Biomedical subjects

P M Bentler

Publications and source records attributed to P M Bentler.

At least 19 recordsLinked to original sources

PubMed2001

Effect of outliers on estimators and tests in covariance structure analysis.

A small proportion of outliers can distort the results based on classical procedures in covariance structure analysis. We look at the quantitative effect of outliers on estimators and test statistics based on normal theory maximum likelihood and the asymptotically distribution-free procedures. Even if a proposed structure is correct for the majority of the data in a sample, a small proportion of outliers leads to biased estimators and significant test statistics. An especially unfortunate consequence is that the power to reject a model can be made arbitrarily--but misleadingly--large by inclusion of outliers in an analysis.

Analysis of Variance↗

PubMed2000

On measures of explained variance in nonrecursive structural equation models.

Whereas measures of explained variance in a regression and an equation of a recursive structural equation model can be simply summarized by a standard R2 measure, this is not possible in nonrecursive models in which there are reciprocal interdependencies among variables. This article provides a general approach to defining variance explained in latent dependent variables of nonrecursive linear structural equation models. A new method of its estimation, easily implemented in EQS or LISREL and available in EQS 6, is described and illustrated.

Analysis of Variance↗

PubMed2000

Robust transformation with applications to structural equation modelling.

Data sets in social and behavioural sciences are seldom normal. Influential cases or outliers can lead to inappropriate solutions and problematic conclusions in structural equation modelling. By giving a proper weight to each case, the influence of outliers on a robust procedure can be minimized. We propose using a robust procedure as a transformation technique, generating a new data matrix that can be analysed by a variety of multivariate methods. Mardia's multivariate skewness and kurtosis statistics are used to measure the effect of the transformation in achieving approximate normality. Since the transformation makes the data approximately normal, applying a classical normal theory based procedure to the transformed data gives more efficient parameter estimates. Three procedures for parameter evaluation and model testing are discussed. Six examples illustrate the various aspects with the robust transformation.

Humans↗

PubMed1998

Use of structural equation modeling to test the construct validity of the SF-36 Health Survey in ten countries: results from the IQOLA Project. International Quality of Life Assessment.

A crucial prerequisite to the use of the SF-36 Health Survey in multinational studies is the reproduction of the conceptual model underlying its scoring and interpretation. Structural equation modeling (SEM) was used to test these aspects of the construct validity of the SF-36 in ten IQOLA countries: Denmark, France, Germany, Italy, the Netherlands, Norway, Spain, Sweden, the United Kingdom, and the United States. Data came from general population surveys fielded to gather normative data. Measurement and structural models developed in the United States were cross-validated in random halves of the sample in each country. SEM analyses supported the eight first-order factor model of health that underlies the scoring of SF-36 scales and two second-order factors that are the basis for summary physical and mental health measures. A single third-order factor was also observed in support of the hypothesis that all responses to the SF-36 are generated by a single, underlying construct--health. In addition, a third second-order factors, interpreted as general well-being, was shown to improve the fit of the model. This model (including eight first-order factors, three second-order factors, and one third-order factor) was cross-validated using a holdout sample within the United States and in each of the nine other countries. These results confirm the hypothesized relationships between SF-36 items and scales and justify their scoring in each country using standard algorithms. Results also suggest that SF-36 scales and summary physical and mental health measures will have similar interpretations across countries. The practical implications of a third second-order SF-36 factor (general well-being) warrant further study.

Cross-Cultural Comparison↗

PubMed1998

Robust mean and covariance structure analysis.

Covariance structure analysis is used to evaluate hypothesized influences among unmeasured latent and observed variables. As implemented, it is not robust to outliers and bad data. Several robust methods in model fitting and testing are proposed. These include direct estimation of M-estimators of structured parameters and a two-stage procedure based on robust M- and S-estimators of population covariances. The large sample properties of these estimators are obtained. The equivalence between a direct M-estimator and a two-stage estimator based on an M-estimator of population covariance is established when sampling from an elliptical distribution. Two test statistics are presented in judging the adequacy of a hypothesized model; both are asymptotically distribution free if using distribution free weight matrices. So these test statistics possess both finite sample and large sample robustness. The two-stage procedures can be easily adapted into standard software packages by modifying existing asymptotically distribution free procedures. To demonstrate the two-stage procedure, S-estimator and M-estimators under different weight functions are calculated for some real data sets.

Analysis of Variance↗

PubMed1998

Normal theory based test statistics in structural equation modelling.

Even though data sets in psychology are seldom normal, the statistics used to evaluate covariance structure models are typically based on the assumption of multivariate normality. Consequently, many conclusions based on normal theory methods are suspect. In this paper, we develop test statistics that can be correctly applied to the normal theory maximum likelihood estimator. We propose three new asymptotically distribution-free (ADF) test statistics that technically must yield improved behaviour in samples of realistic size, and use Monte Carlo methods to study their actual finite sample behaviour. Results indicate that there exists an ADF test statistic that also performs quite well in finite sample situations. Our analysis shows that various forms of ADF test statistics are sensitive to model degrees of freedom rather than to model complexity. A new index is proposed for evaluating whether a rescaled statistic will be robust. Recommendations are given regarding the application of each test statistic.

Humans↗

PubMed1997

Maximum likelihood estimation in covariance structure analysis with truncated data.

We study an estimation procedure for maximum likelihood estimation in covariance structure analysis with truncated data, and obtain the statistical properties of the estimator as well as a test of the model structure. Truncated data with and without knowledge about the number of unmeasured observations are both considered. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which requires only first derivatives, is proposed to obtain the maximum likelihood estimates. We illustrate the statistics and parameter estimates by a fictitious example. The maximum likelihood method is compared to an alternative two-stage method.

Algorithms↗

PubMed1996

Test of linear trend in eigenvalues of a covariance matrix with application to data analysis.

Principal component analysis and factor analysis are the most widely used tools for dimension reduction in data analysis. Both methods require some good criterion to judge the number of dimensions to be kept. The classical method focuses on testing the equality of eigenvalues. As real data hardly have this property, practitioners turn to some ad hoc criterion in judging the dimensionality of their data. One such popular method, the 'scree test' or 'scree plot' as described in many texts and statistical programs, is based on the trend in eigenvalues of sample covariance (correlation) matrix. The principal components or common factors corresponding to eigenvalues which exhibit a slow linear decrease are discarded in further data analysis. This paper develops a formal statistical test for the 'scree plot'. A special case of this test is the classical test for equality of eigenvalues which has been suggested in several texts as the criterion to decide the number of principal components to retain. Comparisons between equality of eigenvalues and the slow linear decrease in eigenvalues on some classical examples support the hypothesis of slow linear decrease. A physical background to such a phenomenon is also suggested.

Analysis of Variance↗

PubMed1995

A two-stage estimation of structural equation models with continuous and polytomous variables.

This paper develops a computationally efficient procedure for analysis of structural equation models with continuous and polytomous variables. A partition maximum likelihood approach is used to obtain the first stage estimates of the thresholds and the polyserial and polychoric correlations in the underlying correlation matrix. Then, based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, a generalized least squares approach is employed to estimate the structural parameters in the correlation structure. Asymptotic properties of the estimators are derived. Some simulation studies are conducted to study the empirical behaviours and robustness of the procedure, and compare it with some existing methods.

Humans↗

PubMed1994

Structural equation analyses of clinical subpopulation differences and comparative treatment outcomes: characterizing the daily lives of drug addicts.

The use of structural equation modeling (SEM) is illustrated for comparative treatment outcome research conducted with heterogeneous clinical subpopulations within large multimodality treatment settings. All analyses are accomplished with SEM analogs of more familiar classical multivariate techniques. The effect of the early period of treatment on the daily lives of 486 clients in two drug abuse treatment modalities (methadone maintenance and outpatient counseling) is evaluated. Structured means analysis is used to assess initial differences between modalities on the latent means of 6 latent constructs reflecting daily life. The effect of treatment modality and attrition from the program on daily life latent constructs is evaluated while initial selection differences are statistically controlled. Effect sizes are computed on the basis of SEM parameter estimates. The advantage of SEM over classic multivariate approaches for correcting for selection bias when assessing comparative outcomes is explained.

Activities of Daily Living↗

PubMed1994

Attitudes and health behavior in diverse populations: drunk driving. Alcohol use, binge eating, marijuana use, and cigarette use.

Five different health behaviors (cigarette use, alcohol use, binge eating, illicit drug use, and drunk driving) were studied prospectively in 5 different groups of subjects. Associations between attitudes toward these behaviors and the behaviors themselves were investigated over at least 2 waves of measurement. Findings revealed that attitudes predicted behavior nonspuriously in 2 instances: alcohol use and marijuana use. Attitudes did not predict drunk driving, binge eating, or smoking behaviors. Past behavior predicted attitude in the domains of binge eating and smoking, but not in the domains of alcohol use, drunk driving, or marijuana use. The results are discussed in terms of several alternative approaches that have implications for interventions that attempt to influence health behavior through attitude change.

Adolescent↗

PubMed1994

Psychosocial correlates and predictors of AIDS risk behaviors, abortion, and drug use among a community sample, of young adult women.

Relations among latent constructs of Social Conformity, Sensation Seeking, Polydrug Use, Sexual Experience, Abortion, and Risky AIDS Behaviors were examined among a community sample of women (N = 438, mean age = 25.5 years) using confirmatory factor analysis (CFA) and predictive structural equation models (SEM). In the CFA, Risky AIDS Behavior was strongly related to more Polydrug Use and less Social Conformity and modestly related to Sexual Experience and Abortions. In SEMs, Social Conformity significantly predicted less Risky AIDS Behavior and less Polydrug Use but did not predict Abortions. Prior Sexual Experience predicted more Polydrug Use and Abortions. We conclude that the same psychological processes and predispositions that relate low social conformity to drug use and other unhealthy behaviors also influence AIDS-risk behaviors, even among a community sample of women.

Abortion, Induced↗

PubMed1994

Bootstrap-corrected ADF test statistics in covariance structure analysis.

The asymptotically distribution-free (ADF) test statistic for covariance structure analysis (CSA) has been reported to perform very poorly in simulation studies, i.e. it leads to inaccurate decisions regarding the adequacy of models of psychological processes. It is shown in the present study that the poor performance of the ADF test statistic is due to inadequate estimation of the weight matrix (W = gamma -1), which is a critical quantity in the ADF theory. Bootstrap procedures based on Hall's bias reduction perspective are proposed to correct the ADF test statistic. It is shown that the bootstrap correction of additive bias on the ADF test statistic yields the desired tail behaviour as the sample size reaches 500 for a 15-variable-3-factor confirmatory factor-analytic model, even if the distribution of the observed variables is not multivariate normal and the latent factors are dependent. These results help to revive the ADF theory in CSA.

Factor Analysis, Statistical↗

PubMed1994

Consequences of adolescent drug use and personality factors on adult drug use.

This study examined the stability of adolescent drug use into young adulthood and explored the possible influence of personality on adolescent and adult drug use. Participants in this longitudinal study (N = 640) completed questionnaires which assessed multiple indicators for latent constructs of tobacco, alcohol, cannabis, and hard drugs, and also for the personality constructs of Socialization. In addition, the effects of obedience and extraversion were examined. Results showed that a general drug use factor in adolescence significantly predicted young adult drug use. A particular effect of adolescent obedience on adult drug use was noted. Within adolescence, obedience, extraversion, and the construct of Socialization were significant predictors of drug use. Early onset of smoking predicted adolescent drug use. The implications of these findings for early drug use education and intervention are discussed. Additional analysis explored the possibility of treating obedience as another indicator of Socialization. This model could not provide as good a fit as the original model. The measure of obedience acted as a better predictor of drug use than an overall factor of Socialization. Gender differences are discussed.

Adolescent↗

PubMed1993

Consequences of adolescent drug use on young adult job behavior and job satisfaction.

Longitudinal data (N = 785) collected during Ss high school years (1971-1973) and in 1981 were used to assess the influence of adolescent drug use on adult job behaviors, job satisfaction, and adverse terminations while accounting for concurrent adult drug use, years of drug use, and adolescent achievement motivation. Relationships were minimal between adolescent drug use and adult work-related indicators in confirmatory factor analyses (CFAs) and predictive path models. Although significantly related in the CFAs, higher adolescent achievement motivation did not predict less adult drug use when adolescent drug use was included as a control. Less achievement motivation in adolescence significantly predicted more negative job behaviors and less job satisfaction, but not terminations. Correlations were significant between more adolescent drug use and less adolescent achievement motivation and between adult job problems and adult drug use.

Adolescent↗

PubMed1992

Cognition and the corpus callosum: verbal fluency, visuospatial ability, and language lateralization related to midsagittal surface areas of callosal subregions.

Normal volunteers (28 women), 20-45 years old, completed tests of visuospatial ability, verbal fluency, and language lateralization, and the midsagittal surface areas of the splenium, isthmus, midregion, and genu of the corpus callosum were measured from inversion recovery magnetic resonance images. Multivariate statistics were used to analyze patterns of correlations. Verbal fluency correlated positively with the area of the splenium and with the area of a posterior callosal factor defined largely by the splenium. The posterior callosum, particularly the splenium, also correlated negatively with language lateralization. There were no other consistent brain-behavior relationships. These results are relevant to understanding factors involved in the development of cognitive characteristics that show sex differences and to understanding the neural basis of language lateralization and verbal abilities.

Adult↗

PubMed1992

Can test statistics in covariance structure analysis be trusted?

Covariance structure analysis uses chi 2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study. The tests performed dramatically differently under 7 distributional conditions at 6 sample sizes. Two normal-theory tests worked well under some conditions but completely broke down under other conditions. A test that permits homogeneous nonzero kurtoses performed variably. A test that permits heterogeneous marginal kurtoses performed better. A distribution-free test performed spectacularly badly in all conditions at all but the largest sample sizes. The Satorra-Bentler scaled test statistic performed best overall.

Female↗

PubMed1992

On the fit of models to covariances and methodology to the Bulletin.

It is noted that 7 of the 10 top-cited articles in the Psychological Bulletin deal with methodological topics. One of these is the Bentler-Bonett (1980) article on the assessment of fit in covariance structure models. Some context is provided on the popularity of this article. In addition, a citation study of methodology articles appearing in the Bulletin since 1978 was carried out. It verified that publications in design, evaluation, measurement, and statistics continue to be important to psychological research. Some thoughts are offered on the role of the journal in making developments in these areas more accessible to psychologists.

Analysis of Variance↗