Geometric consistency of principal component scores for high-dimensional mixture models and its application

In this article, we consider clustering based on principal component analysis (PCA) for high-dimensional mixture models. We present theoretical reasons why PCA is effective for clustering high-dimensional data. First, we derive a geometric representation of high-dimension, low-sample-size (HDLSS) data taken from a two-class mixture model. With the help of the geometric representation, we give geometric consistency properties of sample principal component scores in the HDLSS context. We develop ideas of the geometric representation and provide geometric consistency properties for multiclass mixture models. We show that PCA can cluster HDLSS data under certain conditions in a surprisingly explicit way. Finally, we demonstrate the performance of the clustering using gene expression datasets.     

Macroeconomic performance of inflation targeting in European and Asian emerging economies

The macroeconomic performance resulting from adopting an inflation targeting policy in emerging economies of Europe and Central Asia are examined. The research includes 26 countries in the period 1997–2019, with a special focus on the period 2008–2019. Our econometric analysis consists of two approaches: dynamic panel modeling and propensity score matching. The results suggest that macroeconomic performance has improved due to the inflation targeting monetary framework. We find that a policy of inflation targeting has been effective in reducing the inflation rate, inflation volatility, and GDP volatility. The results are particularly robust for the subperiod that started in 2008. Econometric results suggest that inflation targeting policy did not affect inflation persistence or GDP growth. Our results suggest that inflation targeting improves the macroeconomic performance of developing countries even when they only partially meet the standard requirements for its implementation.     

Propensity score prediction for electronic healthcare databases using super learner and high-dimensional propensity score methods

ABSTRACT

The optimal learner for prediction modeling varies depending on the underlying data-generating distribution. Super Learner (SL) is a generic ensemble learning algorithm that uses cross-validation to select among a ‘library’ of candidate prediction models. While SL has been widely studied in a number of settings, it has not been thoroughly evaluated in large electronic healthcare databases that are common in pharmacoepidemiology and comparative effectiveness research. In this study, we applied and evaluated the performance of SL in its ability to predict the propensity score (PS), the conditional probability of treatment assignment given baseline covariates, using three electronic healthcare databases. We considered a library of algorithms that consisted of both nonparametric and parametric models. We also proposed a novel strategy for prediction modeling that combines SL with the high-dimensional propensity score (hdPS) variable selection algorithm. Predictive performance was assessed using three metrics: the negative log-likelihood, area under the curve (AUC), and time complexity. Results showed that the best individual algorithm, in terms of predictive performance, varied across datasets. The SL was able to adapt to the given dataset and optimize predictive performance relative to any individual learner. Combining the SL with the hdPS was the most consistent prediction method and may be promising for PS estimation and prediction modeling in electronic healthcare databases.     

On Tests for Group Variation With a Small to Moderate Number of Groups

This paper considers a family of penalized likelihood score tests for group variation. The tests can be indexed by a measure of degrees of freedom. At one extreme, with degrees of freedom one less than the number of groups, is the usual score test for a fixed effects alternative using indicator variables for the groups, while at the other extreme, in the limit as the degrees of freedom 0, is a test closely related to a score test based on a random effects alternative. Asymptotic power comparisons are made for the tests in the family. As would be expected, different members of the family are more efficient for different alternatives. Generally the tests with smaller degrees of freedom appear to have better power than the standard test for alternatives focusing on differences among the larger groups, and lower power for alternatives focusing on differences among the smaller groups. Simulations indicate the asymptotic approximation to the distribution performs better for the tests with small degrees of freedom.     

The relationship between neighborhood racial concentration and verbal ability: An investigation using the institutional resources model

Relatively few studies examine the relationship between racial residential segregation and educational or cognitive outcomes. Using data from the National Longitudinal Study of Adolescent Health and the institutional resources model of neighborhood effects, I investigate one account of how macrostructural arrangements between race, neighborhood segregation, and school quality interact to produce inequalities in test scores. Consistent with the institutional resources model, results suggest that school quality varies across neighborhoods based, in part, on their degree of racial concentration. Indeed, school quality and other school characteristics mediate the relationship between racial concentration and verbal skills, particularly among black males. These findings have implications not only for inequalities in cognitive skills among blacks across residential space, but also between blacks and whites given high levels of residential segregation in the United States. In sum, findings illustrate yet another way in which residential segregation contributes to, and not merely reflects, racial inequalities.     

A Conditional Likelihood Ratio Test for Structural Models

This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced‐form covariance matrix. These tests are shown to be similar under weak‐instrument asymptotics when the reduced‐form covariance matrix is estimated and the errors are non‐normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local‐to‐null asymptotics, but it has better power when identification is weak.     

Covariate handling approaches in combination with dynamic borrowing for hybrid control studies

Borrowing data from external control has been an appealing strategy for evidence synthesis when conducting randomized controlled trials (RCTs). Often named hybrid control trials, they leverage existing control data from clinical trials or potentially real-world data (RWD), enable trial designs to allocate more patients to the novel intervention arm, and improve the efficiency or lower the cost of the primary RCT. Several methods have been established and developed to borrow external control data, among which the propensity score methods and Bayesian dynamic borrowing framework play essential roles. Noticing the unique strengths of propensity score methods and Bayesian hierarchical models, we utilize both methods in a complementary manner to analyze hybrid control studies. In this article, we review methods including covariate adjustments, propensity score matching and weighting in combination with dynamic borrowing and compare the performance of these methods through comprehensive simulations. Different degrees of covariate imbalance and confounding are examined. Our findings suggested that the conventional covariate adjustment in combination with the Bayesian commensurate prior model provides the highest power with good type I error control under the investigated settings. It has desired performance especially under scenarios of different degrees of confounding. To estimate efficacy signals in the exploratory setting, the covariate adjustment method in combination with the Bayesian commensurate prior is recommended.     

Causal inference with observational data: A tutorial on propensity score analysis

When treatment cannot be manipulated, propensity score analysis provides a useful way to making causal claims under the assumption of no unobserved confounders. However, it is still rarely utilised in leadership and applied psychology research. The purpose of this paper is threefold. First, it explains and discusses the application and key assumptions of the method with a particular focus on propensity score weighting. This approach is readily implementable since a weighted regression is available in most statistical software. Moreover, the approach can offer a “double robust” protection against misspecification of either the propensity score or the outcome model by including confounding variables in both models. A second aim is to discuss how propensity score analysis (and propensity score weighting, specifically) has been conducted in recent management studies and examine future challenges. Finally, we present an advanced application of the approach to illustrate how it can be employed to estimate the causal impact of leadership succession on performance using data from Italian football. The case also exemplifies how to extend the standard single treatment analysis to estimate the separate impact of different managerial characteristic changes between the old and the new manager.     

Simultaneous semi-sequential testing of dual alternatives for pattern recognition

In this paper, we propose a new nonparametric simultaneous test for dual alternatives. Simultaneous tests for dual alternatives are used for pattern detection of arsenic contamination level in ground water. We consider two possible patterns, namely, monotone shift and an umbrella-type location alternative, as the dual alternatives. Pattern recognition problems of this nature are addressed in Bandyopadhyay et al. [5], stretching the idea of multiple hypotheses tests as in Benjamini and Hochberg [6]. In the present context, we develop an alternative approach based on contrasts that helps us to detect three underlying pattern much more efficiently. We illustrate the new methodology through a motivating example related to highly sensitive issue of arsenic contamination in ground water. We provide some Monte-Carlo studies related to the proposed technique and give a comparative study between different detection procedures. We also obtain some related asymptotic results.     

Two-tailed asymptotic inferences for a proportion

This paper evaluates 29 methods for obtaining a two-sided confidence interval for a binomial proportion (16 of which are new proposals) and comes to the conclusion that: Wilson's classic method is only optimal for a confidence of 99%, although generally it can be applied when n≥50; for a confidence of 95% or 90%, the optimal method is the one based on the arcsine transformation (when this is applied to the data incremented by 0.5), which behaves in a very similar manner to Jeffreys’ Bayesian method. A simpler option, though not so good as those just mentioned, is the classic-adjusted Wald method of Agresti and Coull.