelling was based on 2,717 VAS and 2,831 TTO values elicited from 225 respondents. A 6-parameter constrained regression model with a supplementary power term was selected for VAS and TTO value sets, as it produces monotonic values, and proved superior in terms of out-of-sample predictive accuracy over the tested alternatives.ConclusionThis is the first EQ-5D-3L TTO based value set in Slovenia and the second in Central and Eastern Europe (besides Poland). It is also the first monotonic and logically consistent VAS value set in Central and Eastern Europe. Comparisons with Polish and UK TTO values show considerable differences, mostly due to mobility with having a substantially greater weight in Slovenia. The UK value set generally produces lower values and the Polish value set higher values for mild states.

CD8+ T cells in tumor parenchyma and stroma by image analysis (IA) and gene expression profiling (GEP): Potential biomarkers for immuno-oncology (I-O) therapy.

2594 Background: Distribution patterns of CD8+ T cells within the tumor microenvironment (TME) can be assessed by IA, which may reflect underlying tumor biology and serve as a potential biomarker to assess the utility of I-O therapy. These patterns are variable and may be classified as immune desert (minimal infiltrate), excluded (T cells confined to tumor stroma or to the invasive margin), or inflamed (T cells diffusely infiltrating tumor parenchyma and stroma). We hypothesized that association of a GEP signature with abundance of parenchymal and stromal T-cell infiltrates may identify biomarkers of response or resistance to I-O therapy. To test this, we applied an AI-powered IA platform to quantify CD8+ T cells by geographical location and used GEP to define both CD8 abundance and associated geographic localization to tumor parenchyma and stroma. Methods: We performed an analysis using a tumor inflammatory GEP assay and CD8 immunohistochemistry on procured specimens (335 melanoma, 391 SCCHN). Digitized slides were used to train a convolutional neural network to quantify the number of CD8+ T cells in stroma, tumor parenchyma, parenchyma-stromal interface, and invasive margin. Generalized constrained regression models were used to predict GEP signatures specifically for stromal and parenchymal CD8+ T cells. Results: Parenchymal and stromal GEP scores were highly concordant with CD8+ infiltrate geography (adj- r2: 0.67, 0.65, respectively; P ≤ 0.01). Little overlap existed between gene sets associated with parenchymal and stromal CD8 T-cell geographies. CSF1R and NECTIN2 gene expression was observed to correlate inversely with parenchymal localization and directly with stromal CD8+ T-cell abundance. Conclusions: GEP signatures can be identified that are concordant with various CD8+ T-cell localization patterns in melanoma and SCCHN, demonstrating that GEP-IA can be developed to identify the immune status of interest in the TME. The specific genes identified have potential to elucidate mechanisms of resistance and/or inform I-O targets that can be further evaluated in relation to clinical significance in future studies.

BsamGP: An R Package for Bayesian Spectral Analysis Models Using Gaussian Process Priors

The Bayesian spectral analysis model (BSAM) is a powerful tool to deal with semiparametric methods in regression and density estimation based on the spectral representation of Gaussian process priors. The bsamGP package for R provides a comprehensive set of programs for the implementation of fully Bayesian semiparametric methods based on BSAM. Currently, bsamGP includes semiparametric additive models for regression, generalized models and density estimation. In particular, bsamGP deals with constrained regression models with monotone, convex/concave, S-shaped and U-shaped functions by modeling derivatives of regression functions as squared Gaussian processes. bsamGP also contains Bayesian model selection procedures for testing the adequacy of a parametric model relative to a non-specific semiparametric alternative and the existence of the shape restriction. To maximize computational efficiency, we carry out posterior sampling algorithms of all models using compiled Fortran code. The package is illustrated through Bayesian semiparametric analyses of synthetic data and benchmark data.

Economic Growth and Optimal Taxation: A Case of Mongolian Economy

We examined three cases of Schully model [1] [2] for Mongolian economy. In the first case, we consider the production function with constant returns to scale. In the second case, we employ an econometric model for the production function with none constant return to scale without constraints on parameters of elasticities. Finally, the constrained regression model has been implemented by solving a convex minimization problem over a convex set. Also, we have proved that Schully production function namely, “U shape function” in the literature [1] [2] [3] in fact is concave function under some assumptions.

A constrained regression model for an ordinal response with ordinal predictors

A regression model is proposed for the analysis of an ordinal response variable depending on a set of multiple covariates containing ordinal and potentially other variables. The proportional odds model (McCullagh in J R Stat Soc Ser B (Methodol) 109–142, 1980) is used for the ordinal response, and constrained maximum likelihood estimation is used to account for the ordinality of covariates. Ordinal predictors are coded by dummy variables. The parameters associated with the categories of the ordinal predictor(s) are constrained, enforcing them to be monotonic (isotonic or antitonic). A decision rule is introduced for classifying the ordinal predictors’ monotonicity directions, also providing information whether observations are compatible with both or no monotonicity direction. In addition, a monotonicity test for the parameters of any ordinal predictor is proposed. The monotonicity constrained model is proposed together with five estimation methods and compared to the unconstrained one based on simulations. The model is applied to real data explaining a 10-points Likert scale quality of life self-assessment variable by ordinal and other predictors.

Nonparametric adaptive Bayesian regression using priors with tractable normalizing constants and under qualitative assumptions

Shape constrained regression models are useful for analyzing data with specific shape responses, such as (monotone) dose-response curves, the (concave) utility functions of a risk averse decision maker, the (increasing) growth curves of children's height through time, that are particularly common in medicine, economic and epidemiological studies. This paper proposes a new adaptive Bayesian approach towards constructing prior distributions, with known normalizing constants, which enables us to take into account combinations of shape constraints and to localize each shape constraint on a given interval. Our strategy enables us to compute the simulation from the posterior distribution using a reversible jump Metropolis–Hastings scheme. The major advantages of the proposal are its flexibility achieved by adjusting local shape restrictions to detect better the high and low variability regions of the data and to facilitate the control of the regression function shape when there is no data at all in some regions. We give asymptotic results that show that our Bayesian method provides consistent function estimator from the adaptive prior. The performance of our method is investigated through a simulation study with small samples. An analysis of two real data sets is presented to illustrate the new approach.

A hierarchical Bayesian regression model for the uncertain functional constraint using screened scale mixtures of Gaussian distributions

This paper considers a hierarchical Bayesian analysis of regression models using a class of Gaussian scale mixtures. This class provides a robust alternative to the common use of the Gaussian distribution as a prior distribution in particular for estimating the regression function subject to uncertainty about the constraint. For this purpose, we use a family of rectangular screened multivariate scale mixtures of Gaussian distribution as a prior for the regression function, which is flexible enough to reflect the degrees of uncertainty about the functional constraint. Specifically, we propose a hierarchical Bayesian regression model for the constrained regression function with uncertainty on the basis of three stages of a prior hierarchy with Gaussian scale mixtures, referred to as a hierarchical screened scale mixture of Gaussian regression models (HSMGRM). We describe distributional properties of HSMGRM and an efficient Markov chain Monte Carlo algorithm for posterior inference, and apply the proposed model to real applications with constrained regression models subject to uncertainty.

Constrained Regression for Interval-Valued Data

Current regression models for interval-valued data do not guarantee that the predicted lower bound of the interval is always smaller than its upper bound. We propose a constrained regression model that preserves the natural order of the interval in all instances, either for in-sample fitted intervals or for interval forecasts. Within the framework of interval time series, we specify a general dynamic bivariate system for the upper and lower bounds of the intervals. By imposing the order of the interval bounds into the model, the bivariate probability density function of the errors becomes conditionally truncated. In this context, the ordinary least squares (OLS) estimators of the parameters of the system are inconsistent. Estimation by maximum likelihood is possible but it is computationally burdensome due to the nonlinearity of the estimator when there is truncation. We propose a two-step procedure that combines maximum likelihood and least squares estimation and a modified two-step procedure that combines maximum likelihood and minimum-distance estimation. In both instances, the estimators are consistent. However, when multicollinearity arises in the second step of the estimation, the modified two-step procedure is superior at identifying the model regardless of the severity of the truncation. Monte Carlo simulations show good finite sample properties of the proposed estimators. A comparison with the current methods in the literature shows that our proposed methods are superior by delivering smaller losses and better estimators (no bias and low mean squared errors) than those from competing approaches. We illustrate our approach with the daily interval of low/high SP500 returns and find that truncation is very severe during and after the financial crisis of 2008, so OLS estimates should not be trusted and a modified two-step procedure should be implemented. Supplementary materials for this article are available online.

Sources of sodium in the lunar exosphere: Modeling using ground-based observations of sodium emission and spacecraft data of the plasma

Observations of the equatorial lunar sodium emission are examined to quantify the effect of precipitating ions on source rates for the Moon’s exospheric volatile species. Using a model of exospheric sodium transport under lunar gravity forces, the measured emission intensity is normalized to a constant lunar phase angle to minimize the effect of different viewing geometries. Daily averages of the solar Lyman α flux and ion flux are used as the input variables for photon-stimulated desorption (PSD) and ion sputtering, respectively, while impact vaporization due to the micrometeoritic influx is assumed constant. Additionally, a proxy term proportional to both the Lyman α and to the ion flux is introduced to assess the importance of ion-enhanced diffusion and/or chemical sputtering. The combination of particle transport and constrained regression models demonstrates that, assuming sputtering yields that are typical of protons incident on lunar soils, the primary effect of ion impact on the surface of the Moon is not direct sputtering but rather an enhancement of the PSD efficiency. It is inferred that the ion-induced effects must double the PSD efficiency for flux typical of the solar wind at 1 AU. The enhancement in relative efficiency of PSD due to the bombardment of the lunar surface by the plasma sheet ions during passages through the Earth’s magnetotail is shown to be approximately two times higher than when it is due to solar wind ions. This leads to the conclusion that the priming of the surface is more efficiently carried out by the energetic plasma sheet ions.

Constrained regression model selection

We propose two improved versions of the Akaike information criterion, AIC C and AIC C * , for the constrained linear and single-index models, respectively. These enhanced versions have corresponding unconstrained selection criteria as their special cases. Our Monte Carlo simulations demonstrate that AIC C and AIC C * are superior to the Akaike information criterion. Additionally, we illustrate the use of AIC C * in an empirical example and generalize AIC C * to the constrained partially linear model.

Clustering financial time series: an application to mutual funds style analysis

Classification can be useful in giving a synthetic and informative description of contexts characterized by high degrees of complexity. Different approaches could be adopted to tackle the classification problem: statistical tools may contribute to increase the degree of confidence in the classification scheme. A classification algorithm for mutual funds style analysis is proposed, which combines different statistical techniques and exploits information readily available at low cost. Objective, representative, consistent and empirically testable classification schemes are strongly sought for in this field in order to give reliable information to investors and fund managers who are interested in evaluating and comparing different financial products. Institutional classification schemes, when available, do not always provide consistent and representative peer groups of funds. A “return-based” classification scheme is proposed, which aims at identifying mutual funds’ styles by analysing time series of past returns. The proposed classification procedure consists of three basic steps: (a) a dimensionality reduction step based on principal component analysis, (b) a clustering step that exploits a robust evolutionary clustering methodology, and (c) a style identification step via a constrained regression model first proposed by William Sharpe. The algorithm is tested on a sample of Italian mutual funds and achieves satisfactory results with respect to (i) the agreement with the existing institutional classification and (ii) the explanatory power of out of sample variability in the cross-section of returns.