On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

Three-dimensional perspective drawing of two-dimensional functions with microcomputers

In this paper, we present a BASIC program for Apple II series computers that allows the user to obtain perspective drawings of two-dimensional functions of known analytical expression. Also, we outline a procedure for obtaining perspective representations of two-dimensional arrays of data using the same program. The program should run on any computer with graphics mode with only slight modifications in the graphics commands.     

The Zeigarnik effect and intrinsic motivation: Are they the same?

The present study focused on delineating the parameters under which intrinsic motivation leads an individual to reengage an activity from those that result in the Zeigarnik effect. In a posttask free-choice period, participants not completing the experimental task displayed more reengagement behavior than participants completing the task (the Zeigarnik effect). When participants were also provided self-efficacious performance feedback via a prearranged competitive outcome manipulation, there was no evidence of the Zeigarnik effect, while there was support for intrinsic motivation from competent self-efficacious performance feedback. Results were discussed in terms of distinguishing between intrinsic motivation and the Zeigarnik effect as sources of reengagement motivation. It was concluded that, in the presence of self-efficacious performance feedback, the competent-incompetent impression was more salient than task-completion feedback.Preparation of this article was supported by Texas Christian University grant TCU/RF 5-23757.     

Accepting inconsistencies from the paradoxes

It has been proposed that the law of non-contradiction be revised to permit the simultaneous truth and falsity of the key sentences of the logical paradoxes, e.g., This sentence is false. In an attempt to show to what extent this bizarre suggestion of inconsistent models or truth-value gluts is a coherent suggestion it is proved that a first-order language for number theory can be semantically closed by having its own global truth predicate under some non-standard interpretation and thus that it actually can contain the Liar sentence. It is proved that in this interpretation the Liar sentence is both true and false, although not every sentence is.     

Beliefs about and experiences with battering: Women and men in two populations

A questionnaire was developed to measure beliefs about and experiences with violence in the family. Two groups of persons in two different states who had attended conferences on battered women participated in this research. Of the 177 subjects (84% women, 16% men), none of the men had been battered, yet over one-third of the women had been; more older women reported having been adult battering victims than did younger women; the women had less formal education than the men; the women in the lower educational groups were more likely to have been battered and to report fear of becoming victims; and the social service workers reported little fear of battering.     

Behavioral consequences of song learning: Discrimination of song types by male white-crowned sparrows

The functional significance of learned population differences in male song in the white-crowned sparrow was explored in natural populations using playback tests. Laboratory results have shown that learning of the population-specific song seems to take place in early life and is strongly dependent upon the nature of the auditory experience at that time. However, the varied results of recent studies make it difficult to reach a confident conclusion about the ecological functions of song learning. The present research took advantage of naturally occurring variation in the differences between songs of adjacent populations to determine a function relating degree of difference in song to intensity of territorial singing elicited. Applying a typological evaluation of syllable structure to the four segments of the song allowed a crude quantitative ranking of the differences between local songs and playback stimuli. These results, together with those of other studies, suggest a unimodal aggressive response function of males to songs of other males. A maximum response to songs slightly different from the local song environment suggests that male exclusion based upon acquired song components may contribute to the maintenance of discrete and stable song dialects.     

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.