多元整合元分析法评介

在传统元分析中, 每个研究只能提取一个效果量, 以满足各效果量相互独立的条件。若出现单个研究多效果量的情况, 就需要采用多元元分析技术予以处理。多元元分析主要包括多元线性模型法和多元整合法, 其中, 多元整合法是应用最为广泛的一种方法, 可较为有效地解决多效果量非独立性问题, 还可借助传统元分析的固定效应模型和混合效应模型进行统计分析。但多元整合法在应用中还存在着统计软件的开发问题、同质性Q检验显著性的稳定问题、不同质混合效果量的同质性检验的可行性问题。     

Multivariate strategies in functional magnetic resonance imaging

We discuss aspects of multivariate fMRI modeling, including the statistical evaluation of multivariate models and means for dimensional reduction. In a case study we analyze linear and non-linear dimensional reduction tools in the context of a 'mind reading' predictive multivariate fMRI model.     

Models for multivariate paired comparison experiments with ties

Three models for multivariate paired comparison experiments are developed using the Farlie-Gumbel-Morgenstern approach to constructing multivariate distributions. Model 3 is a direct extension of the multivariate paired comparison model with no ties due to Davidson and Bradley.     

The mixed model for multivariate repeated measures: validity conditions and an approximate test

Repeated measures on multivariate responses can be analyzed according to either of two models: a doubly multivariate model (DMM) or a multivariate mixed model (MMM). This paper reviews both models and gives three new results concerning the MMM. The first result is, primarily, of theoretical interest; the second and third have implications for practice. First, it is shown that, given multivariate normality, a condition called multivariate sphericity of the covariance matrix is both necessary and sufficient for the validity of the MMM analysis. To test for departure from multivariate sphericity, the likelihood ratio test can be employed. The second result is an approximation to the null distribution of the likelihood ratio test statistic, useful for moderate sample sizes. Third, for situations satisfying multivariate normality, but not multivariate sphericity, a multivariate correction factor is derived. The correction factor generalizes Box's and can be used to construct an adjusted MMM test.I am grateful to an anonymous referee for carefully attending to the mathematical details of this paper.     

Multivariate analysis with linearizable regressions

We study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables. This class seems more realistic than the multivariate normal or the elliptical distributions, and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis. In particular a two-stage procedure which first scales the variables optimally, and then fits a simultaneous equations model, is studied in detail and is shown to have some desirable properties.     

Effects of Covariance Heterogeneity on Three Procedures for Analyzing Multivariate Repeated Measures Designs

Empirical Type I error and power rates were estimated for (a) the doubly multivariate model, (b) the Welch-James multivariate solution developed by Keselman, Carriere and Lix (1993) using Johansen's results (1980), and for (c) the multivariate version of the modified Brown-Forsythe (1974) procedure. The performance of these procedures was investigated by testing within- blocks sources of variation in a multivariate split-plot design containing unequal covariance matrices. The results indicate that the doubly multivariate model did not provide effective Type I error control while the Welch-James procedure provided robust and powerful tests of the within-subjects main effect, however, this approach provided liberal tests of the interaction effect. The results also indicate that the modified Brown-Forsythe procedure provided robust tests of within-subjects main and interaction effects, especially when the design was balanced or when group sizes and covariance matrices were positively paired.     

The Study Of Effects In Manova

A particular strategy for investigating effects resulting from a MANOVA is proposed. The strategy involves multiple two-group multivariate analyses. The two groups result from considering multivariate pairwise group contrasts or multivariate complex group contrasts. Assuming a given two-group analysis yields real effects, the resultant single linear discriminant function (LDF) may be studied. A rationale based on a transformation of LDF weights, due to V. Y. Urbakh, is recommended for assessing variable relative contribution. The analysis strategy is described in detail and illustrated with real data sets.     

Generating multivariate data from nonnormal distributions: Mihal and Barrett revisited

An algorithm described by Graybill (1969) factors a population correlation matrix, R, into an upper and lower triangular matrix, T and T′, such that R=T′T. The matrix T is used to generate multivariate data sets from a multinormal distribution. When this algorithm is used to generate data for nonnormal distributions, however, the sample correlations are systematically biased downward. We describe an iterative technique that removes this bias by adjusting the initial correlation matrix. R, factored by the Graybill algorithm. The method is illustrated by simulating a multivariate study by Mihal and Barrett (1976). Large-N simulations indicate that the iterative technique works: multivariate data sets generated with this approach successfully model both the univariate distributions of the individual variables and their multivariate structure (as assessed by intercorrelation and regression analyses).     

A Robust Bayesian Approach for Structural Equation Models with Missing Data

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear structural equation model with fixed covariates, robust Bayesian methods are developed for estimation and model comparison. Results from simulation studies are reported to reveal the characteristics of estimation. The methods are illustrated by using a real data set obtained from diabetes patients.     

Standard Errors of Multivariate Range-Corrected Validities

The multivariate rather than the univariate range correction is used for estimating unrestricted applicant population validities in many military test validity studies but not uniformly. A Monte Carlo approach compared the standard errors of range-corrected validities under various experimental conditions adhering to the assumptions underlying correction accuracy. The multivariate corrected validities had smaller standard errors than both the univariate-corrected validities and the unrestricted validities. We conclude that using the univariate correction could fail to reveal the most valid selection instrument and that the multivariate correction should be used when scores for relevant predictors are available for the unrestricted population.     

The psychology of moderate prediction : I. Experience with multiple determination

In the experiments reported here, individuals with experience in a multivariate prediction setting showed considerable moderation of subsequent univariate predictions, compared to those without such experience. We show that such moderation of prediction does not result from an abstract rule of regression to the mean; rather, it can be explained by the named error model. According to this model, missing predictors are treated as an error term, with their unknown values replaced by central tendencies. Experiment 1 demonstrates the phenomenon of moderation following multivariate experience and explores its generalization to novel predictors. Moderation occurs even for a perfectly valid predictor, contrary to normative application of a regression strategy. Experiment 2 shows that the phenomenon depends on lack of correlation among the multivariate predictors. This accords with the named error model, which asserts that if missing predictors are perceived to be correlated with the available predictor, their unknown values are replaced by extreme values rather than by central tendencies. Experiment 3 shows that mere exposure to additional predictors has no effect; experience in which multiple predictors are used to make numerical predictions seems to be necessary in order to obtain subsequent moderation. In Experiment 4, feedback is introduced. Moderation of prediction results even without prior multivariate experience. However, multivariate experience produces the moderation effect much more quickly.     

Dynamic and Static Balancing Ability of Preschool Children

Performance differences in dynamic and static balance ability of 150 preschool Ss aged 3,4, and 5 yr. were studied. Ss performed 4 balance-beam tasks and 2 balance-board tasks. An Age by Sex (3 × 2) factorial, design employing both univariate and multivariate ANOVA techniques were the statistics used. For both dynamic and static balance Age was highly significant, and the use of multivariate ANOVA indicated significant sex differences on the static balance tasks. The appropriateness of multivariate techniques where more than one dependent variable is measured on the same population was discussed, and the need to take into account the relationship between these variables when analyzing the data was noted.     

Design and analysis considerations in research.

This short note emphasizes the need for multivariate analysis when multiple correlated dependent variables are used in a study. The use of multivariate analysis and the consequences of not using it are illustrated in relation to a previously published study that used self-concept subscales as dependent variables.     

Multidimensional scale types and invariant multivariate statistics

This paper proposes an extension of the definition of one‐dimensional ordinal, interval, ratio, difference and absolute scales to the multidimensional case. The connection between measurement structures and statistical structures suggested in a previous paper is also extended to the multivariate case, and examples of invariance properties of multivariate functions and statistics are discussed.     

Some symmetric,invariant measures of multivariate association

A distinction is drawn between redundancy measurement and the measurement of multivariate association for two sets of variables. Several measures of multivariate association between two sets of variables are examined. It is shown that all of these measures are generalizations of the (univariate) squared-multiple correlation; all are functions of the canonical correlations, and all are invariant under linear transformations of the original sets of variables. It is further shown that the measures can be considered to be symmetric and are strictly ordered for any two sets of observed variables. It is suggested that measures of multivariate relationship may be used to generalize the concept of test reliability to the case of vector random variables.     

A Counterexample To Miller And Farr's Algorithm For The Index Of Redundancy

Miller and Farr's algorithm for the index of redundancy is shown to be incorrect by means of a counterexample. It is also argued that their interpretation of the proportion of the total variance in one multivariate response explained by another multivariate response with respect to a given component of the first response is misleading.     

Power comparison of new tests to analyze repeated measures data

This work compares the sensitivity of five modern analytical techniques for detecting the effects of a design with measures which are partially repeated when the assumptions of the traditional ANOVA approach are not met, namely: the approach of the mixed model adjusted by means of the SAS Proc Mixed module, the Bootstrap-F approach, the Brown-Forsythe multivariate approach, the Welch-James multivariate approach and Welch-James multivariate approach with robust estimators. Previously, Livacic-Rojas, Vallejo and Fernández found out that these methods are comparable in terms of their Type I error rates. The results obtained suggest that the mixed model approach, as well as the Brown-Forsythe and Welch-James approaches, satisfactorily controlled the Type II error rates corresponding to the main effects of the measurement occasions under most of the conditions assessed.     

NORMUL: A FORTRAN program for testing multivariate normality

NORMUL is a FORTRAN program that provides a test of whether data conform to a multivariate normal distribution. The method involves correlating Mahalanobis distances for observed data with expected chi-square percentile values. This obtained correlation is then tested for significance by empirically evaluating the probability of its belonging to a distribution generated from multivariate normal data.