Xiao-Li Meng

Comparing correlated correlation coefficients

The purpose of this article is to provide simple but accurate methods for comparing correlation coefficients between a dependent variable and a set of independent variables. The methods are simple extensions of Dunn & Clarks (1969) work using the Fisher z transformation and include a test and confidence interval for comparing two correlated correlations, a test for heterogeneity, and a test and confidence interval for a contrast among k (>2) correlated correlations. Also briefly discussed is why the traditional Hotellings t test for comparing correlated correlations is generally not appropriate in practice

Prevalence of Mental Illness in Immigrant and Non-Immigrant U.S. Latino Groups

OBJECTIVE Although widely reported among Latino populations, contradictory evidence exists regarding the generalizability of the immigrant paradox, i.e., that foreign nativity protects against psychiatric disorders. The authors examined whether this paradox applies to all Latino groups by comparing estimates of lifetime psychiatric disorders among immigrant Latino subjects, U.S-born Latino subjects, and non-Latino white subjects. METHOD The authors combined and examined data from the National Latino and Asian American Study and the National Comorbidity Survey Replication, two of the largest nationally representative samples of psychiatric information. RESULTS In the aggregate, risk of most psychiatric disorders was lower for Latino subjects than for non-Latino white subjects. Consistent with the immigrant paradox, U.S.-born Latino subjects reported higher rates for most psychiatric disorders than Latino immigrants. However, rates varied when data were stratified by nativity and disorder and adjusted for demographic and socioeconomic differences across groups. The immigrant paradox consistently held for Mexican subjects across mood, anxiety, and substance disorders, while it was only evident among Cuban and other Latino subjects for substance disorders. No differences were found in lifetime prevalence rates between migrant and U.S.-born Puerto Rican subjects. CONCLUSIONS Caution should be exercised in generalizing the immigrant paradox to all Latino groups and for all psychiatric disorders. Aggregating Latino subjects into a single group masks significant variability in lifetime risk of psychiatric disorders, with some subgroups, such as Puerto Rican subjects, suffering from psychiatric disorders at rates comparable to non-Latino white subjects. Our findings thus suggest that immigrants benefit from a protective context in their country of origin, possibly inoculating them against risk for substance disorders, particularly if they emigrated to the United States as adults.

The EM algorithm : an old folk-song sung to a fast new tune

Celebrating the 20th anniversary of the presentation of the paper by Dempster, Laird and Rubin which popularized the EM algorithm, we investigate, after a brief historical account, strategies that aim to make the EM algorithm converge faster while maintaining its simplicity and stability (e.g. automatic monotone convergence in likelihood). First we introduce the idea of a ‘working parameter’ to facilitate the search for efficient data augmentation schemes and thus fast EM implementations. Second, summarizing various recent extensions of the EM algorithm, we formulate a general alternating expectation–conditional maximization algorithm AECM that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations. We illustrate these methods using multivariate t-models with known or unknown degrees of freedom and Poisson models for image reconstruction. We show, through both empirical and theoretical evidence, the potential for a dramatic reduction in computational time with little increase in human effort. We also discuss the intrinsic connection between EM-type algorithms and the Gibbs sampler, and the possibility of using the techniques presented here to speed up the latter. The main conclusion of the paper is that, with the help of statistical considerations, it is possible to construct algorithms that are simple, stable and fast.

Disparity in Depression Treatment Among Racial and Ethnic Minority Populations in the United States

OBJECTIVE Prior research on racial and ethnic disparities in depression treatment has been limited by the scarcity of national samples that include an array of diagnostic and quality indicators and substantial numbers of non-English-speaking individuals from minority groups. Using nationally representative data for 8,762 persons, the authors evaluated differences in access to and quality of depression treatments between patients in racial-ethnic minority groups and non-Latino white patients. METHODS Access to mental health care was assessed by past-year receipt of any mental health treatment. Adequate treatment for acute depression was defined as four or more specialty or general health provider visits in the past year plus antidepressant use for 30 days or more or eight or more specialty mental health provider visits lasting at least 30 minutes, with no antidepressant use. RESULTS For persons with past-year depressive disorder, 63.7% of Latinos, 68.7% of Asians, and 58.8% of African Americans, compared with 40.2% of non-Latino whites, did not access any past-year mental health treatment (significantly different at p<.001). Disparities in the likelihood of both having access to and receiving adequate care for depression were significantly different for Asians and African Americans in contrast to non-Latino whites. CONCLUSIONS Simply relying on present health care systems without consideration of the unique barriers to quality care that ethnic and racial minority populations face is unlikely to affect the pattern of disparities observed. Populations reluctant to visit a clinic for depression care may have correctly anticipated the limited quality of usual care.

Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm

Abstract The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic variance–covariance matrices using only the code for computing the complete-data variance–covariance matrix, the code for EM itself, and code for standard matrix operations. The basic idea is to use the fact that the rate of convergence of EM is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete-data variance–covariance matrix. We call this supplemented EM algorithm the SEM algorithm. Theory and particular examples reinforce the conclusion that the SEM alg...

The art of data augmentation

The term data augmentation refers to methods for constructing iterative optimization or sampling algorithms via the introduction of unobserved data or latent variables. For deterministic algorithms, the method was popularized in the general statistical community by the seminal article by Dempster, Laird, and Rubin on the EM algorithm for maximizing a likelihood function or, more generally, a posterior density. For stochastic algorithms, the method was popularized in the statistical literature by Tanner and Wongs Data Augmentation algorithm for posterior sampling and in the physics literature by Swendsen and Wangs algorithm for sampling from the Ising and Potts models and their generalizations; in the physics literature, the method of data augmentation is referred to as the method of auxiliary variables. Data augmentation schemes were used by Tanner and Wong to make simulation feasible and simple, while auxiliary variables were adopted by Swendsen and Wang to improve the speed of iterative simulation. In general, however, constructing data augmentation schemes that result in both simple and fast algorithms is a matter of art in that successful strategies vary greatly with the (observed-data) models being considered. After an overview of data augmentation/auxiliary variables and some recent developments in methods for constructing such efficient data augmentation schemes, we introduce an effective search strategy that combines the ideas of marginal augmentation and conditional augmentation, together with a deterministic approximation method for selecting good augmentation schemes. We then apply this strategy to three common classes of models (specifically, multivariate t, probit regression, and mixed-effects models) to obtain efficient Markov chain Monte Carlo algorithms for posterior sampling. We provide theoretical and empirical evidence that the resulting algorithms, while requiring similar programming effort, can show dramatic improvement over the Gibbs samplers commonly used for these models in practice. A key feature of all these new algorithms is that they are positive recurrent subchains of nonpositive recurrent Markov chains constructed in larger spaces.

Applications of multiple imputation in medical studies: from AIDS to NHANES

Rubins multiple imputation is a three-step method for handling complex missing data, or more generally, incomplete-data problems, which arise frequently in medical studies. At the first step, m (> 1) completed-data sets are created by imputing the unobserved data m times using m independent draws from an imputation model, which is constructed to reasonably approximate the true distributional relationship between the unobserved data and the available information, and thus reduce potentially very serious nonresponse bias due to systematic difference between the observed data and the unobserved ones. At the second step, m complete-data analyses are performed by treating each completed-data set as a real complete-data set, and thus standard complete-data procedures and software can be utilized directly. At the third step, the results from the m complete-data analyses are combined in a simple, appropriate way to obtain the so-called repeated-imputation inference, which properly takes into account the uncertainty in the imputed values. This paper reviews three applications of Rubins method that are directly relevant for medical studies. The first is about estimating the reporting delay in acquired immune deficiency syndrome (AIDS) surveillance systems for the purpose of estimating survival time after AIDS diagnosis. The second focuses on the issue of missing data and noncompliance in randomized experiments, where a school choice experiment is used as an illustration. The third looks at handling nonresponse in United States National Health and Nutrition Examination Surveys (NHANES). The emphasis of our review is on the building of imputation models (i.e. the first step), which is the most fundamental aspect of the method.

Fitting Full-Information Item Factor Models and an Empirical Investigation of Bridge Sampling

Abstract Based on item response theory, Bock and Aitken introduced a method of item factor analysis, termed full-information item factor (FIIF) analysis by Bartholomew because it uses all distinct item response vectors as data. But a limitation of their fitting algorithm is its reliance on fixed-point Gauss—Hermite quadrature, which can produce appreciable numerical errors, especially in high-dimension problems. The first purpose of this article is to offer more reliable methods by using recent advances in statistical computation. Specifically, we illustrate two ways of implementing Monte Carlo Expectation Maximization (EM) algorithm to fit a FIIF model, using the Gibbs sampler to carry out the computation for the E steps. We also show how to use bridge sampling to simulate the likelihood ratios for monitoring the convergence of a Monte Carlo EM, a strategy that is useful in general. Simulations demonstrate substantial improvement over Bock and Aitkens algorithm in recovering known factor loadings in hig...

Fast EM‐type implementations for mixed effects models

The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM‐type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the ‘working parameter’ approach to derive alternative EM‐type implementations for fitting mixed effects models, which we show empirically can be hundreds of times faster than the common EM‐type implementations. In our limited simulations, they also compare well with the routines in S‐PLUS® and Stata® in terms of both speed and reliability. The central idea of the working parameter approach is to search for efficient data augmentation schemes for implementing the EM algorithm by minimizing the augmented information over the working parameter, and in the mixed effects setting this leads to a transfer of the mixed effects variances into the regression slope parameters. We also describe a variation for computing the restricted maximum likelihood estimate and an adaptive algorithm that takes advantage of both the standard and the alternative EM‐type implementations.

To Center or Not to Center: That Is Not the Question—An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency

For a broad class of multilevel models, there exist two well-known competing parameterizations, the centered parameterization (CP) and the non-centered parameterization (NCP), for effective MCMC implementation. Much literature has been devoted to the questions of when to use which and how to compromise between them via partial CP/NCP. This article introduces an alternative strategy for boosting MCMC efficiency via simply interweaving—but not alternating—the two parameterizations. This strategy has the surprising property that failure of both the CP and NCP chains to converge geometrically does not prevent the interweaving algorithm from doing so. It achieves this seemingly magical property by taking advantage of the discordance of the two parameterizations, namely, the sufficiency of CP and the ancillarity of NCP, to substantially reduce the Markovian dependence, especially when the original CP and NCP form a “beauty and beast” pair (i.e., when one chain mixes far more rapidly than the other). The ancillarity–sufficiency reformulation of the CP–NCP dichotomy allows us to borrow insight from the well-known Basu’s theorem on the independence of (complete) sufficient and ancillary statistics, albeit a Bayesian version of Basu’s theorem is currently lacking. To demonstrate the competitiveness and versatility of this ancillarity–sufficiency interweaving strategy (ASIS) for real-world problems, we apply it to fit (1) a Cox process model for detecting changes in source intensity of photon counts observed by the Chandra X-ray telescope from a (candidate) neutron/quark star, which was the problem that motivated the ASIS strategy as it defeated other methods we initially tried; (2) a probit model for predicting latent membranous lupus nephritis; and (3) an interval-censored normal model for studying the lifetime of fluorescent lights. A bevy of open questions are presented, from the mysterious but exceedingly suggestive connections between ASIS and fiducial/structural inferences to nested ASIS for further boosting MCMC efficiency. This article has supplementary material online.