Interactive versus passive dynamics and the exploratory analysis of multivariate data

In two experiments, we examined subjects’ ability to infer structure from three-dimensional data presented dynamically in interactive versus passive mode and in static scatterplots. Accuracy of estimating the number of clusters in three-dimensional data sets was measured for each of these conditions, as a function of cluster discriminability.     

Dynamic analysis of multivariate panel data with non-linear transformations

Many models for multivariate data analysis can be seen as special cases of the linear dynamic or state space model. Contrary to the classical approach to linear dynamic systems analysis, in which high-dimensional exact solutions are sought, the model presented here is developed from a social science framework where low-dimensional approximate solutions are preferred. Borrowing concepts from the theory on mixture distributions, the linear dynamic model can be viewed as a multi-layered regression model, in which the output variables are imprecise manifestations of an unobserved continuous process. An additional layer of mixing makes it possible to incorporate non-normal as well as ordinal variables.Using the EM-algorithm, we find estimates of the unknown model parameters, simultaneously providing stability estimates. The model is very general and cannot be well estimated by other estimation methods. We illustrate the applicability of the obtained procedure through an example with generated data.     

The effectiveness of dynamic graphics in revealing structure in multivariate data

Previous work by the authors showed no significant benefit for dynamic graphical presentation as opposed to static scatterplots in determining the number of data clusters present in multidimensional data sets. In the present study, subjects interactively looked for different types of structure, such as linear trends, clusters, or increases in variance of one variable, rather than discriminating number of clusters, to more closely mimic actual exploratory data-analysis features of interest. Searching for structure failed to prove significant benefits for dynamic data presentation.     

The use of APL in teaching multivariate data analysis

APL is recommended for introducing students in multivariate data analysis to computer applications of statistical formulas. Limitations and advantages of the language for this purpose are discussed, and examples of basic operations and statistical analyses are presented.     

Dynamic factor analysis of nonstationary multivariate time series

A dynamic factor model is proposed for the analysis of multivariate nonstationary time series in the time domain. The nonstationarity in the series is represented by a linear time dependent mean function. This mild form of nonstationarity is often relevant in analyzing socio-economic time series met in practice. Through the use of an extended version of Molenaar's stationary dynamic factor analysis method, the effect of nonstationarity on the latent factor series is incorporated in the dynamic nonstationary factor model (DNFM). It is shown that the estimation of the unknown parameters in this model can be easily carried out by reformulating the DNFM as a covariance structure model and adopting the ML algorithm proposed by Jöreskog. Furthermore, an empirical example is given to demonstrate the usefulness of the proposed DNFM and the analysis.     

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.     

On using multiple imputation for exploratory factor analysis of incomplete data

A simple multiple imputation-based method is proposed to deal with missing data in exploratory factor analysis. Confidence intervals are obtained for the proportion of explained variance. Simulations and real data analysis are used to investigate and illustrate the use and performance of our proposal.     

An exploratory analysis of the latent structure of process data via action sequence autoencoders

Computer simulations have become a popular tool for assessing complex skills such as problem-solving. Log files of computer-based items record the human–computer interactive processes for each respondent in full. The response processes are very diverse, noisy, and of non-standard formats. Few generic methods have been developed to exploit the information contained in process data. In this paper we propose a method to extract latent variables from process data. The method utilizes a sequence-to-sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human–computer interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes.     

Clusterwise simultaneous component analysis for analyzing structural differences in multivariate multiblock data

Many studies yield multivariate multiblock data, that is, multiple data blocks that all involve the same set of variables (e.g., the scores of different groups of subjects on the same set of variables). The question then rises whether the same processes underlie the different data blocks. To explore the structure of such multivariate multiblock data, component analysis can be very useful. Specifically, 2 approaches are often applied: principal component analysis (PCA) on each data block separately and different variants of simultaneous component analysis (SCA) on all data blocks simultaneously. The PCA approach yields a different loading matrix for each data block and is thus not useful for discovering structural similarities. The SCA approach may fail to yield insight into structural differences, since the obtained loading matrix is identical for all data blocks. We introduce a new generic modeling strategy, called clusterwise SCA, that comprises the separate PCA approach and SCA as special cases. The key idea behind clusterwise SCA is that the data blocks form a few clusters, where data blocks that belong to the same cluster are modeled with SCA and thus have the same structure, and different clusters have different underlying structures. In this article, we use the SCA variant that imposes equal average cross-products constraints (ECP). An algorithm for fitting clusterwise SCA-ECP solutions is proposed and evaluated in a simulation study. Finally, the usefulness of clusterwise SCA is illustrated by empirical examples from eating disorder research and social psychology.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Political socialization: A multivariate analysis of Swedish political attitude and preference data

Studied the socio-political attitudes and political party preferences of 532 Swedish high school students as a function of seven background variables: (I) the mother's political party preference, (2) the father's political party preference, (3) the mother's education, (4) the father's education, (5) the mother's income, (6) the father's income and (7) social class identification. Multiple classification analysis and multivariate nominal analysis were used to uncover the most important possible determinants of political socialization of the youth in both bivariate and multivariate aspects. The results showed that, of the seven predictor or background variables studied, only three had any substantial relationship with socio-political attitudes and political party preferences of the youth: (a) the mother's political party preference, (b) class identification and (c) the father's political party preference in that general order of importance. Furthermore, the superiority of the mother's political party preference over the father's political party preference was especially marked for girls. Among other things, the results also disclosed that ‘left-wing’ youth tended to be more loyal to parental political beliefs than ‘moderate’ and ‘right-wing’ youth. Several alternative explanations were proposed for these findings.     

Describing the elephant: Structure and function in multivariate data

There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain.     

Graphing multivariate data with Chernoff''s faces

Chernoff's faces is one of several icon graphics routines accessible through the SYGRAPH module available through SYSTAT Inc. SYSTAT is a very sophisticated statistics package that has been previously reviewed in the Journal of School Psychology (Roberts, D. M. JSP 25, 313–318, 1987). SYSTAT and SYGRAPH are available for both the IBM PC and the Apple Macintosh computers. The output from this example was produced with SYSTAT 5.1 on a Macintosh computer.     

Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure

Exploratory factor analysis (EFA) is used routinely in the development and validation of assessment instruments. One of the most significant challenges when one is performing EFA is determining how many factors to retain. Parallel analysis (PA) is an effective stopping rule that compares the eigenvalues of randomly generated data with those for the actual data. PA takes into account sampling error, and at present it is widely considered the best available method. We introduce a variant of PA that goes even further by reproducing the observed correlation matrix rather than generating random data. Comparison data (CD) with known factorial structure are first generated using 1 factor, and then the number of factors is increased until the reproduction of the observed eigenvalues fails to improve significantly. We evaluated the performance of PA, CD with known factorial structure, and 7 other techniques in a simulation study spanning a wide range of challenging data conditions. In terms of accuracy and robustness across data conditions, the CD technique outperformed all other methods, including a nontrivial superiority to PA. We provide program code to implement the CD technique, which requires no more specialized knowledge or skills than performing PA.     

Visualization of multivariate data: Human-factors considerations

Recent software provides new tools for visualizing multivariate data that facilitate data analysis. We focus on (1) the learnability and use of visualization systems, and (2) the perceptual and cognitive processes involved in viewing visualizations. Effective visualization systems support a broad range of user tasks and abilities, are easy to learn, and provide powerful and flexible output formatting. Effective visualizations incorporate Gestalt and other perceptual and cognitive principles that encourage more rapid, automatic processing, and less slow, controlled processing.     

An exploratory analysis of head-tilting in dogs

Animal Cognition - Little is known about head-tilts in dogs. Based on previous investigations on the head turning and the lateralised brain pattern of human speech processing in dogs, we...     

Classification by multivariate analysis

The problem considered is the use of a set of measurements on an individual to decide from which of several populations he has been drawn. It is assumed that in each population there is a probability distribution of the measurements. Principles for choosing the rule of classification are based on costs of misclassification. Optimum procedures are derived in general terms. If the measurements are normally distributed, the procedures use one discriminant function in the case of two populations and several discriminant functions in the cases of more populations. The numerical example given involves three normal populations.Sponsored in part by the Office of Naval Research.