Neither fixed nor random: weighted least squares meta-regression

Our study revisits and challenges two core conventional meta-regression estimators: the prevalent use of‘mixed-effects’ or random-effects meta-regression analysis and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS-MRA) estimator is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias that is as good as FE-MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS-MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta-regression is likely to give practically equivalent or superior estimates to fixed-effects, random-effects, and mixed-effects meta-regression approaches. However, random-effects meta-regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the ‘true’ regression coefficient.

Methods of construction of OWA operators from data

This paper investigates the problem of obtaining the weights of the ordered weighted aggregation (OWA) operators from observations. The problem is formulated as a restricted least squares and uniform approximation problems. We take full advantage of the linearity of the problem. In the former case, a well known technique of non-negative least squares is used. In a case of uniform approximation, we employ a recently developed cutting angle method of global optimisation. Both presented methods give results superior to earlier approaches, and do not require complicated nonlinear constructions. Additional restrictions, such as degree of orness of the operator, can be easily introduced

Appropriate choice of aggregation operators in fuzzy decision support systems

Fuzzy logic provides a mathematical formalism for a unified treatment of vagueness and imprecision that are ever present in decision support and expert systems in many areas. The choice of aggregation operators is crucial to the behavior of the system that is intended to mimic human decision making. This paper discusses how aggregation operators can be selected and adjusted to fit empirical data—a series of test cases. Both parametric and nonparametric regression are considered and compared. A practical application of the proposed methods to electronic implementation of clinical guidelines is presented

The cost of granting executive stock options with strike prices adjusted by the cost of capital

Purpose – The purpose of this paper is to estimate the cost of granting executive stocks with strike prices adjusted by the cost of capital.

Design/methodology/approach – In the paper a Monte Carlo simulation approach developed in Longstaff and Schwartz is used in conjunction with the subjective valuation model developed in Ingersoll to value these executive stock options that are subject to performance hurdles.

Findings – The paper finds that standard European Black-Scholes-Merton option values overstate the true cost to the firm of granting these executive stock options. The option values also decrease with a higher dividend yield, a higher performance hurdle, a longer vesting period, and a shorter maturity.

Research limitations/implications – While the study in the paper is limited to the valuation of executive options, the methodology can be used to study incentive effects of executive stock options that have a performance hurdle.

Practical implications – The approach used in this paper to estimate the cost of granting executive stock options is a clear improvement over standard European option pricing approaches that often result in biased estimates.

Originality/value – This paper presents a first attempt to integrate the Ingersoll utility-theoretic model and the Longstaff and Schwartz least squares Monte Carlo algorithm to estimate the subjective value and the objective cost of executive stock options with a performance hurdle. This valuation approach will be useful in the study of other types of executive compensation.

OWA operators in linear regression and detection of outliers

We consider the use of Ordered Weighted Averaging (OWA) in linear regression. Our goal is to replace the traditional least squares, least absolute deviation, and maximum likelihood criteria with an OWA function of the residuals. We obtain several high breakdown robust regression methods as special cases (least median, least trimmed squares, trimmed likelihood methods). We also present new formulations of regression problem. OWA-based regression is particularly useful in the presence of outliers.

OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.

Maximum likelihood estimation for rician distributed data in analytical q-ball imaging

Analytical q-ball imaging is widely used for reconstruction of orientation distribution function (ODF) using diffusion weighted MRI data. Estimating the spherical harmonic coefficients is a critical step in this method. Least squares (LS) is widely used for this purpose assuming the noise to be additive Gaussian. However, Rician noise is considered as a more appropriate model to describe noise in MR signal. Therefore, the current estimation techniques are valid only for high SNRs with Gaussian distribution approximating the Rician distribution. The aim of this study is to present an estimation approach considering the actual distribution of the data to provide reliable results particularly for the case of low SNR values. Maximum likelihood (ML) is investigated as a more effective estimation method. However, no closed form estimator is presented as the estimator becomes nonlinear for the noise assumption of the Rician distribution. Consequently, the results of LS estimator is used as an initial guess and the more refined answer is achieved using iterative numerical methods. According to the results, the ODFs reconstructed from low SNR data are in close agreement with ODFs reconstructed from high SNRs when Rician distribution is considered. Also, the error between the estimated and actual fiber orientations was compared using ML and LS estimator. In low SNRs, ML estimator achieves less error compared to the LS estimator.

N-acetyl cysteine for depressive symptoms in bipolar disorder - a double blind, randomized, placebo-controlled trial

Background: Treatment-resistant subthreshold depression is a major problem in bipolar disorder. Both depression and bipolar disorderare complicated by glutathione depletion. We hypothesized that treatment with N-acetyl cysteine (NAC), a safe, orally bioavailable precursor of glutathione, may improve the depressive component of bipolar disorder.

Methods: A randomized, double-blind, multicenter, placebo-controlled study of individuals (n 75) with bipolar disorder in the maintenance phase treated with NAC (1 g twice daily) adjunctive to usual medication over 24 weeks, with a 4-week washout. The two primary outcomes were the Montgomery Asberg Depression Rating Scale (MADRS) and time to a mood episode. Secondary outcomes included the Bipolar Depression Rating Scale and 11 other ratings of clinical status, quality of life, and functioning.

Results: NAC treatment caused a significant improvement on the MADRS (least squares mean difference [95% confidence interval]: 8.05 [13.16, 2.95], p .002) a n d most secondary scales at end point. Benefit was evident by 8 weeks on the Global Assessment of Functioning Scale and Social and Occupational Functioning Assessment Scale and at 20 weeks on the MADRS. Improvements were lost after washout. There was no effect of NAC on time to a mood episode (log-rank test: p .968) and no significant between-group differences inadverse events. Effect sizes at end point were medium to high for improvements in MADRS and 9 of the 12 secondary readouts.

Conclusions: NAC appears a safe and effective augmentation strategy for depressive symptoms in bipolar  disorder.

Determinants of local abundance in a major radiation of Australian passerines (Aves: Meliphagoidea)

Aim  To identify the factors that contribute to variation in abundance (population density), and to investigate whether habitat breadth and diet breadth predict macroecological patterns in a suborder of passerine birds (Meliphagoidea).
Location  Australia (including Tasmania).
Methods  Mean abundance data were collated from site surveys of bird abundance (the Australian Bird Count); range size and latitudinal position data from published distribution maps; and body mass and diet breadth information from published accounts. A diversity index of habitats used (habitat breadth) was calculated from the bird census data. We used bivariate correlation and multiple regression techniques, employing two phylogenetic comparative methods: phylogenetic generalized least squares and independent contrasts.

Results  Body mass and latitude were the only strong predictors of abundance, with larger-bodied and lower-latitude species existing at lower densities. Together, however, body mass and latitude explained only 11.1% of the variation in mean abundance. Range size and habitat breadth were positively correlated, as were diet breadth and body mass. However, neither range size, nor habitat breadth and diet breadth, explained patterns in abundance either directly or indirectly.
Main conclusions  Levels of abundance (population density) in meliphagoid birds are most closely linked to body mass and latitudinal position, but not range size. As with many other macroecological analyses, we find little evidence for aspects of niche breadth having an effect on patterns of abundance. We hypothesize that evolutionary age may also have a determining effect on why species tend to be rarer (less abundant) in the tropics.

Range size-abundance relationships in Australian passerines

Aim  To investigate the relationship between geographical range size and abundance (population density) in Australian passerines.
Location  Australia (including Tasmania).
Methods   We analysed the relationship between range size and local abundance for 272 species of Australian passerines, across the whole order and within families. We measured abundance as mean and maximum abundance, and used a phylogenetic generalized least-squares regression method within a maximum-likelihood framework to control for effects of phylogeny. We also analysed the relationship within seven different habitat types.
Results  There was no correlation between range size and abundance for the whole set of species across all habitats. Analyses within families revealed some strong correlations but showed no consistent pattern. Likewise we found little evidence for any relationship or conflicting patterns in different habitats, except that woodland/forest habitat species exhibit a negative correlation between mean abundance and range size, whilst species in urban habitats exhibit a significant positive relationship between maximum abundance and range size. Despite the general lack of correlation, the raw data plots of range size and abundance in this study occupied a triangular space, with narrowly distributed species exhibiting a greater variation in abundances than widely distributed species. However, using a null model analysis, we demonstrate that this was due to a statistical artefact generated by the frequency distributions for the individual variables.
Conclusions   We find no evidence for a positive range size-abundance relationship among Australian passerines. This absence of a relationship cannot be explained by any conflicting effects introduced by comparing across different habitats, nor is it explained by the fact that large proportions of Australia are arid. We speculate that the considerable isolation and evolutionary age of Australian passerines may be an explanatory factor.

Derivative-free optimization and neural networks for robust regression

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.

FTIR microspectroscopy for rapid screening and monitoring of polyunsaturated fatty acid production in commercially valuable marine yeasts and protists

The increase in polyunsaturated fatty acid (PUFA) consumption has prompted research into alternative resources other than fish oil. In this study, a new approach based on focal-plane-array Fourier transform infrared (FPA-FTIR) microspectroscopy and multivariate data analysis was developed for the characterisation of some marine microorganisms. Cell and lipid compositions in lipid-rich marine yeasts collected from the Australian coast were characterised in comparison to a commercially available PUFA-producing marine fungoid protist, thraustochytrid. Multivariate classification methods provided good discriminative accuracy evidenced from (i) separation of the yeasts from thraustochytrids and distinct spectral clusters among the yeasts that conformed well to their biological identities, and (ii) correct classification of yeasts from a totally independent set using cross-validation testing. The findings further indicated additional capability of the developed FPA-FTIR methodology, when combined with partial least squares regression (PLSR) analysis, for rapid monitoring of lipid production in one of the yeasts during the growth period, which was achieved at a high accuracy compared to the results obtained from the traditional lipid analysis based on gas chromatography. The developed FTIR-based approach when coupled to programmable withdrawal devices and a cytocentrifugation module would have strong potential as a novel online monitoring technology suited for bioprocessing applications and large-scale production.

On exploratory factor analysis: a review of recent evidence, an assessment of current practice, and recommendations for future use

Exploratory factor analysis (hereafter, factor analysis) is a complex statistical method that is integral to many fields of research. Using factor analysis requires researchers to make several decisions, each of which affects the solutions generated. In this paper, we focus on five major decisions that are made in conducting factor analysis: (i) establishing how large the sample needs to be, (ii) choosing between factor analysis and principal components analysis, (iii) determining the number of factors to retain, (iv) selecting a method of data extraction, and (v) deciding upon the methods of factor rotation. The purpose of this paper is threefold: (i) to review the literature with respect to these five decisions, (ii) to assess current practices in nursing research, and (iii) to offer recommendations for future use. The literature reviews illustrate that factor analysis remains a dynamic field of study, with recent research having practical implications for those who use this statistical method. The assessment was conducted on 54 factor analysis (and principal components analysis) solutions presented in the results sections of 28 papers published in the 2012 volumes of the 10 highest ranked nursing journals, based on their 5-year impact factors. The main findings from the assessment were that researchers commonly used (a) participants-to-items ratios for determining sample sizes (used for 43% of solutions), (b) principal components analysis (61%) rather than factor analysis (39%), (c) the eigenvalues greater than one rule and screen tests to decide upon the numbers of factors/components to retain (61% and 46%, respectively), (d) principal components analysis and unweighted least squares as methods of data extraction (61% and 19%, respectively), and (e) the Varimax method of rotation (44%). In general, well-established, but out-dated, heuristics and practices informed decision making with respect to the performance of factor analysis in nursing studies. Based on the findings from factor analysis research, it seems likely that the use of such methods may have had a material, adverse effect on the solutions generated. We offer recommendations for future practice with respect to each of the five decisions discussed in this paper.

On the asymptotic distribution of the Dickey Fuller-GLS test statistic

In a very influential paper, Elliott et al. [Efficient tests for an autoregressive unit root. Econometrica. 1996;64:813–836] show that no uniformly most powerful test for the unit root testing problem exits, derive the relevant power envelope and characterize a family of point-optimal tests. As a by-product, they also propose a ‘generalized least squares (GLS) detrended’ version of the conventional Dickey–Fuller test, denoted DF-GLS, that has since then become very popular among practitioners, much more so than the point-optimal tests. In view of this, it is quite strange to find that, while conjectured in Elliott et al. [Efficient tests for an autoregressive unit root. Econometrica. 1996;64:813–836], so far there seems to be no formal proof of the asymptotic distribution of the DF-GLS test statistic. By providing three separate proofs, the current paper not only substantiates the required result, but also provides insight regarding the pros and cons of different methods of proof.

Effects of asenapine in bipolar I patients meeting proxy criteria for moderate-to-severe mixed major depressive episodes: a post hoc analysis

OBJECTIVE: Depression is the predominant psychosocial and suicide burden in bipolar disorder, yet there is a paucity of evidence-based treatments for bipolar depression. METHODS: This post hoc subgroup analysis of data pooled from two 3-week, randomized, placebo- and olanzapine-controlled trials (December 2004-April 2006, N = 489 and November 2004-April 2006, N = 488) examined a subgroup of patients meeting criteria for moderate-to-severe mixed major depressive episodes, defined using DSM-IV-TR criteria for mixed episodes (mania and major depression simultaneously) with a baseline Montgomery-Asberg Depression Rating Scale (MADRS) total score ≥ 20. RESULTS: Decreases in MADRS scores (least squares mean [SE]), the a priori primary outcome, were significantly greater in the asenapine group than in the placebo group from baseline to day 7 (-11.02 [1.82] vs -4.78 [1.89]; P = .0195), day 21 (-14.03 [2.01] vs -7.43 [2.09]; P = .0264), and endpoint (-10.71 [1.76] vs -5.19 [1.98]; P = .039). Decreases in MADRS scores with asenapine were significantly greater than with olanzapine from baseline to day 7 (-6.26 [1.47]; P = .0436). Decreases in Young Mania Rating Scale mean total score were greater with asenapine than with placebo or olanzapine at all time points assessed. A significantly greater reduction from baseline to day 21 in the Short Form-36 mental component summary score was observed with asenapine, but not olanzapine, compared with placebo (16.57 vs 5.97; P = .0093). Asenapine was generally well tolerated. CONCLUSIONS: These data provide support for the potential efficacy of asenapine in mixed major depressive episodes; however, these data cannot be linearly extrapolated to nonmixed major depression.