Maximum Likelihood Confirmatory Factor Analysis Research Articles

Sample Size and Number of Parameter Estimates in Maximum Likelihood Confirmatory Factor Analysis: A Monte Carlo Investigation

A number of authors have proposed that determining an adequate sample size in structural equation modeling can be aided by considering the number of parameters to be estimated. This study directly investigates this assumption in the context of maximum likelihood confirmatory factor analysis. The findings support previous research on the effect of sample size, measured-variable reliability, and the number of measured variables per factor. However, no practically significant effect was found for the number of observations per estimated parameter.

A confirmatory factor analysis of the Myers–Briggs Type Indicator

Abstract The 95×95 covariance matrix of the Italian edition of the Myers–Briggs Type Indicator (MBTI) Form F was subjected to a series of three maximum likelihood confirmatory factor analyses using EQS 3.0 ( Bentler, 1989 ) on a sample of 1798 subjects. The purpose was to try to test the fit of three plausible correlated non-nested factor models: the traditional four-factor model assumed by the 4 MBTI scales (Model 1), a three-factor model (Model 2) corresponding, respectively, to the MBTI EI scale (Factor 1), to the MBTI TF scale (Factor 2) and to the MBTI SN and JP scales (Factor 3), as suggested in a study by Saggino and Kline (1996b) (The location of the Myers–Briggs Type Indicator in personality factor space. Personality and Individual Differences , 21, 591–597) and a five-factor model (Model 3) based on the exploratory work of Saggino and Kline (1995) (Item factor analysis of the Italian version of the Myers–Briggs Type Indicator. Personality and Individual Differences , 19, 243–249) who found five factors. All the three models converged satisfactorily. Model 3 had the best fit to the data, even if its NFI and chi-square/df ratio are lower than one would normally expect.

Factor structure and validity of the affect intensity measure in a Swedish sample

Abstract Despite the fact that Larsen’s [Larsen, R.J. (1984). Theory and measurement of affect intensity as an individual difference characteristic. Dissertation Abstracts International. 85, 2297B (University Microfilms No. 84-22112.)] Affect Intensity Measure (AIM) is a widely used measure of affect intensity, there is an ongoing debate concerning certain of its presumed theoretical and statistical qualities and its basic, underlying assumptions. The debate has most often centered around the inventory’s dimensionality; i.e., is the AIM tapping one or more dimensions of intensity? The purpose of the present study was to investigate the dimensional structure of the Swedish translation of the AIM, to find the best structural model for the Swedish AIM data, and to study its validity. Data from 409 subjects (153 males, 256 females) were subjected to maximum-likelihood confirmatory factor analysis to assess how well different structural models fit the AIM data. The results showed that all of the multidimensional AIM models were superior to Larsen’s original 40-item uni-dimensional model, on all the fit indices. The best-fitting model was a newly derived three-factor model, based on 27 items resulting in the factors Positive Affectivity, Negative Intensity, and Negative reactivity. Validation of this model in a community sample of 208 adults clearly showed different correlational patterns between negative intensity and negative reactivity, on the one hand, and positive affectivity, on the other, which demonstrates the value of treating affect intensity as a multidimensional construct.

A Construct Validity Study of Scores on a Korean Version of an Academic Self-Concept Scale for Secondary School Students

For each of three samples of 213 8th-grade girls, 191 11th-grade boys, and 213 11th-grade girls attending schools in Korea, the twofold purpose of this investigation was to obtain evidence of the internal-consistency reliability and construct validity of scores on each of the five factor subscales of a Korean version of an academic self-concept instrument titled Dimensions of Self-Concept (DOSC), Form S. Internal-consistency estimates of the reliability of scores on the five 14-item factor subscales fell between .63 and .89, with a median value approximating .78. Confirmatory maximum-likelihood factor analyses for five alternative substantive factor models indicated that both a five-factor oblique model and a hierarchical factor model comprising a general factor correlated with interrelated first-order factors explained the greatest percentage of covariance in the two matrices for the two samples of 11th-grade students. The five hypothesized constructs of the DOSC, Form S (Korean version) received at least modest empirical support.

A Structural Equation Analysis of the Wide Range Assessment of Memory and Learning in a Clinical Sample

A maximum likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wide Range Assessment of Memory and Learning (WRAML) in a clinical sample (N = 271). Analyses were designed to determine which of 10 hypothesized oblique factor solutions could best explain memory as measured by the WRAML. Competing latent variable models were identified in previous studies and monographs on memory. Findings supported a three-factor model including Verbal Memory, Visual Memory, and Attention/Concentration factors. Our results are consistent with previous studies suggesting that attention is an important component of memory as measured by the WRAML. This study replicates previous research in which the Learning Index was not empirically supported.

A Construct Validity Investigation of Scores on a Japanese Version of an Academic Self-Concept Scale for Secondary School Students

For a sample of 354 students taken from two highly similar college preparatory, girls-only Catholic high schools in Japan, the twofold purpose of this study was to obtain evidence of the internal consistency reliability and construct validity of scores on each of five dimensions of a Japanese version of an academic self-concept measure titled Dimensions of Self-Concept (DOSC), Form S, Japanese version. Internal consistency estimates of reliability of scores on the five 14-item subscales varied between .71 and .84, with a median value of .77. From each of the five factor subscales, three subtests each comprising four or five items were formed, scored, and intercorrelated (15 subtests in all). Confirmatory maximum-likelihood factor analyses for several alternative factor models indicated that a five-factor oblique model accounted for the greatest proportion of covariance in the matrix of 15 subtests.

Confirmatory factor analysis of the Parental Bonding Instrument in a Japanese population.

There is controversy surrounding the factor structure of the Parental Bonding Instrument (PBI), a widely used instrument for assessing perceived parental rearing behaviours. Recent studies have proposed five different factor structures, including Parker et al.'s original two-factor model. Four hundred and eighteen employed Japanese adults filled out the PBI. Maximum likelihood confirmatory factor analyses were performed to compare the five different factor structures in terms of model-fit. Parker's original two-factor structure fitted the data poorly. In general, three-factor structures showed better fit. Among the three-factor structures, Murphy's model and Kendler's model were superior (the adjusted goodness-of-fit index > 0.8), with the latter providing the best fit to the data (the goodness-of-fit index > 0.9). When considering invariance of factor structure across gender subgroups and across age subgroups, only Kendler's model was acceptable. Parker's two-factor structure of the PBI may not be appropriate for assessing perceived parental rearing behaviours in a Japanese population. Three-factor structures, in particular Murphy's model and Kendler's model, are preferable. Kendler's model provided the best fit to the data and was relatively invariant across the subgroups in this study. Thus, Kendler's model might prove to be very important for obtaining a factor structure invariant across different cultures.

A Construct Validity Study of a Self-Concept Scale for a Sample of Hospital Nurses

Using a sample of 107 registered nurses who were employed on medical-surgical units and intensive care units in two acute care hospitals in California, the twofold purpose of this study was to provide additional evidence of the internal-consistency reliability and construct validity of scores on each of six dimensions of the Dimensions of Self-Concept (DOSC) Scale, Form W. Internal consistency estimates of reliability of scores on the six subscales varied between .83 and .92. From each of the six factor subscales, 3 subtests each of five items were formed, scored, and intercorrelated (18 subtests in all). Confirmatory maximum likelihood factor analyses for several alternative factor models indicated that a six-factor oblique model accounted for the greatest proportion of covariance in the matrix of 18 subtests.

A structural equation analysis of the WISC-III in children with traumatic head injury

Abstract Maximum likelihood confirmatory factor analysis was performed on the WISC-III data of a sample of 171 children with traumatic head injury (THI). Analyses were designed to determine which of eight hypothesized oblique factor solutions, based on competing latent variable models that were identified in previous studies, could best explain cognition as measured by the WISC-III. The findings supported the four-factor model, as proposed in the WISC-III manual. This model (composed of Verbal Comprehension, Perceptual Organization, Freedom from Distractibility, and Processing Speed) outperformed all other models in terms of model fit and parsimony. It is concluded that this four-factor model is the most accurate predictor of WISC-III performance variability in children with THI.

A structural equation analysis of the wide range assessment of memory and learning in the standardization sample

Abstract A maximum likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wide Range Assessment of Memory and Learning standardization sample (N = 2363). Analyses were designed to determine which of nine hypothesized oblique factor solutions could best explain memory as measured by the WRAML. Competing latent variable models were identified in previous studies and monographs on memory. Models were tested separately in two samples of children used in the standardization of the scale, providing a cross-validation of results. Findings supported a three-factor model including Verbal Memory, Visual Memory, and Attention/Concentration factors. Our results are consistent with previous characterizations of attention as an important component of memory as measured by the WRAML. A distinct Learning Index was not empirically supported in the current analysis.

A five-factor versus six-factor model of personality structure

We evaluated two models of the factor structure underlying the variables of Jackson's ( Personality Research Form Manual, 1984) Personality Research Form (PRF). One model posits the well-known Big Five factors of personality. The second model, in contrast, splits the Conscientiousness factor of the Big Five into an Achievement factor, having to do with ambition and hard work, and a Methodicalness factor, having to do with the need for organization and orderliness. Substantial support for the latter of these two models is presented in three studies, both from results of confirmatory maximum likelihood factor analyses and from the differential predictability of the factors with regard to various criteria. It is concluded that at least six factors are needed to account for behavior consistencies at the highest level of the personality hierarchy.

A structural equation analysis of the Kaufman Brief Intelligence Test and the Wechsler Adult Intelligence Scale—Revised.

A maximum likelihood confirmatory factor analysis was performed by applying LISREL VII to the Kaufman Brief Intelligence Test (K-BIT ; A. S. Kaufman & N. L. Kaufman, 1990) and Wechsler Adult Intelligence Scale-Revised (WAIS-R ; D. Wechsler, 1981). Analyses were designed to determine which of six hypothesized oblique factor solutions would best explain the pattern of relationships among different combinations of K-BIT and WAIS-R subtests in a neurologically disordered sample (N = 186). Results indicated that a 4-factor model including K-BIT Verbal Intelligence, and WAIS-R Verbal Intelligence, Nonverbal Intelligence, and Freedom From Distractibility factors provided the best fit to the data. The K-BIT Verbal Intelligence factor appeared to have a significant visuospatial component, calling into question the assumption that the WAIS-R and K-BIT provide equivalent measures of verbal intelligence.

Construct Validity of the Educators Survey for a Sample of Middle School Teachers

For a sample of 150 middle school teachers (101 females and 49 males) from a suburban California community, the major purpose of this investigation was to ascertain whether the factor structure of the 22-item Educators Survey (ES) comprising three subscales reflecting three dimensions of burnout-Emotional Exhaustion (9 items), Depersonalization (5 items), and Personal Accomplishment (8 items)-would be more interpretable within a framework of either a two-factor or a three-factor conceptualization of its underlying constructs. In a comprehensive reanalysis of the factor structure of the correlation matrices of item scores from six studies using the Maslach Burnout Inventory, from which the parallel form of the ES was derived for use with educators rather than with other professional groups, Walkey and Green expressed a preference for a two-factor structure comprising a fusion of Emotional Exhaustion and Depersonalization factors into one factor named Core of Burnout and for a second factor identified as Personal Accomplishment. Use of oblique and orthogonal exploratory factor analyses revealed a high degree of simple structure for either a two-factor or three-factor solution. Evaluation of a one-factor (a general dimension) model and of two- and three-dimensional orthogonal and oblique models through application of confirmatory maximum likelihood factor analyses indicated that the three-factor oblique model accounted for the greatest amount of covariation among the 22 items of the ES, but that the two-factor oblique model afforded nearly as close a degree of fit as that afforded by the three-factor oblique model as well as a meaningful alternative conceptualization of the factor structure of the ES.

Burnout among Dutch Teachers: An Mbi-Validity Study

The study investigates the internal consistency as well as the factorial and discriminant validity of the Maslach Burnout Inventory (MBI) in a sample of 326 Dutch secondary teachers. Compared to other teacher samples, the internal consistency of the three subscales (Emotional Exhaustion-EEX, Depersonalization-DEP, Reduced Personal Accomplishment-PAC) is relatively high. Using confirmatory maximum likelihood factor analysis with LISREL, it is shown that the three-factor oblique model fits relatively well compared to various alternative models. As in some other studies, one ambiguous item was identified ("I feel very energetic") that loads on two factors simultaneously (i.e., EEX and PAC). Moreover, burnout can be distinguished successfully from self-reported psychological strain as well as from somatic complaints. Nevertheless, EEX is substantially related to these more general symptoms. Finally, levels of EEX, psychological strain, and somatic complaints are significantly higher compared to Dutch reference groups, whereas levels of DEP and reduced PAC are significantly lower. It is concluded that the MBI is a valid and reliable self-report instrument to assess burnout in a non-English-speaking country like the Netherlands.

Structural equation analysis of the Wechsler Adult Intelligence Scale—Revised in a normal elderly sample.

A maximum-likelihood confirmatory factor analysis was performed by applying LISREL VII to the Wechsler Adult Intelligence Scale-Revised (D. Wechsler, 1981) results of a normal elderly sample (N = 225). Analyses were designed to determine which of seven hypothesized factor solutions best explained the intellectual ability of older adults. Oblique and orthogonal solutions were tested for each of the factor models. The impact of age, education, and gender was examined. Results indicated that an oblique three-factor model including Verbal, Performance, and Freedom From Distractibility factors fit the best across all sample combinations. A mild gender effect was also evident

Confirmatory factor analysis of the wechsler memory scale-revised standardization sample

A maximum likelihood confirmatory factor analysis was preformed by applying LISREL to the variance-covariance matrix obtained from standardization of the Wechsler Memory Scale-Revised (WMS-R) ( N = 316). Analyses were designed to determine which of seven hypothesized factor solutions could best explain memory function as measured by the WMS-R. Competing latent variable models were identified in previous exploratory and confirmatory factor analytic studies. The measurement error matrix was set to remove method variance shared by the immediate and delayed trials of the same subtest. Hypothesized factors were fixed and allowed to correlate. Results indicated that a three-factor model, including Attention/Concentration, Immediate and Delayed Memory, explained 91% of the score variance and produced a significantly better fit than the Attention/Concentration — General Memory or Attention Concentration — Visual/Verbal Memory solutions. Findings support previous work suggesting that the WMS-R measures separate memory functions, and that the verbal/nonverbal Index distinction may not be a viable one.

The beck anxiety inventory: Psychometric properties in a community population

This study presents data on the norms and psychometric properties of the Beck Anxiety Inventory (BAI), using a sample of 225 community adult volunteers. Maximum-likelihood confirmatory factor analyses of previously published models of the BAI: a two-factor model and a five-factor model, showed that the fit of each model was unacceptable. Also, the fit of the single-factor model was poor. Exploratory principal-components analyses with varimax and oblique rotations suggested four BAI components within this sample. Satisfactory levels of reliability were established for the BAI subscales. Finally, the relations between the BAI total and subscale scores and a related measure of anxiety and with another self-report measure of psychological distress were examined.

First-Order and Higher-Order Factors of Creative Social Intelligence Within Guilford'S Structure-Of-Intellect Model: A Reanalysis of a Guilford Data Base

The major purpose of this investigation was to ascertain through the use of confirmatory maximum likelihood factor analysis (CM-LFA) (Joreskog and Sorbom, 1989b) how accurately each of several hypothesized combinations of first-order and higher-order factors reflecting creativity in social intelligence for a sample of 192 high school students in a middle-class suburban community could describe the covariation within selected submatrixes taken from the total correlation matrix originally analyzed by Hendricks, Guilford, and Hoepfner (1969). Exploratory factor analyses involving both orthogonal (varimax) and oblique (promax) solutions were also completed and compared with the original orthogonal factor analysis of the total correlation matrix by Hendricks et al. The exploratory factor analyses showed a moderate degree of correspondence with the solution offered by Hendricks et al. It was concluded that CMLFA lent support to hypothesized first- and higher-order factors within the context of Guilford's structure-of-intellect model.

The Development and Validation of an Arabic Version of an Academic Self-Concept Scale

For a sample of 175 Arabic students attending three universities in the United States (one in Los Angeles and two in Colorado), the psychometric results arising from the development and validation of an Arabic version of an existing college level form of a standardized academic self-concept scale are presented. Both exploratory orthogonal and oblique factor analyses lent support to three of the original five hypothesized constructs underlying three factor subscales and afforded evidence in terms of loadings on a fourth factor of the fusion of two remaining hypothesized constructs. Confirmatory maximum likelihood factor analyses indicated that among many alternative first-order and higher-order factor models the one for which five oblique first-order factors were hypothesized yielded overall indexes revealing the closest degree of fit. It was concluded that the Arabic version demonstrated what could be considered satisfactory levels of reliability and homogeneity for all five factor subscales as well as substantial support for the validity of three of its hypothesized constructs.

Confirmatory factor analysis of the wechsler memory scale-revised standardization sample

A maximum likelihood confirmatory factor analysis was preformed by applying LISREL to the variance-covariance matrix obtained from standardization of the Wechsler Memory Scale-Revised (WMS-R) ( N = 316). Analyses were designed to determine which of seven hypothesized factor solutions could best explain memory function as measured by the WMS-R. Competing latent variable models were identified in previous exploratory and confirmatory factor analytic studies. The measurement error matrix was set to remove method variance shared by the immediate and delayed trials of the same subtest. Hypothesized factors were fixed and allowed to correlate. Results indicated that a three-factor model, including Attention/Concentration, Immediate and Delayed Memory, explained 91% of the score variance and produced a significantly better fit than the Attention/Concentration — General Memory or Attention Concentration — Visual/Verbal Memory solutions. Findings support previous work suggesting that the WMS-R measures separate memory functions, and that the verbal/nonverbal Index distinction may not be a viable one.