The use of matrix manipulation programs in teaching statistical methods

An array manipulation package, the Symbolic Matrix Interpretive System and Statistical Interpretive System (SMIS/SIS), is described. Using SMIS/SIS, one can declare matrices and arrays of real or randomly generated data and then manipulate the matrices using simple commands to produce virtually any desired analysis. The package, designed for use by nonprogrammers and programmers alike, features a full complement of matrix algebra operations and a smaller set of statistical functions. The package, while useful as a research tool, is especially useful in teaching statistical methods, particularly multivariate analysis in which the correspondence between mathematical formulas and program code has definite pedagogical advantages over the use of statistical program packages like SPSS, BMDP, and SAS.     

Establishing normative data for repeated cognitive assessment: A comparison of different statistical methods

Serial cognitive assessment is conducted to monitor changes in the cognitive abilities of patients over time. At present, mainly the regression-based change and the ANCOVA approaches are used to establish normative data for serial cognitive assessment. These methods are straightforward, but they have some severe drawbacks. For example, they can only consider the data of two measurement occasions. In this article, we propose three alternative normative methods that are not hampered by these problems—that is, multivariate regression, the standard linear mixed model (LMM), and the linear mixed model combined with multiple imputation (LMM with MI) approaches. The multivariate regression method is primarily useful when a small number of repeated measurements are taken at fixed time points. When the data are more unbalanced, the standard LMM and the LMM with MI methods are more appropriate because they allow for a more adequate modeling of the covariance structure. The standard LMM has the advantage that it is easier to conduct and that it does not require a Monte Carlo component. The LMM with MI, on the other hand, has the advantage that it can flexibly deal with missing responses and missing covariate values at the same time. The different normative methods are illustrated on the basis of the data of a large longitudinal study in which a cognitive test (the Stroop Color Word Test) was administered at four measurement occasions (i.e., at baseline and 3, 6, and 12 years later). The results are discussed and suggestions for future research are provided.     

CPCA: A program for principal component analysis with external information on subjects and variables

A program is described for principal component analysis with external information on subjects and variables. This method is calledconstrained principal component analysis (CPCA), in which regression analysis and principal component analysis are combined into a unified framework that allows a full exploration of data structures both within and outside known information on subjects and variables. Many existing methods are special cases of CPCA, and the program can be used for multivariate multiple regression, redundancy analysis, double redundancy analysis, dual scaling with external criteria, vector preference models, and GMANOVA (growth curve models).     

Modified Brown–Forsythe Procedure for Testing Interaction Effects in Split-Plot Designs

The standard univariate and multivariate methods are conventionally used to analyze continuous data from groups by trials repeated measures designs, in spite of being extremely sensitive to departures from the multisample sphericity assumption when group sizes are unequal. However, in the last 10 years several authors have offered alternative solutions to these tests that do not rest on this assumption. In an attempt to improve the precision of the Brown–Forsythe (BF) procedure, a new approximate degrees of freedom (df) approach is presented in this article. Unlike the BF test, the new method not only assures that the df will be always positive but also provides invariant solutions under linear transformations of the data. Monte Carlo methods are used to compare the new solution, in terms of control of Type I error rates, with the modified empirical generalized least squares and BF methods. Our extensive numerical studies show that the modified BF procedure outperformed the other two methods for a wide range of conditions.     

Some supplementary methods for the analysis of WAIS-IV index scores in neuropsychological assessment

Objectives. To develop supplementary methods for the analysis of the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) in neuropsychological assessment. Design and Methods. Psychometric. Results. The following methods are made available: (a) provision of traditional confidence intervals (CIs) on index scores, (b) expression of the endpoints of CIs as percentile ranks; (c) quantification of the number of abnormally low index scores exhibited by a case and accompanying estimate of the percentage of the normative population expected to exhibit at least this number of low scores; (d) quantification of the reliability and abnormality of index score deviations from an individual's index score mean (thereby offering an alternative to the pairwise approach to index score comparisons available in the WAIS-IV manual); (e) provision of CIs on an individual's deviation scores or pairwise difference scores, (f) estimation of the percentage of the normative population expected to exhibit at least as many abnormal deviations or abnormal pairwise differences as a case; and (g) calculation of a case's Mahalanobis distance index (MDI), thereby providing a multivariate estimate of the overall abnormality of an index score profile. With the exception of the MDI, all the methods can be applied using tables provided in this paper. However, for ease and speed of application, and to reduce the possibility of clerical error, all the methods have also been implemented in a computer program. Conclusions. The methods are useful for neuropsychological interpretation of the WAIS-IV.     

Robust tests for multivariate factorial designs under heteroscedasticity

The question of how to analyze several multivariate normal mean vectors when normality and covariance homogeneity assumptions are violated is considered in this article. For the two-way MANOVA layout, we address this problem adapting results presented by Brunner, Dette, and Munk (BDM; 1997) and Vallejo and Ato (modified Brown-Forsythe [MBF]; 2006) in the context of univariate factorial and split-plot designs and a multivariate version of the linear model (MLM) to accommodate heterogeneous data. Furthermore, we compare these procedures with the Welch-James (WJ) approximate degrees of freedom multivariate statistics based on ordinary least squares via Monte Carlo simulation. Our numerical studies show that of the methods evaluated, only the modified versions of the BDM and MBF procedures were robust to violations of underlying assumptions. The MLM approach was only occasionally liberal, and then by only a small amount, whereas the WJ procedure was often liberal if the interactive effects were involved in the design, particularly when the number of dependent variables increased and total sample size was small. On the other hand, it was also found that the MLM procedure was uniformly more powerful than its most direct competitors. The overall success rate was 22.4% for the BDM, 36.3% for the MBF, and 45.0% for the MLM.     

How to perform multiblock component analysis in practice

To explore structural differences and similarities in multivariate multiblock data (e.g., a number of variables have been measured for different groups of subjects, where the data for each group constitute a different data block), researchers have a variety of multiblock component analysis and factor analysis strategies at their disposal. In this article, we focus on three types of multiblock component methods—namely, principal component analysis on each data block separately, simultaneous component analysis, and the recently proposed clusterwise simultaneous component analysis, which is a generic and flexible approach that has no counterpart in the factor analysis tradition. We describe the steps to take when applying those methods in practice. Whereas plenty of software is available for fitting factor analysis solutions, up to now no easy-to-use software has existed for fitting these multiblock component analysis methods. Therefore, this article presents the MultiBlock Component Analysis program, which also includes procedures for missing data imputation and model selection.     

Factors Underlying the Psychological and Behavioral Characteristics of Office of Strategic Services Candidates: The Assessment of Men Data Revisited

During World War II, the Office of Strategic Services (OSS), the forerunner of the Central Intelligence Agency, sought the assistance of clinical psychologists and psychiatrists to establish an assessment program for evaluating candidates for the OSS. The assessment team developed a novel and rigorous program to evaluate OSS candidates. It is described in Assessment of Men: Selection of Personnel for the Office of Strategic Services (OSS Assessment Staff, 1948). This study examines the sole remaining multivariate data matrix that includes all final ratings for a group of candidates (n = 133) assessed near the end of the assessment program. It applies the modern statistical methods of both exploratory and confirmatory factor analysis to this rich and highly unique data set. An exploratory factor analysis solution suggested 3 factors underlie the OSS assessment staff ratings. Confirmatory factor analysis results of multiple plausible substantive models reveal that a 3-factor model provides the best fit to these data. The 3 factors are emotional/interpersonal factors (social relations, emotional stability, security), intelligence processing (effective IQ, propaganda skills, observing and reporting), and agency/surgency (motivation, energy and initiative, leadership, physical ability). These factors are discussed in terms of their potential utility for personnel selection within the intelligence community.     

Field Trial of a Complicated Grief Psychosocial Program for Adolescents in Occupied Palestine

The current study evaluated the new “Children and Grief” program for Palestinian adolescents (n = 158), aged 10–18, referred to counselors for complicated grief. A mixed methods quasi-experimental design involved non-randomized intervention group (n = 79), waitlist (n = 79), and measures of program fidelity and cost. Traumatic loss was identified from case files. Standardized measures assessed complicated grief, posttraumatic stress, and depression at pre and post-test. Interviews of 9 adolescents and 9 presenters explored subjective experience of program delivery. Analysis involved multivariate analysis of variance (MANOVA) and quasi-qualitative analysis of interviews. A large effect size was found for reduced complicated grief. Randomized control trials, longitudinal research, and studies that explore the impact of martyrdom on coping with grief are needed.     

Implementation of nonparametric multivariate statistics with S

Multivariate nonparametric statistical methods have not been widely used by psychologists. One reason for this may have been that the usual general-purpose packages do not provide easy implementation of these methods. In this article, we briefly describe the multivariate extensions of the sign, signed-rank, and rank-sum tests and use S, a programming environment for data analysis, to implement these statistical procedures. Three numerical examples are used to illustrate the flexibility and efficiency of these computations in S.     

Multiple Imputation for Multivariate Missing-Data Problems: A Data Analyst's Perspective

Analyses of multivariate data are frequently hampered by missing values. Until recently, the only missing-data methods available to most data analysts have been relatively ad1 hoc practices such as listwise deletion. Recent dramatic advances in theoretical and computational statistics, however, have produced anew generation of flexible procedures with a sound statistical basis. These procedures involve multiple imputation (Rubin, 1987), a simulation technique that replaces each missing datum with a set of m > 1 plausible values. The rn versions of the complete data are analyzed by standard complete-data methods, and the results are combined using simple rules to yield estimates, standard errors, and p-values that formally incorporate missing-data uncertainty. New computational algorithms and software described in a recent book (Schafer, 1997a) allow us to create proper multiple imputations in complex multivariate settings. This article reviews the key ideas of multiple imputation, discusses the software programs currently available, and demonstrates their use on data from the Adolescent Alcohol Prevention Trial (Hansen & Graham, 199 I).     

Modeling on the simulation writer interactive program

The Simulation Writer Interactive Program (SWIP) is an extension of the Michigan Experimental Simulation Supervisor program series, and is designed to permit individuals who are not skilled programmers to create numerical simulation models, primarily for instructional purposes. SWIP elicts from the user information about the manipulable (independent), central (intermediate), and observable (dependent) variables in the user’s model, as well as any necessary tables and control information. A powerful editor is available within SWIP for making modifications. SWIP deduces the structure of the user’s model from the information about the variables, and produces an interpreted version of the model which is used to generate simulated data. A variety of model structures are possible in SWIP, including multivariate models, models for repeated measures experiments, and timeseries models. A context-dependent question-answering facility is also available.     

A reanalysis of the influence of a "friendly visitor" program

A paper in the American Journal of Community Psychology (AJCP), by Reinke, Holmes, and myself, reported the results of a study of the influence of a friendly visitor program on the cognitive functioning and morale of elderly individuals. The program was reported to have had a significant multivariate effect on a combination of cognitive and morale measures and significant univariate effects on memory, self-perceived health, and activity director's ratings. Being intrigued by the memory finding, I conducted a follow-up study to further investigate the effect of a visitation program on cognitive functioning. In this second study the dependent measures included all of the cognitive variables included in the original study as well as some additional memory variables. The visitation program in the follow-up study had no effect on any of these measures. As a result of my failure to obtain a significant memory effect such as that reported in Reinke et al. (1981), I reanalyzed the data from the original study. In my reanalysis, the only significant effect was a borderline univariate effect for self-perceived health; the multivariate effect did not approach significance. On the basis of my inability to produce the results reported in Reinke et al. when I reanalyzed the original data, I must conclude that the friendly visitor program did not have the effects attributed to it in the original report.     

Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features

Homogeneity analysis, or multiple correspondence analysis, is usually applied tok separate variables. In this paper we apply it to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological survey is presented.This research was partly supported by SWOV (Institute for Road Safety Research) in Leidschendam, The Netherlands.     

Drop Out from Behavioral Management Training Programs for ADHD: A Prospective Study

To investigate dropout from parenting programs for disruptive behavior disorders, we followed 18 clients prospectively from the beginning of a manualized treatment program to three month follow-up. Using qualitative and quantitative methods, we then compared those who dropped out of the program with those who completed it. We found that in general, those participants who dropped out of the program were parents of children with more disturbed behavior, who perceived their children to be more difficult than others, and who experienced more subjective parenting stress. Those who dropped out were also not convinced that the strategies proposed in the program to help manage their children were useful. On the other hand, those who completed the program reported a determination to persevere with the strategies which they saw as assisting them to re-establish positive relationships with their adolescent children. The findings are discussed in the context of how manualized programs might be modified to increase retention.     

Practical Considerations and Alternative Research Methods for Evaluating HR Programs

Program evaluation methods capitalizing on quasi-experimental designs are introduced as useful alternatives for evaluating human resources (HR) programs such as selection systems, training courses, performance measurement systems, and 360 degree feedback. A case study is presented to illustrate the benefits of program evaluation methods for evaluating HR programs. In addition, several post-hoc considerations that often moderate results from HR evaluations are described. It is suggested that when these considerations are addressed, quasi-experimental program evaluation methods provide a promising tool for demonstrating bottom line impact of HR initiatives.     

Robust principal components: A generalized variance perspective

This article compares several methods for performing robust principal component analysis, two of which have not been considered in previous articles. The criterion here, unlike that of extant articles aimed at comparing methods, is how well a method maximizes a robust version of the generalized variance of the projected data. This is in contrast to maximizing some measure of scatter associated with the marginal distributions of the projected scores, which does not take into account the overall structure of the projected data. Included are comparisons in which distributions are not elliptically symmetric. One of the new methods simply removes outliers using a projection-type multivariate outlier detection method that has been found to perform well relative to other outlier detection methods that have been proposed. The other new method belongs to the class of projection pursuit techniques and differs from other projection pursuit methods in terms of the function it tries to maximize. The comparisons include the method derived by Maronna (2005), the spherical method derived by Locantore et al. (1999), as well as a method proposed by Hubert, Rousseeuw, and Vanden Branden (2005). From the perspective used, the method by Hubert et al. (2005), the spherical method, and one of the new methods dominate the method derived by Maronna.     

Observations on the design and specification of a wrist-worn human activity monitoring system

Monitoring motor activity provides an important index of sleep, rest, and activity in field studies of sustained operations, shift-work schedules, and sleep deprivation. Poor results with previous methods led to development of a program to design a technologically improved monitoring system. In this 3-year program, specific issues were examined, ranging from the empirical characteristics of the wrist-movement signal and transduction methods to conversion of that signal to a useful index of motility. In this report, we discuss the several design issues encountered as well as observations, conclusions, and resulting specifications. The product of this program is a microprocessor-controlled, self-contained activity recording system, with 16K of digital storage and an operating life of over 30 days. The Walter Reed Activity Monitoring System is designed to examine further the behavioral and physiological correlates of activity.     

Community policing to take guns off the street

Despite the difficulty in current attempts to precisely measure gun density or availability (Cook, 1991), there can be little doubt from research that firearm availability does impact the homicide and other violent crime rates. There is nonetheless a dearth of information regarding specific police strategies for reducing gun violence (Reiss & Roth, 1993). Describing one component of the Weed and Seed strategy in Kansas City, Missouri, this article examines an innovative approach with this goal as the primary focus. Specific questions addressed were (1) whether the police can successfully gain community support in obtaining immediate, pertinent information about illegal gun carrying, and (2) whether the police can successfully use that information to seize illegally carried guns. The fact that this program did not produce the desired gun tips or gun arrests may be useful for other jurisdictions seeking new strategies by both identifying a number of potential problems and suggesting areas for improvement.