A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Self-selection biases in correlational studies based on questionnaires

It is commonly held that even where questionnaire response is poor, correlational studies are affected only by loss of degrees of freedom or precision. We show that this supposition is not true. If the decision to respond is correlated with a substantive variable of interest, then regression or analysis of variance methods based upon the questionnaire results may be adversely affected by self-selection bias. Moreover such bias may arise even where response is 100%. The problem in both cases arises where selection information is passed to the score indirectly via the disturbance or individual effects, rather than entirely via the observable explanatory variables. We suggest tests for the ensuing self-selection bias and possible ways of handling the ensuing problems of inference.The author would like to thank members of the Psychology Department at UWA for references on the illustrative example, namely the effects of sex-stereotyping on achievements in mathematics; thanks are also due to the anonymous reviewers whose comments resulted in material improvements to the paper.     

Inferential procedures for multifaceted coefficients of generalizability

A two-facet measurement model with broad application in the behavioral sciences is identified, and its coefficient of generalizability (CG) is examined. A normalizing transformation is proposed, and an asymptotic variance expression is derived. Three other multifaceted measurement models and CGs are identified, and variance expressions are presented. Next, an empirical investigation of the procedures follows, and it is shown that, in most cases, Type I error control in inferential applications is precise, and that the estimates are relatively efficient compared with the correlation coefficient. Implications for further research and for practice are noted. In an Appendix, four additional models, CGs, and variance expressions are presented.The research reported herein formed part of a doctoral dissertation conducted by Marsha Schroeder (Schroeder, 1986), under the direction of Ralph Hakstian, at the University of British Columbia. We acknowledge with thanks the contributions to this research of Todd Rogers and James Steiger. We are also very indebted to an mous reviewer who provided some important clarifications in connection with two of the models considered. Some support for this research was provided by a grant to Ralph Hakstian from the Natural Sciences and Engineering Research Council of Canada.     

Testing for independence between pairs of autocorrelated binomial data sequences

A problem arises in analyzing the existence of interdependence between the behavioral sequences of two individuals: tests involving a statistic such as chi-square assume independent observations within each behavioral sequence, a condition which may not exist in actual practice. Using Monte Carlo simulations of binomial data sequences, we found that the use of a chi-square test frequently results in unacceptable Type I error rates when the data sequences are autocorrelated. We compared these results to those from two other methods designed specifically for testing for intersequence independence in the presence of intrasequence autocorrelation. The first method directly tests the intersequence correlation using an approximation of the variance of the intersequence correlation estimated from the sample autocorrelations. The second method uses tables of critical values of the intersequence correlation computed by Nakamuraet al. (J. Am. Stat. Assoc., 1976,71, 214–222). Although these methods were originally designed for normally distributed data, we found that both methods produced much better results than the uncorrected chi-square test when applied to binomial autocorrelated sequences. The superior method appears to be the variance approximation method, which resulted in Type I error rates that were generally less than or equal to 5% when the level of significance was set at .05.     

Safety of micro-mobility: Riders’ psychological factors and risky behaviors of cargo TTWs in China

Cargo two- or three-wheeled vehicles (TTWs), as a new form of micro-mobility, have become a popular mode of urban cargo transportation in China. Cargo TTW riders’ psychological factors and risky behaviors lead to a number of accidents. A questionnaire is designed by comprehensively considering these factors and behaviors of cargo TTW riders that includes eleven risk factors to quantitatively analyze the risky behaviors based on structural equation modeling (SEM). One thousand three hundred nineteen participants reported using cargo TTWs on a questionnaire distributed across the country. The characteristics of riding behavior data are analyzed to verify the three-layer risk theoretical framework of “Psychological factors (Personality traits/specific factors) - Psychological acceptability of risks (confidence/perception/attitude) - Risky behaviors”. The results show that anger has a strong direct effect on riding violations, while normlessness and altruism have a direct effect on riding errors. Workload has a weak but direct effect on risky behaviors, and riding feedback has a weak and mixed effect. In addition, high-risk groups are identified by analysis of variance (ANOVA) with rider population attributes. These quantitative analyses can help guide safety countermeasures to mitigate accidents involving cargo TTWs.     

Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995–1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.     

Studies of Work: Achieving Hybrid Disciplines in IT Design and Management Studies

We explore the relationship between ethnomethodology (EM), ethnography and the needs of managers and designers in industry, considering both ethnomethodological and industrial criteria of adequacy and explicating their relationship through the concept of “audience.” We examine a range of studies in this light, with a view to their possible candidacy as hybrid studies and identify three types of application of EM studies of work: market research, design, and business improvement. Application in the first of these fields we dub “anthropological,” in that it consists in studying and reporting back on the ways of exotic people (customers). This is the application most commonly found in studies of computer supported co-operative work (CSCW). A second CSCW application, “technomethodology,” involves the introduction of EM concepts into the design process. A further application, dubbed “holding-up-a-mirror,” involves reporting back to members of a setting upon their own activities. We argue that technomethodology and holding-up-a-mirror both offer the possibility of creating hybrid disciplines. We consider the objection that improvement and design involve the introduction of value judgements that threaten the practice of EM indifference, arguing that action research can serve as a guarantee of unique adequacy (UA) by testing the researcher’s understanding as analysis in action in the setting. Furthermore, the standard of reporting required by the UA criterion contributes to the effectiveness of proposed solutions.     

Altering the Shape of Punishment Distributions Affects Decision Making in a Modified Iowa Gambling Task

Neuroeconomics research has shown that preference for gambling is altered by the statistical moments (mean, variance, and skew) of reward and punishment distributions. Although it has been shown that altered means can affect feedback‐based decision making tasks, little is known if the variance and skew will have an effect on these tasks. To investigate, we systematically controlled the variance (high, medium, and low) and skew (negative, zero, and positive) of the punishment distributions in a modified version of the Iowa Gambling Task. The Iowa Gambling Task has been used extensively in both academic and clinical domains to understand decision making and diagnose decision making impairments. Our results show that decision making can be altered by an interaction of variance and skew. We found a significant decrease over trials in choices from the decks with high variance and asymmetrically skewed punishments and from the decks with low variance and zero skew punishments. These results indicate that punishment distribution shape alone can change human perception of what is optimal (i.e., mean expected outcome) and may help explain what guides our day‐to‐day decisions. Copyright © 2013 John Wiley & Sons, Ltd.     

Sex Differences in Variability in Vocational Interests: Evidence from Two Large Samples

Greater male variability has been established in cognitive abilities and physical attributes. This study investigated sex differences in variability in vocational interests with two large samples (N > 40 000 and N > 70 000). The results show that although men varied more in Realistic and Enterprising interests, women varied more in Artistic and Conventional interests. These differences in variability had considerable influence on the female–male tail ratios in vocational interests that have been found to contribute to reported gender disparities in certain fields of work and academic disciplines. Moreover, differences in means and variability interacted non‐linearly in shaping tail‐ratio imbalances. An age‐specific analysis additionally revealed that differences in variability diminished with age: Older samples showed smaller differences in variance in Realistic, Artistic, and Social interests than younger samples. Thus, I found no evidence that greater male variability applies for vocational interests in general. Copyright © 2015 European Association of Personality Psychology