A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

Balance,Proprioception, and Gross Motor Development of Chinese Children Aged 3 to 6 Years

The authors' aim was to find the features of balance, proprioception, and gross motor development of Chinese children 3–6 years old and their correlations, provide theoretical support for promoting children's motor development, and enrich the world theoretical system of motor development. This study used a Tekscan foot pressure measurement instrument (Tekscan, Inc., Boston, MA), walking on a balance beam, Xsens 3-dimensional positional measuring system (Xsens Technologies, Enschede, the Netherlands), and Test of Gross Motor Development-2 to assess static balance, dynamic balance, knee proprioception, and levels of gross motor development (GMD) of 3- to 6-year-old children (n = 60) in Beijing. The results are as follows: children had significant age differences in static balance, dynamic balance, proprioception, and levels of GMD; children had significant gender differences in static balance, proprioception, and levels of GMD; children's static balance, dynamic balance, and proprioception had a very significant positive correlation with GMD (p < .01), but no significant correlation with body mass index.     

Who’s afraid of the big bad wolf? The interweaving of values and science

The role of values in the scientific process is widely debated. But evidence and values cannot be neatly separated. Instead, values infuse the entire scientific process, starting with the choice of research questions. Research avenues are selected based on prior beliefs about the workings of the world. In fact, informally assigned prior probabilities and normalizing constants play an essential role in distinguishing causes from correlations and ignoring irrelevant associations that would otherwise be suggested by raw data. But since these initial probabilities often have a heterogeneous pedigree – often not all that went into their formation is known or knowable – it becomes difficult to cleanly separate evidence from values. At the same time, this reality does not undermine science’s unique status in generating knowledge. This is because it is not the evidence per se generated by science, but rather the method by which science generates it, that justifies science’s privileged role.     

Photic Stimulation of Young Rats

Zajonc, Harrison, and their colleagues have recently conducted a series of studies demonstrating a positive, monotonic relation between frequency of “mere” exposure and liking for stimuli. Other studies have found either the inverted-U relation or a decrease in liking. It was proposed that an emphasis upon mere exposure may be somewhat misleading, and that a concern with degree of stimulus familiarity might be more fruitful. Conflicting forms of the exposure-liking relation seem to be potentially reconcilable if consideration is given to factors that influence the rate at which stimuli become familiar, or capable of being anticipated and represented in memory.

Two experiments using stimuli and procedures taken from Zajonc (23) yielded a positive, monotonic relation between frequency and liking. A third experiment, designed to produce greater attention to the stimuli and thus hasten familiarization, yielded an inverted-U relation. A fourth experiment used simpler verbal stimuli than the first three. This was designed to result in even faster familiarization. As expected, there was a negative relation between liking and exposure frequency.

The “frequency group” of investigators has explained the monotonic exposure effect in terms of the response competition hypothesis. However, the latter is incapable of handling a nonmonotonic relation. A reasonable alternative seems to be the expectancy arousal hypothesis (5): viz., that liking is maximum for stimuli that arouse moderately strong expectancies of either a “molar” or a “molecular” nature. Previous research (5, 6, 7, 8) has supported this hypothesis, although some of the studies are also amenable to the response competition hypothesis. A further experiment was designed to distinguish between predictions from the response competition and the expectancy arousal hypotheses. The results supported the latter.     

Synchronistic mind‐matter correlations in therapeutic practice: a commentary on Connolly (2015)

This commentary adds some ideas and refinements to the inspiring discussion in a recent paper by Connolly ( 2015 ) that makes use of a dual‐aspect framework developed by us earlier. One key point is that exceptional experiences (of which synchronicities are a special case) cannot in general be identified with experiences of non‐categorial or acategorial mental states. In fact, most exceptional experiences reported in the literature are experiences of categorial states. Conversely, there are non‐categorial and acategorial states whose experience is not exceptional. Moreover, the psychodynamics of a synchronistic experience contain a subtle mesh of interacting processes pertaining to categorial, non‐categorial and acategorial domains. We outline how this mesh may be addressed in particular cases of synchronicity described by Connolly.     

Some relationships between factors and components

The asymptotic correlations between the estimates of factor and component loadings are obtained for the exploratory factor analysis model with the assumption of a multivariate normal distribution for manifest variables. The asymptotic correlations are derived for the cases of unstandardized and standardized manifest variables with orthogonal and oblique rotations. Based on the above results, the asymptotic standard errors for estimated correlations between factors and components are derived. Further, the asymptotic standard error of the mean squared canonical correlation for factors and components, which is an overall index for the closeness of factors and components, is derived. The results of a Monte Carlo simulation are presented to show the usefulness of the asymptotic results in the data with a finite sample size.The author is indebted to anonymous referees for their comments, corrections and suggestions which have led to the improvement of this article.     

Limited information estimation and testing of discretized multivariate normal structural models

Discretized multivariate normal structural models are often estimated using multistage estimation procedures. The asymptotic properties of parameter estimates, standard errors, and tests of structural restrictions on thresholds and polychoric correlations are well known. It was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators. It is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy. A test of the overall model specification is proposed, as well as a test of the distributional specification (i.e., discretized multivariate normality). Also, the small sample performance of overall, distributional, and structural tests, as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and/or distributional misspecification. It is found that relatively small samples are needed for parameter estimates, standard errors, and structural tests. Larger samples are needed for the distributional and overall tests. Furthermore, parameter estimates, standard errors, and structural tests are surprisingly robust to distributional misspecification. This research was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grants BSO2000-0661 and BSO2003-08507 of the Spanish Ministry of Science and Technology.     

Measuring cognitive factors in speech comprehension: The value of using the Text Reception Threshold test as a visual equivalent of the SRT test

The ability to comprehend speech in noise is influenced by bottom-up auditory and top-down cognitive capacities. Separate examination of these capacities is relevant for various purposes. Speech-Reception-Threshold (SRT) tests measure an individual's ability to comprehend speech. This paper addresses the value of the Text-Reception-Threshold (TRT) test (a visual parallel of the SRT test) to assess the cognitive capacities allocated during speech comprehension. We conducted a secondary data analysis, including 87 normally-hearing adults (aged 18 to 78 years). Correlation coefficients between age, TRT, working memory (Spatial Span) and SRT were examined. The TRT and SRT correlated significantly ( r  =   0.30), supporting the value of TRT in explaining inter-individual differences in SRTs. The relations between age and TRT and between SSP and TRT were non-significant. The results indicate that the current TRT test does not fully cover the cognitive aspects relevant in speech comprehension. Adaptation of the test is required before clinical implementation can be considered.