Factor analysis by instrumental variables methods

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.     

Participants' perceptions of smartphone travel surveys

Smartphone travel surveys are becoming of central importance in collecting detailed, accurate data of people’s travel activities. As with their conventional survey counterparts, the quality of data collected through these surveys is adversely affected by participants’ non-response and resulting biases. However, little is known about the factors affecting people’s perceptions and intentions to continue participating in such surveys. Although literature has investigated the associations between individuals’ socio-demographic attributes and their likelihood of survey participation, the impact of their subjective perceptions and attitudes on their survey participation intentions and behaviour is underexplored. Hence, through a model of participants’ perceptions of smartphone travel survey applications (survey apps), this study aims to reveal such impacts and how they affect the participants’ intentions to continue participating in these surveys. In this study, a survey is designed and used to collect data in a smartphone travel survey before the participants are asked about their personal perceptions and attitudes. Partial least squares path modelling (PLS-PM) is applied to analyse the data, as it allows simultaneous estimation of the relationships between multiple latent constructs as well as the indicators of each construct. The results showed a significant, positive impact of the perceived “ease of use” and “usefulness” of the survey app as the technological medium of data collection on the participants’ “satisfaction” and “intention” to continue participating in the corresponding survey. The study also found that participants’ perceived “risk” associated with privacy concerns did not have any significant impact on their intention to continue participating in the survey.     

Tableau algorithms for factor analysis by instrumental variable methods

Simple tableau algorithms are given for the noniterative instrumental variable (FABIN 2) and two stage regression (FABIN 3) factor loading estimates of Hägglund. Corresponding generalized least squares estimates of factor covariances and unique variances are introduced. An example is given for the purpose of illustration and comparison.This research was supported by NSF Grant MCS-8301587.     

PROVIDING A LESS RESTRICTIVE ENVIRONMENT FOR PROFOUNDLY RETARDED PERSONS BY TEACHING INDEPENDENT WALKING SKILLS

A basic right of all handicapped persons is to live in the least restrictive environment possible. In this investigation, procedures were evaluated for teaching four institutionalized males with profound retardation necessary skills to increase their individual freedom of movement. Following baseline, a travel training program with a backward chaining format was implemented to teach each person to walk independently from his living area to school. Travel training included instructions, practice, praise, feedback, verbal reprimands, prompts, and edible reinforcers. Each resident began walking the entire distance to school independently during training and also began walking back to the living area, although the latter set of skills was not specifically trained. Following termination of the formal investigation, follow-up measures of 1 to 8 weeks showed the residents continued going to school independently. A survey of residential facilities in 43 states provided social validation for the seriousness of the problems associated with transporting seriously retarded persons to school. Also, time efficiency measures indicated that training independent travel resulted in reductions of staff time required in school transportation. Results were discussed in light of the potential contributions of behavior analysis in providing less restrictive environments for seriously handicapped persons.     

Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution. Supported by The Netherlands Organization for Scientific Research (NWO) by grant nr. 030-56403 for the “PIONEER” project “Subject Oriented Multivariate Analysis” to the third author. We would like to thank the anonymous referees for their valuable remarks that have improved the quality of this paper.     

A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning

Perhaps the most common criterion for partitioning a data set is the minimization of the within-cluster sums of squared deviation from cluster centroids. Although optimal solution procedures for within-cluster sums of squares (WCSS) partitioning are computationally feasible for small data sets, heuristic procedures are required for most practical applications in the behavioral sciences. We compared the performances of nine prominent heuristic procedures for WCSS partitioning across 324 simulated data sets representative of a broad spectrum of test conditions. Performance comparisons focused on both percentage deviation from the “best-found” WCSS values, as well as recovery of true cluster structure. A real-coded genetic algorithm and variable neighborhood search heuristic were the most effective methods; however, a straightforward two-stage heuristic algorithm, HK-means, also yielded exceptional performance. A follow-up experiment using 13 empirical data sets from the clustering literature generally supported the results of the experiment using simulated data. Our findings have important implications for behavioral science researchers, whose theoretical conclusions could be adversely affected by poor algorithmic performances.     

A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen’s (Psychometrika 61:109–121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models. We also provide an estimator of the variance and covariance parameters of the model, asymptotic standard errors for these, and test statistics of overall model fit. We examine this estimator via an empirical study and also via a small simulation study. Our results illustrate the greater robustness of the PIV estimator to structural misspecifications than the system-wide estimators that are commonly applied in SEMs. Kenneth Bollen gratefully acknowledges support from NSF SES 0617276, NIDA 1-RO1-DA13148-01, and DA013148-05A2. Albert Maydeu-Olivares was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grant BSO2003-08507 from the Spanish Ministry of Science and Technology. We thank Sharon Christ, John Hipp, and Shawn Bauldry for research assistance. The comments of the members of the Carolina Structural Equation Modeling (CSEM) group are greatly appreciated. An earlier version of this paper under a different title was presented by K. Bollen at the Psychometric Society Meetings, June, 2002, Chapel Hill, North Carolina.     

Analysis of Variance Models with Stochastic Group Weights

The analysis of variance (ANOVA) is still one of the most widely used statistical methods in the social sciences. This article is about stochastic group weights in ANOVA models – a neglected aspect in the literature. Stochastic group weights are present whenever the experimenter does not determine the exact group sizes before conducting the experiment. We show that classic ANOVA tests based on estimated marginal means can have an inflated type I error rate when stochastic group weights are not taken into account, even in randomized experiments. We propose two new ways to incorporate stochastic group weights in the tests of average effects – one based on the general linear model and one based on multigroup structural equation models (SEMs). We show in simulation studies that our methods have nominal type I error rates in experiments with stochastic group weights while classic approaches show an inflated type I error rate. The SEM approach can additionally deal with heteroscedastic residual variances and latent variables. An easy-to-use software package with graphical user interface is provided.     

Regularized Partial and/or Constrained Redundancy Analysis

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collinear, and the ordinary least squares estimator is poorly determined. The ridge estimation method was extended to PRA, CRA, and PCRA, where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion. It was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter. An optimal value of the ridge parameter is found by G-fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations. We thank Jim Ramsay for his insightful comments on an earlier draft of this paper. The work reported in this paper is supported by Grants 10630 from the Natural Sciences and Engineering Research Council of Canada to the first author.     

Combining standardized mean differences using the method of maximum likelihood

A maximum likelihood procedure for combining standardized mean differences based on a noncentratt-distribution is proposed. With a proper data augmentation technique, an EM-algorithm is developed. Information and likelihood ratio statistics are discussed in detail for reliable inference. Simulation results favor the proposed procedure over both the existing normal theory maximum likelihood procedure and the commonly used generalized least squares procedure.