A second generation nonlinear factor analysis

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum-likelihood-ratio and ordinary-least-squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood-ratio criterion.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Grant No. A6346.     

One line decreases the visibility of a simultaneous identical distant second line

A top line decreased the visibility of a simultaneous, identical, distant bottom line. This context-produced decrease in visibility (DV) occurred when the bottom line was masked by flanking lines and hence was less visible than the top line. It continued when the top line was three times as far from the bottom line. It disappeared without the mask. There was a hint of an opposing context-produced increase in visibility (IV) when the lines were close together. The DV is not accounted for by numerous extant phenomena and theories. It means that the top line decreased the similarity in visibility between it and the bottom line, a contrast effect for visibility, rather than for a typical attribute. Contrast does not occur between two attributes that are perceptually equal. Therefore, the reason why two distant equally visible objects fail to result in a DV may be that their equal visibility precludes the occurrence of contrast. This DV-as-contrast theory is consistent with evidence that two groups (phenomenal wholes) are associated with both contrast and DVs, and thus also with evidence that one group is associated with both assimilation and IVs.     

Influence analysis for the factor analysis model with ranking data

Influence analysis is an important component of data analysis, and the local influence approach has been widely applied to many statistical models to identify influential observations and assess minor model perturbations since the pioneering work of Cook (1986) . The approach is often adopted to develop influence analysis procedures for factor analysis models with ranking data. However, as this well‐known approach is based on the observed data likelihood, which involves multidimensional integrals, directly applying it to develop influence analysis procedures for the factor analysis models with ranking data is difficult. To address this difficulty, a Monte Carlo expectation and maximization algorithm (MCEM) is used to obtain the maximum‐likelihood estimate of the model parameters, and measures for influence analysis on the basis of the conditional expectation of the complete data log likelihood at the E‐step of the MCEM algorithm are then obtained. Very little additional computation is needed to compute the influence measures, because it is possible to make use of the by‐products of the estimation procedure. Influence measures that are based on several typical perturbation schemes are discussed in detail, and the proposed method is illustrated with two real examples and an artificial example.     

Separation of data as a principle in factor analysis

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.     

Mean performance and the factor analysis of learning data

The difference in factor structure resulting from the factorization of correlations, covariances, and cross products is discussed. Factoring cross products has the advantage of retaining information on both means and variances; this method of factoring learning data is recommended. The conditions under which factoring covariances and cross products lead to the same essential structure are investigated.     

A factor structure of child home observation data

Both normal and antisocial children were extensively observed in their natural home environments. A factor analysis of the baseline data was conducted that differed from the typical factor study in two respects. Equal numbers of deviant and nondeviant behaviors were included in the analysis, and the unit of analysis was the rate-per-minute occurrence of actual child behavior. The factor structure was interpretable, and scaling of the dimensions-I, Verbal Emotionality, II, Physical Dependency, HI, Social Involvement, IV, Hostile: Controlling, and V, Hostile: Impulsive-separated groups of normal, socially aggressive, hyperactive-aggressive, and stealing children. Reported differences between aggressive and stealing children on rates of total aversive behavior were found to be due to differences in the verbal behaviors loading on the first factor.The data reported in this paper were collected with support from a grant from the National Institute of Mental Health, Section on Crime and Delinquency, Grant No. MH 15985 to Oregon Social Learning Center. The authors wish to thank Gerald R. Patterson for granting access to the data files and for very patient continuing support and advice.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Generalized locus of control: An analysis of factor analytic data

Despite discouraging empirical evidence concerning a general expectancy of internal or external (I-E) locus of control, researchers appear reluctant to abandon Rotter's original hypothesis. A possible methodological flaw in most I-E research involves the failure to test the measured tendency against multiple act criteria. Data which address this concern may be found in factor analytic studies of I-E scales. This evidence is reviewed with respect to three predictions derived from a generalized expectancy hypothesis. First the expectancy should be measured by a single dimension. Second, this dimension should have breadth of application across situations. Third, the dimension should generalize to a variety of populations. Factor analytic data provide little support for these predictions. It is suggested that goal-specific multidimensional locus of control scales hold greater promise for predicting behaviour.     

On using multiple imputation for exploratory factor analysis of incomplete data

A simple multiple imputation-based method is proposed to deal with missing data in exploratory factor analysis. Confidence intervals are obtained for the proportion of explained variance. Simulations and real data analysis are used to investigate and illustrate the use and performance of our proposal.     

A factor analysis of verbal abilities

A multiple-factor analysis was made of a battery of 42 tests of verbal abilities administered to 119 college adults. Where necessary, the distributions of test scores were normalized before the inter-test correlations were computed. Thurstone'sM (Memory or Rote Learning) factor has been confirmed, but hisV (Verbal Relations) factor seems to have been split into two or possibly three factors,C,J, andG; and hisW (Word Fluency) factor has been split into two factors,A andE. TheC factor seems to represent the richness of the individual's stock of linguistic responses, and theJ factor seems to involve the ability to handle semantic relationships. No satisfactory interpretation can as yet be made of theG factor. TheA factor seems to correspond to the speed of association for common words where there is a high degree of restriction as to appropriate responses. TheE factor is described as an associational facility with verbal material where the only restriction is that the responses must be syntactically coherent. The new factors are:F, facility and fluency in oral speech;H, facility in attaching appropriate names or symbols to stimuli; andD, speed of articulatory movements.This paper is a condensation of the writer's doctoral dissertation, A Factor Analysis of Verbal Abilities, on file at the library of the University of Minnesota.     

A factor analysis of verbal ability

The Psychological Record -     

A simple method of factor analysis

A simple method for extracting correlated factors simultaneously is described. The method is based on the idea that the centroid pattern coefficients for the sections of unit rank of the complete matrix may be interpreted as structure values for the entire matrix. Only the routine centroid average process is required.     

Publication visibility of sensitive public health data: When scientists bury their results

What happens when the scientific tradition of openness clashes with potential societal risks? The work of American toxic-exposure epidemiologists can attract media coverage and lead the public to change health practices, initiate lawsuits, or take other steps a study’s authors might consider unwarranted. This paper, reporting data from 61 semi-structured interviews with U.S. toxic-exposure epidemiologists, examines whether such possibilities shaped epidemiologists’ selection of journals for potentially sensitive papers. Respondents manifested strong support for the norm of scientific openness, but a significant minority had or would/might, given the right circumstances, publish sensitive data in less visible journals, so as to prevent unwanted media or public attention. Often, even those advocating such limited “burial” upheld openness, claiming that less visible publication allowed them to avoid totally withholding the data from publication. However, 15% of the sample had or would, for the most sensitive types of data, withhold publication altogether. Rather than respondents explaining their actions in terms of an expected split between “pure science” and “social advocacy” models, even those publishing in the more visible journals often described their actions in terms of their “responsibility”. Several practical limitations (particularly involving broader access to scientific literature via the Internet) of the strategy of burial are discussed, and some recommendations are offered for scientists, the media, and the public.     

Publication visibility of sensitive public health data: When scientists bury their results

What happens when the scientific tradition of openness clashes with potential societal risks? The work of American toxic-exposure epidemiologists can attract media coverage and lead the public to change health practices, initiate lawsuits, or take other steps a study’s authors might consider unwarranted. This paper, reporting data from 61 semi-structured interviews with U.S. toxic-exposure epidemiologists, examines whether such possibilities shaped epidemiologists’ selection of journals for potentially sensitive papers. Respondents manifested strong support for the norm of scientific openness, but a significant minority had or would/might, given the right circumstances, publish sensitive data in less visible journals, so as to prevent unwanted media or public attention. Often, even those advocating such limited “burial” upheld openness, claiming that less visible publication allowed them to avoid totally withholding the data from publication. However, 15% of the sample had or would, for the most sensitive types of data, withhold publication altogether. Rather than respondents explaining their actions in terms of an expected split between “pure science” and “social advocacy” models, even those publishing in the more visible journals often described their actions in terms of their “responsibility”. Several practical limitations (particularly involving broader access to scientific literature via the Internet) of the strategy of burial are discussed, and some recommendations are offered for scientists, the media, and the public.