Psychometric properties of the Danish MCMI-I translation

A translation of the MCMI-I has been in use in Denmark for some years. An untested assumption in the interpretation of the pattern of test results is that the psychometric characteristics of the Danish and American versions are similar. The purpose of this study was to evaluate the psychometric properties of the questionnaire by using traditional psychometric analysis techniques on the results of a sample consisting of 423 patients and 179 normal controls. Coefficient alpha was calculated for the 20 clinical subscales of the test and the Danish results were strikingly similar to the original coefficients reported by Millon. Furthermore, factor analysis of the subscales showed a factor structure very similar to American findings, and it is concluded that the psychometric properties of the Danish MCMI are not significantly different from the original.     

Structural equation modeling: reviewing the basics and moving forward

This tutorial begins with an overview of structural equation modeling (SEM) that includes the purpose and goals of the statistical analysis as well as terminology unique to this technique. I will focus on confirmatory factor analysis (CFA), a special type of SEM. After a general introduction, CFA is differentiated from exploratory factor analysis (EFA), and the advantages of CFA techniques are discussed. Following a brief overview, the process of modeling will be discussed and illustrated with an example using data from a HIV risk behavior evaluation of homeless adults (Stein & Nyamathi, 2000). Techniques for analysis of nonnormally distributed data as well as strategies for model modification are shown. The empirical example examines the structure of drug and alcohol use problem scales. Although these scales are not specific personality constructs, the concepts illustrated in this article directly correspond to those found when analyzing personality scales and inventories. Computer program syntax and output for the empirical example from a popular SEM program (EQS 6.1; Bentler, 2001) are included.     

Inequalities among lower bounds to reliability: With applications to test construction and factor analysis

A chain of lower-bound inequalities leading to the greatest lower bound to reliability is established for the internal consistency of a composite of unit-weighted components. The chain includes the maximum split-half coefficient, the lowest coefficient consistent with nonimaginary common factors, and the lowest coefficient consistent with nonimaginary common and unique factors. Optimization theory is utilized to determine the conditions that are requisite for the inequalities. Convergence proofs demonstrate that the coefficients can be attained. Rapid algorithms obtain estimates of the coefficients with sample data. The theory yields methods for splitting items into maximally similar sets and for exploratory factor analysis based on a theoretical solution to the communality problem.     

The Yale-Brown Obsessive-Compulsive Scale: Confirmatory Factor Analytic Findings

The psychometric properties of the Yale-Brown Obsessive-Compulsive Scale (Y-BOCS) have recently been heavily examined. Specifically, a number of researchers have been interested in determining the factor structure of this scale to find whether it best forms a one, two, or three factor model. The present study continued this examination by considering different scaling models using confirmatory factor analysis with a sample of individuals diagnosed with Obsessive-Compulsive Disorder (OCD). One hundred and forty-six individuals diagnosed with OCD participated and were administered the Y-BOCS and scales measuring depression (Hamilton Depression Rating Scale) and anxiety (Hamilton Anxiety Rating Scale). It was found that the Y-BOCS forms two different two-factor models. One model consisted of an obsessions and compulsions factor; the other composed of disturbance and symptom severity factors. It was likewise found that depression and anxiety were related to both factors in one model (disturbance and symptom severity). The finding that depression was related to obsessions and anxiety to compulsions was found, as in a previous factor analysis of the Y-BOCS. These findings suggest that OCD may be best characterized as a multidimensional syndrome that may not be adequately examined by a single unitary factor as described in the Y-BOCS.     

On the relations among regular, equal unique variances, and image factor analysis models

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.Kentaro Hayashi is a visiting Assistant Professor, Department of Mathematics, Bucknell University, Lewisburg PA 17837, and Peter M. Bentler is Professor, Departments of Psychology and Statistics, University of California, Los Angeles CA 90095-1563. (Emails: Khayashi@bucknell.edu, bentler@ucla.edu) Parts of this paper were discussed in a session on Factor Analysis (J. ten Berge, Chair) at the IFCS-98 International Conference, Rome, July, 1998. This work was supported by National Institute on Drug Abuse grant DA 01070. The authors thank Professors Hans Schneeweiss and Ke-Hai Yuan, and four anonymous referees, for their invaluable comments which led to an improved version of this paper.     

Factor analysis for non-normal variables

Factor analysis for nonnormally distributed variables is discussed in this paper. The main difference between our approach and more traditional approaches is that not only second order cross-products (like covariances) are utilized, but also higher order cross-products. It turns out that under some conditions the parameters (factor loadings) can be uniquely determined. Two estimation procedures will be discussed. One method gives Best Generalized Least Squares (BGLS) estimates, but is computationally very heavy, in particular for large data sets. The other method is a least squares method which is computationally less heavy. In one example the two methods will be compared by using the bootstrap method. In another example real life data are analyzed.This paper has partly been written while the author was a visiting scholar at the Department of Psychology, University of California, Los Angeles. He wants to thank Peter Bentler who made this stay at UCLA possible and for his valuable contributions to this paper. This research was supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O) under number R56-150 and by USPHS Grant DA01070.     

Three‐factor structure and psychometric properties of Witte's Risk Behaviour Diagnosis Scale: A French version adapted to diabetes

The aim of this study was to verify the psychometric properties and the factorial structure of Witte's Risk Behaviour Diagnosis (RBD). This article shows the results of a French version of the RBD adapted to diabetes screening. An exploratory factor analysis was carried out in order to understand the number of underlying factors, a confirmatory factor analysis was performed and the four‐factor model proposed by the author and alternative models were compared. The concurrent validity was tested by a correlational analysis with the Perceived Fear Emotions Scale. The results confirmed a stable factor structure for the 12‐item version, with three factors reflecting total efficacy, severity of and susceptibility to threat. The value of having a psychometrically valid instrument to assess the impact of fear appeal‐based campaigns is linked to the current lack of a comprehensive assessment tool and the importance of preventing health risk behaviours.     

Psychometric Properties of the Alabama Parenting Questionnaire

  We examined the psychometric properties of a German translation of the Child Global Report version of the Alabama Parenting Questionnaire (APQ). A total of 1219 German school-children (644 boys and 575 girls), ages 10–14 years participated in the study. The APQ was subjected to exploratory and confirmatory factor analysis. Exploratory factor analysis produced five factors that were largely consistent with the a priori scale structure. These factors included dimensions of parental involvement, positive parenting, poor monitoring/supervision, inconsistent discipline, and corporal punishment. Fit indexes from confirmatory factor analyses suggested that the five factor model represented a satisfactory solution for the data, with some minor modifications in scale content. These findings provide initial support for the factorial validity of the child report version of the APQ in German families.     

More on EM for ML factor analysis

We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.This work was partially supported by the Program Statistics Research Project at Educational Testing Service.     

Sample size and bentler and Bonett's nonnormed fit index

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.     

Alpha,Dimension-Free,and Model-Based Internal Consistency Reliability

As pointed out by Sijtsma (in press), coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score. Better estimators of internal consistency are available. In addition to those mentioned by Sijtsma, an old dimension-free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency. The various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items. Research supported in part by grants DA00017 and DA01070 from the National Institute on Drug Abuse. This paper is based in part on Bentler (2003).     

A factor simplicity index

We propose an index for assessing the degree of factor simplicity in the context of principal components and exploratory factor analysis. The new index, which is called Loading Simplicity, is based on the idea that the communality of each variable should be related to few components, or factors, so that the loadings in each variable are either zero or as far from zero as possible. This index does not depend on the scale of the factors, and its maximum and minimum are only related to the degree of simplicity in the loading matrix. The aim of the index is to enable the degree of simplicity in loading matrices to be compared.The author would like to thank the review team for their insights and recommendations. This work was supported by a grant SEC2001-3821-C05-C02 from the Spanish Ministry of Science and Technology.     

Psychometric properties of the Danish 16PF and EPQ

A Danish translation of the Cattell's 16PF has been used in studies evaluating the effects of prenatal drug exposure. This paper reports a psychometric analysis of the 16PF and Eysenck's EPQ based on a sample of 558 young Danes. Many 16PF scales had unacceptable psychometric properties (as indicated by coefficient alpha and item–total score correlations), but more satisfactory results were obtained with the EPQ N and E scales. A factor analysis of all 16PF and EPQ scales suggested a six factor solution that roughly corresponds to the second-order factor structure obtained by Krug and Johns (1986). It is concluded that the second-order factor structure should be the basis of interpretation of the 16PF in both practical and research contexts.     

Comparison of several shortened versions of the EMBU: exploratory and confirmatory factor analyses

The aim of the present study was to analyze the psychometric properties of different versions of the EMBU (Egna Minnen av Barndoms Uppfostran – My memories of upbringing) in a non-clinical sample of adolescents. The factor structure of the questionnaire was studied by means of more adequate exploratory and confirmatory factor procedures in order to ascertain which version achieves a better fit to data. The 64-item version of the EMBU was administered to a non-clinical sample of 832 adolescents. Exploratory and Confirmatory factor analyses were carried out for successive versions of 64, 37, 24 and 23 items. The theoretical four-factor structure of the 64-item version is not replicated in a factor analysis through principal axis extraction with direct oblimin rotation. The "Favoring Subject" factor was not found. 37 items present loadings equal to or larger than 0.30 for the "Rejection", "Emotional Warmth" and "Overprotection" factors. A re-analysis of these items shows a clear three-factor structure. When Arrindell et al .'s (1999 ) 23-item version was analysed, the three expected factors were also found. Confirmatory factor analyses allow us to reduce the 36-item version to a shorter one of 24 items. This last version achieves the best fit to data, including the 23-item version. The new 24-item version improves the construct validity of the EMBU and presents similar reliability coefficients.     

A Swedish translation of the 20-item Toronto Alexithymia Scale: cross-validation of the factor structure

The purpose of this study was to develop a new Swedish translation of the twenty-item Toronto Alexithymia Scale (TAS-20) and to examine if the theoretical structure that underlies the factor structure of the English version of the TAS-20 could be recovered in this Swedish translation of the instrument. A sample of 157 undergraduate students of psychology was tested. Using confirmatory factor analysis, the previously established three-factor TAS-20 model was found to be replicable in this sample. In addition, the Swedish translation of the TAS-20 showed adequate internal reliability. The present study also illustrates the importance of using back translation methodology when transposing psychometric instruments from one language to another.     

A validation and short form of the Basic Character Inventory

The Basic Character Inventory (BCI) contains 136 items, 17 lower-order personality factors and three higher-order personality factors derived from psychoanalytic theory: Oral, Obsessive Compulsion, and Hysteria. Previous research that investigated the BCI's psychometric properties examined small, special populations and did not use modern statistical methods to validate the BCI. The present study validates the BCI via confirmatory factor analyses using a large sample of 6,285 Norwegian nursing and teaching students. Reliability, convergent validity, and divergent validity of the BCI were also assessed. Results indicated general support for the original BCI factor structure in a reduced form of the BCI that possesses strong reliability and validity, and is suitable for use in time-limited measurement settings.     

Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.     

Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.     

A parent-report measure of children's anxiety: psychometric properties and comparison with child-report in a clinic and normal sample

This study examined the psychometric properties of the parent version of the Spence Children's Anxiety Scale (SCAS-P); 484 parents of anxiety disordered children and 261 parents in a normal control group participated in the study. Results of confirmatory factor analysis provided support for six intercorrelated factors, that corresponded with the child self-report as well as with the classification of anxiety disorders by DSM-IV (namely separation anxiety, generalized anxiety, social phobia, panic/agoraphobia, obsessive-compulsive disorder, and fear of physical injuries). A post-hoc model in which generalized anxiety functioned as the higher order factor for the other five factors described the data equally well. The reliability of the subscales was satisfactory to excellent. Evidence was found for both convergent and divergent validity: the measure correlated well with the parent report for internalizing symptoms, and lower with externalizing symptoms. Parent-child agreement ranged from 0.41 to 0.66 in the anxiety-disordered group, and from 0.23 to 0.60 in the control group. The measure differentiated significantly between anxiety-disordered children versus controls, and also between the different anxiety disorders except GAD. The SCAS-P is recommended as a screening instrument for normal children and as a diagnostic instrument in clinical settings.