Some simple procedures for handling missing data in multivariate analysis

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with missing value correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.This research was supported by NIH Special Research Resources Grant RR-3. The author expresses his gratitude to Robert I. Jennrich and the referees for their suggestions.     

External analyses of preference models

Using Carroll's external analysis, several studies have found that unfolding models account for more, although seldom significantly more, variance in preferences than Tucker's vector model. In studies of sociometric ratings and political preferences, the unfolding model again rarely outpredicted the vector model by a significant amount. Yet on cross-validation, the unfolding model consistently accounted for more variance. Results suggest that sometimes significance tests are less sensitive than cross-validation procedures to the small but consistent superiority of the unfolding model. Future researchers may wish to use significance tests and cross-validation techniques in comparing models.     

Monotonic weighted power transformations to additivity

A class of monotonic transformations which generalize the power transformation is fit to the independent and dependent variables in multiple regression so that the resulting additive relationship is optimized. This is achieved by minimizing a quadratic fitting criterion with linear inequality constraints on the parameters. A quadratic programming technique which works reliably and quickly in this application is outlined. Some examples of the analysis of artificial and real data are offered.This work was supported by National Research Council of Canada Grant APA 320 to the author.     

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.Preparation of this article was supported in part by PSC-CUNY Grant #665365 to Roger E. Millsap and by National Institute of Aging Grant NIA-AG03164-03 to William Meredith. The authors thank John Nesselroade for permitting the use of the data presented in the article.     

Convergence theory for partial images and revision of the definition of total images

Guttman's assumption underlying his definition of “total images” is rejected: Partial images are not generally convergent everywhere. Even divergence everywhere is shown to be possible. The convergence type always found on partial images is convergence in quadratic mean; hence, total images are redefined as quadratic mean-limits. In determining the convergence type in special situations, the asymptotic properties of certain correlations are important, implying, in some cases, convergence almost everywhere, which is also effected by a countable population or multivariate normality or independent variables. The interpretations of a total image as a predictor, and a “common-factor score”, respectively, are made precise.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

Cross-cultural consistency of coding the strange situation

This study tested whether or not cross-cultural differences in attachment classification distributions result from systematic differences in coding practices. First, we investigated whether or not the interactive scales have been scored consistently in several different cross-cultural samples. Second, the Richters, Waters, and Vaughn (1988) functions were applied to address the question of whether or not attachment classifications were consistently based upon the same pattern of interactive behaviors. Third, cross-cultural coding differences were described from a multivariate perspective. Data sets from seven investigators in six countries were available for analysis. Analyses on this “multinational data set” revealed that except for distance interaction, the interactive scales in the two reunion episodes were scored in accordance with the original coding rules. Furthermore, a good to reasonable agreement appeared to exist between the original classifications and those computed by the functions, except for infants older than 20 months of age. The multivariate principal component analysis showed that classification groups across cultures were more alike than cultures across classification groups. Our data showed, therefore, that attachment classifications have been consistently coded across cultures.     

A simulated annealing methodology for clusterwise linear regression

In many regression applications, users are often faced with difficulties due to nonlinear relationships, heterogeneous subjects, or time series which are best represented by splines. In such applications, two or more regression functions are often necessary to best summarize the underlying structure of the data. Unfortunately, in most cases, it is not known a priori which subset of observations should be approximated with which specific regression function. This paper presents a methodology which simultaneously clusters observations into a preset number of groups and estimates the corresponding regression functions' coefficients, all to optimize a common objective function. We describe the problem and discuss related procedures. A new simulated annealing-based methodology is described as well as program options to accommodate overlapping or nonoverlapping clustering, replications per subject, univariate or multivariate dependent variables, and constraints imposed on cluster membership. Extensive Monte Carlo analyses are reported which investigate the overall performance of the methodology. A consumer psychology application is provided concerning a conjoint analysis investigation of consumer satisfaction determinants. Finally, other applications and extensions of the methodology are discussed.     

The Italian Red Brigades and the structure and dynamics of terrorist groups

One of the problems in dealing with terrorism is that we have virtually no access to individual terrorists; only their actions are visible. The founders of the Italian terrorist group, the Red Brigades, on the other hand, have written about their experiences and have exhaustively explained their motivations. The author’s premise is that these autobiographies and her interviews with several of the group’s members give us access to the unconscious processes involved in the formation and operation of the group. After terrorist attacks, it is natural to ask whether the terrorists’ capacity for collective violence is an indication of personal pathology. This paper argues that the relevant pathology in the terrorist enterprise is not that of the individual but that of the group. Relying on the theories of groups of Freud (1921), Bion (1961), Anzieu (1984) and Kaes (2007), the author argues that psychoanalytic theory is essential to understanding the motivations and actions of violent groups which otherwise remain obscure. Although the discussion has been confined to one terrorist group, the author hopes that it can also be useful for understanding the unconscious dynamics of other groups structured around an ideology which mandates the destruction of human life.