Tests for linear trend in the smallest eigenvalues of the correlation matrix

A test for linear trend among a set of eigenvalues of a correlation matrix is developed. As a technical implementation of Cattell's scree test, this is a generalization of Anderson's test for the equality of eigenvalues, and extends Bentler and Yuan's work on linear trends in eigenvalues of a covariance matrix. The power of minimumx ² and maximum likelihood ratio tests are compared. Examples show that the linear trend hypothesis is more realistic than the standard hypothesis of equality of eigenvalues, and that the hypothesis is compatible with standard decisions on the number of factors or components to retain in data analysis.This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017. The assistance of Maia Berkane and several anonymous reviewers is gratefully acknowledged.     

Gender and projective imagination of threat in achievement and affiliation situations

In a study by Pollak and Gilligan (1982) where fantasies of violence were seen as indicative of perception of danger, women responded with more violent imagery to situations of achievement, whereas men responded with more violent imagery to affiliation situations. This indicates gender differences in motivational needs, which corresponds to modern gender development theories (e.g., Chodorow, 1978). In the present studies, the hypotheses that women fear achievement situations whereas men fear situations of affiliation were tested on Swedish samples totaling 44 men and 47 women. In Study 1, the hypothesis that violent imagery correlates with affiliation themes in the stories written by men was partly supported, whereas the hypothesis that violent imagery would be highly correlated with achievement themes in the stories written by women was not confirmed. In Study 2, no support was obtained for the hypotheses. In sum, contrary to previous studies, no substantial support was obtained for the hypothesis that women connect violent imagery with achievement situations, whereas some evidence was found for the hypothesis that men construe danger as arising from affiliation situations. The greater incidence of violence in men’s fantasy reported in previous studies was not supported in either of the two studies. The results are discussed in the context of cross-cultural differences.     

The rasch model,the law of comparative judgment and additive conjoint measurement

Relationships between the Rasch model and both the law of comparative judgment and additive conjoint measurement are discussed. The distance between the ability of Persona and the difficult of Itemi is, in the Rasch model, the baseline value corresponding to the probability thata will respond correctly toi, where this probability is interpreted as the area under a logistic curve (which is substantially equivalent to the normal curve) and is thus an application of the law of comparative judgment. Under certain assumptions, the Rasch model is also a special case of additive conjoint measurement and, properly reinterpreted, may be usefully applied in contexts other than individual differences.     

A note on parameter estimation for Lazarsfeld's latent class analysis

As the literature indicates, no method is presently available which takes explicitly into account that the parameters of Lazarsfeld's latent class analysis are defined as probabilities and are therefore restricted to the interval [0, 1]. In the present paper an appropriate transform on the parameters is performed in order to satisfy this constraint, and the estimation of the transformed parameters according to the maximum likelihood principle is outlined. In the sequel, a numerical example is given for which the basis solution and the usual maximum likelihood method failed. The different results are compared and the advantages of the proposed method discussed.     

Goodness of fit tests for paired comparison models

A goodness of fit test presented by Andersen is shown to be incorrect. The correct test is described and a re-analysis of Andersen's data is provided.     

AN OPERANT TRACKING PROCEDURE IN THE AUDITORY ASSESSMENT OF PROFOUNDLY RETARDED INDIVIDUALS

The present study investigated a discrete-trials, operant tracking and a descending-series procedure for the determination of hearing levels with profoundly retarded individuals. These individuals were previously diagnosed as untestable. Following stimulus-control training with errorless discrimination procedures, hearing levels for each individual were examined with both procedures. For P-1 and P-2, the operant tracking procedure was administered following a descending-series procedure. Both were observed to “track” their own hearing levels. For P-3, the operant tracking procedure was administered first, followed by the descending-series procedure. Although P-3 also “tracked” her own hearing level, more variable responding was observed. Nonetheless, the operant tracking procedure proved quite workable and may provide for improved hearing testing with “difficult-to-test” individuals.     

A simplified accurate algorithm for the fisher-yates exact test

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented: the algorithm is quick, simple and accurate.I am grateful to the Editor and two reviewers for a number of constructive and helpful suggestions.     

Periodicities within a fixed-interval session

Within-session periodicities in number of responses per interval and postreinforcement pauses were investigated on fixed-interval schedules of 1, 2, and 3 minutes with rats. Postreinforcement pause values and the number of responses in successive intervals were not systematically related. The direction of change of these variables from one pair of intervals to the next revealed periodicities in that the direction of change varied more than would be expected by chance. A response prevention technique used to manipulate the length of time spent responding in an interval had little effect on the postreinforcement pause value of the next interval except when only a single response was permitted in an interval. This procedure tended to reduce the postreinforcement pause value of the next interval to an abnormally low level.     

A study of algorithms for covariance structure analysis with specific comparisons using factor analysis

Several algorithms for covariance structure analysis are considered in addition to the Fletcher-Powell algorithm. These include the Gauss-Newton, Newton-Raphson, Fisher Scoring, and Fletcher-Reeves algorithms. Two methods of estimation are considered, maximum likelihood and weighted least squares. It is shown that the Gauss-Newton algorithm which in standard form produces weighted least squares estimates can, in iteratively reweighted form, produce maximum likelihood estimates as well. Previously unavailable standard error estimates to be used in conjunction with the Fletcher-Reeves algorithm are derived. Finally all the algorithms are applied to a number of maximum likelihood and weighted least squares factor analysis problems to compare the estimates and the standard errors produced. The algorithms appear to give satisfactory estimates but there are serious discrepancies in the standard errors. Because it is robust to poor starting values, converges rapidly and conveniently produces consistent standard errors for both maximum likelihood and weighted least squares problems, the Gauss-Newton algorithm represents an attractive alternative for at least some covariance structure analyses.Work by the first author has been supported in part by Grant No. Da01070 from the U. S. Public Health Service. Work by the second author has been supported in part by Grant No. MCS 77-02121 from the National Science Foundation.