# Method

RUNNING HEAD: Structural Analysis of the 16PF

An investigation of the factor structure of the 16PF, Version 5: A confirmatory factor analytic and invariance study.

Abstract

In order to examine its higher-order factor structure, we applied confirmatory factor and invariance analysis to item level data from the US standardization sample of the 16PF5, divided into a calibration sample (N = 5130) and a validation sample (N = 5131). Using standard assessments of model fit, all primary factors displayed good to excellent model fit, thus suggesting the scales to be broadly unidimensional. Both structural and invariance analyses pointed to some level of misspecification in the global scales of Extraversion, Anxiety, Tough Mindedness, Independence and Self-Control. However, the degree of misspecification was slight. Overall, the analyses generally supported the proposed structure of the 16PF5

Key Words: Personality; Personality Structure; 16PF; Confirmatory Factor Analysis; Measurement Invariance.

1.0. Introduction

The Sixteen Personality Factor Questionnaire (16PF) has been historically one of the most widely used and rigorous psychometrically developed personality inventories of those in use today, especially in organizational settings where the opaqueness of its item content makes it an attractive option when faking might be an issue. However, despite this, since the early research of Raymond B. Cattell, questions have been raised as to whether it conforms to its claimed factor structure. The primary aim of the current paper was to test the structure of the 16PF version 5 (16PF5), as stipulated in the test manual, by applying confirmatory factor analysis (CFA) and invariance analyses to assess primary scale uni-dimensionality and the first and second order factor structure. In doing so, we aimed to provide the most thorough psychometric investigation of the structure of the 16PF5 to date.

Space does not allow a full exploration of the vast historical work on the factor structure of the 16PF across each of its revisions. Evidence from analyses of previous versions of the 16PF suggested that a number of primary scales may display poor alpha reliabilities (e.g. Barrett & Kline, 1982; Saville & Blinkhorn, 1981); that primary factors fail to load on theorized items (e.g. Aluja & Blanch, 2003; Gerbing & Tuley, 1991; Matthews, 1989); and second order factors show some variability in their loadings on the primary factors (e.g. Boyle, 1989; Hofer, Horn & Eber, 1997). The issue of low Cronbach alpha reliabilities is perhaps somewhat mitigated by various criticisms which have been made of this index as a measure of reliability (e.g. Zinbarg, Revelle, Yovel & Li, 2005). However, in his early studies concerning the development of the 16PF, Cattell himself identified various problems with the primary scales of Emotional Stability, Dominance, Abstractedness, Privateness, Apprehension, Openness to Change, Self-Reliance and Tension (Cattell, 1956, 1974; Cattell & Gibbons, 1968). Whilst these early studies have come in for criticism on methodological grounds (Cattell & Krug, 1986), they provide the back drop for the development of the 16PF5.

According to the current technical manual (Conn & Rieke, 1994), the 16PF comprises 15 primary personality factors, and five second order factors, namely: Extraversion (Self-Reliance (Q2), Warmth(A), Liveliness(F), Privateness(N), Social Boldness(H)); Anxiety (Tension(Q4), Apprehension(O), Emotional Stability(C), Vigilance(L)); Tough-Mindedness (Sensitivity(I), Openness to Change(Q1), Warmth(A), Abstractness(M)); Independence (Dominance(E), Social Boldness(H), Vigilance(L), Openness to Change(Q1)); and Self-Control (Abstractness(M), Rule Consciousness(G), Perfectionism(Q3), Liveliness(F)). Thus, the proposed structure for the second order factors of the 16PF5 includes a small number of a priori cross-loadings from first order factors.

There have been a limited number of studies which have considered the psychometric properties of the most recent 16PF5. Chernyshenko Stark, Chan, Drasgow and Williams (2001) used confirmatory factor analysis to investigate unidimensionality in the primary scales of the 16PF5. They produced single factor models for each of the primary scales of the 16PF, and judged dimensionality by assessing model fit indices. The authors concluded that in fact the primary scales were unidimensional. However, model fit indices from the single factor CFA models suggested many scales had CFI and NFI values below .90, and as such, would be considered to have poor fit according to widely accepted criteria (e.g. Hu & Bentler, 1998; 1999).

It is important to note that personality items are, often contended to be inherently complex (McCrae, Zonderman, Costa, Bond & Paunonen, 1996), and so we may not expect to see all items load perfectly as hypothesised in large exploratory analyses. Indeed, the possibility of primary scale item complexity and multi-dimensionality was explicitly acknowledge by Cattell and Krug (1986), who noted that the 16PF items were written to include a small number of factors not included in the 16 primary factors (p.512). However, when specific confirmatory models, like those of Chernyshenko et al. (2001) are estimated, we may still expect to see good model fit.

Four studies were located which specifically analysed the second order factor solutions of the 16PF5 (Aluja, Blanch & Garcia, 2005; Chernyshenko, Stark & Chan, 2001; Dancer & Woods, 2006; Rossier, de Stadelhofen & Berthoud, 2004). The results of these studies are summarised in Table 1.

(Insert Table 1 about here)

In general the studies described in Table 1 suggest that the global factors of the 16PF5 are reproducible, yet a number of issues warrant comment. Firstly, no single study was able to identify all five factors with the same pattern of primary factor loadings specified by Conn and Rieke (1994). This is of note as some studies (e.g. Dancer & Woods, 2006) take their findings to support the 5 factor structure of the global factors of the 16PF5, yet it is clear their study did not identify the same 5 factors as proposed by the test publishers. Second, whilst the global factors of Anxiety and Self-control are generally identified relatively consistently, the factors of Tough-Mindedness and Independence are more inconsistently identified.

The key issues this paper seeks to address, viz. the primary scale dimensionality, and the second-order factor structure of the 16PF5, can all be investigated through the implementation of confirmatory factor analysis (CFA). CFA is a methodology specifically designed to test hypothesised models (Bollen, 1989). In analyses of the 16PF, CFA has primarily been used to confirm the results of exploratory factor analyses (Aluja, et al., 2005; Gerbing & Tuley, 1991; Hofer et al., 1997). For example, Aluja et al., (2005) estimated 3, 4, 5 and 6 factor second-order solutions using exploratory factor analysis. Each of these solutions was then tested within the confirmatory model. The authors concluded that a five factor solution was optimal, but they noted that all solutions initially fell below acceptable levels of model fit. Additional cross loadings and correlated error terms were required to reach acceptable fit.

Other applications of CFA include scale dimensionality (Chernyshenko et al., 2001, discussed above) and analysis of measurement invariance (Hofer at al., 1997). In their study, Hofer et al. (1997) used measurement invariance to assess the stability of the 16PF structure across a number of different groups (Police, Felons & Police Applicants). They found that despite the pattern of factor loadings being invariant across groups, the magnitude of factor loadings were not, violating the assumptions of metric invariance. These results were found by testing a six factor second-order solution, which included an ability factor and second-order factors which did not correspond to the authors’ proposed structure. In totality, therefore, evidence from studies which have employed CFA indicates possible deficiencies in both the primary and second order structure of the 16PF.

The current study adopted all three of these applications of CFA to the 16PF5. Primary scale dimensionality was assessed, followed by a confirmatory analysis of the proposed second-order structure. Similar CFA investigations of other extant personality measures have recently been published (e.g. Vassend & Skrondal, 2011, study of the NEO-PI-R). Finally, the structural models analyses were assessed for measurement invariance in two representative samples. In this case the samples were provided by dividing the US standardization sample into two equal halves. Essentially, therefore we were examining whether sampling variability contributed significantly to the generalizability of structural model estimates.

2.0. Method

2.1. Sample

The data for the current study were taken from the American standardisation sample of the 16PF, 5th Edition1 (N= 10,261; Conn & Rieke, 1994). The standardisation sample was reviewed in 2002 based on the US census in 2000 to ensure it remained representative of the general population of the USA with regard to gender, ethnicity, age and geographical distribution. However, the level of education of the sample is greater than that of the US population.

The sample was randomly split into a calibration (N=5,130) and validation (N=5,131) sample. The calibration sample was used for all initial assessments of structure, while the validation sample used for cross-validation, and the invariance analyses.

2.2. Measure

The 16PF was designed as a multi-level measure of human personality traits, incorporating specific narrow primary, and broad global factors. The measure contains 185 items organised into 15 primary personality scales. Each of the primary scales consists of between 10 and 15 items. The proposed organisation of primary and secondary factors is presented above (p. 3). In addition to the 15 primary personality scales, the 16PF5 includes a 15 item Reasoning scale and a 12 item Impression Management Scale. The response format for each of the items consists of a choice from three; “No”, “?” and “Yes”, scored as 0, 1 and 2 respectively.

2.3. Analyses

The tests of unidimensionality and of the primary and second order structural analyses were estimated using robust maximum likelihood (RML). RML was selected as the use of alternative estimators for categorical data, such as diagonally weighted least squares, has been shown to be problematic in invariance analyses in that the chance of Type I error increases with sample size (French & Finch, 2006). Given the large sample in the current analysis, and the desire to utilise the same estimation method throughout the current study, RML was applied in all analyses.

2.4. Dimensionality Analysis

Single factor item level confirmatory factor analyses (CFA) were conducted for each of the primary scales. Where single factor congeneric models displayed poor fit (see below) ordinal exploratory factor analyses were conducted on the calibration sample in PRELIS (Jöreskog & Moustaki, 2006), followed by estimation of preferred multiple factor solutions using confirmatory factor analysis in the validation sample. The fit and empirical content of the single and multiple factor solutions were compared.

2.5. Item Parcelling

Item parcels were created following the procedures outlined by Little, Cunningham, Shahar and Widaman (2002). Three parcels were created per primary factor each containing between 3 and 5 items dependent on the total number of items in the scale. Items were allocated to parcels based on the item loadings on the single factor models from the scale dimensionality analyses. The three highest loading items were first allocated to separate parcels, the next three highest loading items were then added to each parcel in inverted order, and this procedure was followed iteratively until all items were exhausted.

2.6. Structural Analysis

The structural analyses sought to provide a strict test of the structure of the 16PF5 as proposed by the test publishers. Firstly, the primary scale factor structure was assessed. In the first order model, each primary factor loaded on three parcels, with no cross-loadings specified. The primary factors were allowed to correlate and were identified by fixing the first factor loading to 1 (Bollen, 1989). In the second order model, five second order latent variables were specified so that the pattern of primary scale loadings accorded with the test manual (Conn & Reike, 1994). The second order factors were also allowed to correlate and were identified by fixing the factor variances to 1 (Bollen, 1989).

2.7. Invariance Analysis

To expand upon the findings from the structural analyses, measurement invariance was investigated across the calibration and validation samples. In the primary structure model, invariance was tested sequentially by placing equality constraints across groups on the pattern of factor loadings (configural invariance), magnitude of factor loading (metric invariance) and finally factor loading intercepts (scalar invariance). In the global model, invariance was assessed at the configural and metric level. In order to ensure identification, an additional constraint was placed on the means of one of the latent primary factors.

2.8. Model Fit

In order to evaluate model fit, we adopted a range of cut-off points for each fit index as there remains debate as to the usefulness of single cut-off values. We applied a range of ≤.05 to .08 for the SRMSR, ≤.06 to .08 for the RMSEA, and ≥ .90 to .95 for the NNFI and CFI as indicative of close fit (Hu & Bentler, 1998, 1999; Schermelleh-Engel, Moosbrugger, & Muller, 2003). Comparisons between models were based on the examination of differences in fit across all reported indices. For the invariance models, we used decline in model fit at a given stage of the analysis as an indication that the assumptions of invariance do not hold in the constrained parameters (French & Finch, 2006). To assess possible decline in model fit, we rely on two papers which have addressed this issue, Cheung and Rensvold (2002) and Chen (2007). Given that Chen’s is the more recent paper we adopted his suggestion that changes of equal to or less than -0.01 in the CFI combined with a change in the RMSEA of ≤ 0.015 indicate that invariance holds.

2.9. Missing Data

The current data contained a very small percentage (0.08%) of missing data. The dimensionality analysis required item level data and so for this analysis, an imputed data matrix was computed using the Expectation-Maximisation Algorithm (EM) in SPSS. For the confirmatory factor analyses, complete data was required at the parcel level only. A single imputation was generated after parcel construction using Schafer’s NORM. NORM utilises multiple imputations based on an unstructured normal model and under the assumption that data are missing with arbitrary patterns (Schafer & Graham, 2002).

3.0 Results

3.1. Dimensionality

Table 2 contains the model fit statistics for the single factor models of the 15 primary scales of the 16PF5. Emotional Stability (C), Dominance (E), Social Boldness (H), and Openness to Change (Q1) all show excellent fit according to all fit criteria. The fit of the remaining 11 scales is good to excellent, dependent on which measure of fit is being considered.

(Insert Table 2 about here)

In only one instance does the model fit for any index fall outside of the suggested ranges of model fit, namely in the case of the RMSEA for Privateness (N). Although each of the other measures of fit suggested good fit, we conducted an EFA forcing a two factor solution on the 10 items of the Privateness scale. The resultant model evidenced improved fit (χ2SB=578.8, df=34, RMSEA=.056, SRMR=.053, CFI=.99, NNFI=.98), however this is not unexpected as CFA will generally favour, in terms of model fit, solutions with greater numbers of latent factors (see Westfall et al., 2012). The two factors correlated at .76. Consideration of the item content suggested that factor 1 was defined by items relating to sharing general information with others, whilst factor 2 concerned sharing problems with others. We suggest this split may represent difficulty/severity as opposed to a conceptual distinction, a conclusion supported by the high inter-factor correlations. As a result, we retained the single factor solution.

3.2. Structural Analysis

Following the dimensionality analysis, all items were parcelled and the primary and global scale structures were estimated in the calibration sample. For the primary structural model, fit indices suggested a close fit to the data (χ2SB=7,286.1, df=840, RMSEA=.039, SRMR=.044, CFI=.97, NNFI=.97). At the level of the global structure, a small decrease in model fit was seen, though the absolute values were still acceptable (χ2SB=11,789.3, df=914, RMSEA=.048, SRMR=.071, CFI=.96, NNFI=.95). This finding suggests a small degree of misspecification in the global model which was explored in more depth in the invariance models. Figure 1 shows the full structural model with parameter estimates from the validation sample in parentheses.

(Insert Figure 1 about here)

3.3. Invariance Analysis

The results of the invariance analysis confirm the findings from the structural analysis (see Table 3). Models A through D assess invariance in the primary scales. As the model difference statistics show, the conditions of configural, metric (Δ Fit Statistics B vs A) and scalar invariance (Δ Fit Statistics C vs B) were met, with all difference indices falling within the recommended cut-off values (Cheung & Rensvold, 2002). The conditions for scalar invariance are also satisfied when the mean of the primary scale F is constrained to provide a strict baseline for assessment of invariance in the higher order factors. However, as can be seen from Model E, and the difference statistics for models D and E, the condition of configural invariance in the higher order factor structure is violated.

(Insert Table 3 about here.)

These results are in conformity with the conclusions from the structural analysis. Measurement invariance holds in the primary scales, suggesting their appropriateness. However, the assumptions of invariance are violated in the second order factors, pointing to a degree of model misspecification. However, given that very strict criteria have been applied throughout the current analysis, the deviation from criteria for change in model fit were small, and the overall model fit remains acceptable, so the 16PF5 structure appears reasonably robust.

4.0. Discussion

The results of the current study provide good evidence as to the structural stability of the 16PF5. All of the primary factor scales displayed good to excellent levels of model fit when estimated as single congeneric factor models. Though the RMSEA for the Privateness scale was outside the suggested range for model fit, investigation of a two factor solution provided limited evidence for a substantive difference in the constructs measured by the items. Further, both the structural and invariance analysis strongly supported the proposed primary factor structure when estimated based on item parcels. At the level of the five global factors, model fit in both the structural and invariance analyses suggested a small degree of misspecification but that on the whole, the proposed structure provided a reasonable explanation for the data.

In terms of future development, while our analysis suggests that the psychometric properties of the 16PF5 are comparable with or better than that attained by other current inventories, nevertheless some revisions would be desirable. Unfortunately language dates, and for that reason some items which worked 20 years ago may not work now. This consideration alone suggests that a revision may be required. Moreover, factor analysis continues to develop both theoretically and in terms of practical applications (e.g. Bernaards & Jennrich, 2005; Muthen & Muthen, 2010), so it is possible that using more modern algorithms that a more robust second-order factor structure could be identified.

In addition to the substantive points noted above, two methodological points emerge from this study. Firstly, it has been proposed that confirmatory factor analysis is unsuitable for the development and investigation of personality scales (McCrae, et al., 1996; Marsh et al., 2010), and instead methods such as principal components analysis (PCA) followed by Varimax or Procrustes rotations have been advocated (McCrae et al., 1996). There are a number of reasons why these suggestions are inappropriate. For example, PCA assumes that indicators are measured without error, an assumption which is difficult to maintain for personality data. Further, PCA estimates components, or formative constructs, whereas personality theory postulates latent (reflective) constructs (Borsboom, Mellenbergh & Van Heerden, 2003). As such, the use of PCA leads to an inconsistency between the assumptions of the theory and the assumptions of the methods applied. Moreover, Varimax rotation assumes orthogonality of factors which rarely reflects the natural properties of the data (Yates, 1987), most especially in the case of personality. Almost certainly oblique methods are preferable since they should correctly locate factor axes whether they are orthogonal or oblique (Sass & Schmitt, 2010).

Confirmatory factor analysis adds many refinements to exploratory factor analysis including exact solutions, improved estimation methods, and numerous means to evaluate model fit (Bollen, 1989). Other things being equal, it might be thought that CFA should be the preferred method of analysing personality scales. Exploratory structural equation modelling (ESEM) has been proposed as an alternative to CFA for complex data (Marsh et al., 2010). ESEM maintains many of the advantages of confirmatory methods such as inclusion of residual variance, the ability to fit invariance models etc., whilst employing an exploratory approach, namely modelling a saturated factor matrix (Asparouhov & Muthén, 2009). To date only a limited number of studies have employed ESEM and so it remains open as to whether it will provide a useful framework for the advancement of both psychometric and applied studies of personality.

In the current study, we follow the suggestion of Hopwood and Donnellan (2010) that CFA, rigorously applied, is still a plausible method for the analysis of personality inventories. We add the current study to that of Vassend and Skrondal (2011) in showing that CFA can be used to analyse personality inventories at multiple levels. In their study, Vassend and Skrondal (2011) investigated the structure of the NEO-PI-R at the individual facet level, individual broad factor level, and as a complete structural model. These authors concluded that CFA is a valuable tool in directly testing theories about the structure of personality inventories. We draw a similar conclusion from a similar set of applied CFA analyses of the 16PF5.

A potential limitation to the current study is the use of item parcels. Item parcelling has been widely discussed in the methodological literature on SEM and is generally considered somewhat controversial (Little, et al., 2002; Meade & Kroustalis, 2006). When the context is one of scale development, then there are strong arguments against parcelling. Firstly, parcelling may disguise the multidimensionality of items (Bandalos & Finney, 2001). If multidimensional items are parcelled inappropriately this may lead to latent constructs confounded with specific variance (Little, et al., 2002). Secondly, according to the simulation of Meade & Kroustalis (2006), parcelling may be detrimental to the detection of biased items, and for this reason item level analysis is recommended for this purpose. Thirdly, even under the circumstance in which reasonable sets of items have been constructed, their allocation to item parcels can lead to different conclusions with regard to substantive parameters and model fit (Sterba & MacCallum, 2010).

We acknowledge these potential issues with item parcelling. However, the current study sought to provide a purely confirmatory analysis of the 16PF5 structure. Given the number of items in the full inventory, an item level analysis is not tractable, even in a sample as large as the current one. Importantly, we tested and demonstrated unidimensionality of the primary scales prior to parcelling and as such, concerns over the masking of multidimensionality seem minimal.

Overall it can be concluded that the 16PF possesses good psychometric properties compared with other major personality inventories. Although the 16PF does not provide a measure which corresponds particularly well with the Five Factor Model, the current consensus model of personality, as a practical measurement tool in high stakes testing, the high level of opacity of the 16PF may well represent a significant advantage, in comparison to other current tests.

References

Aluja, A., & Blanch, A. (2003). Replicability of the first-order 16PF-5 factors: an analysis of three parcelling methods. Personality and Individual Differences, 37, 667-677.

Aluja, A., Blanch, A., & Garcia, L. F. (2005). Reanalyzing the 16pf-5 second order structure: Exploratory versus confirmatory factorial analysis. European Journal of Psychology of Education, 20, 343-353.

Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438.

Bandalos, D. L., & Finney, S. J. (2001). Item parcelling issues in structural equation modeling. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 269–296). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

Barrett, P. & Kline, P. (1982). An Item and Radial Parcel Factor Analysis of the 16PF Questionnaire. Personality and Individual Differences, 3, 259-270.

Bernaards, C. A., & Jennrich, R. I. (2005). Gradient projection algorithms and software for arbitrary rotation criteria in factor analysis. Educational and Psychological Measurement, 65, 676-696.

Bollen, K. A. (1989). Structural Equations with Latent Variables. New York: Wiley.

Borsboom, D., Mellenbergh, G. J., & Van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110, 203-219.

Boyle, G. (1989). Re-examination of the major personality-type factors in the Cattell, Comrey and Eysenck Scales: Were the factor solutions of Noller et al. optimal? Personality and Individual Differences, 10, 1289-1299.

Cattell, R. B. (1956). Validation and intensification of the sixteen personality factor questionnaire. Journal of Clinical Psychology, 12, 205-214.

Cattell, R. B. (1974). Radial parcel factoring-vs-item factoring in defining personality structure in questionnaires: Theory and experimental checks. Australian Journal of Psychology, 26, 103-119.

Cattell, R. B. & Gibbons, B. D. (1968). Personality factor structure of the combined Guildford and Cattell personality questionnaire. Journal of Personality and Social Psychology, 9, 107-120.

Cattell, R. B., & Krug, S. E. (1986). The Number of Factors in the 16PF: A Review of the Evidence with Special Emphasis on Methodological Problems. Educational and Psychological Measurement, 46, 509-521.

Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14, 464-504.

Chernyshenko, O. S., Stark, S. & Chan, K. Y. (2001). Investigating the Hierarchical Factor Structure of the Fifth Edition of the 16PF: An Application of the Schmid-Leiman Orthogonalization Procedure. Educational and Psychological Measurement, 61, 290-302.

Chernyshenko, O. S., Stark, S., Chan, K. Y., Drasgow, F. & Williams, B. (2001). Fitting Item Response Theory Models to Two Personality Inventories: Issues and Insights. Multivariate Behavioral Research, 36, 523-562.

Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9, 235-255.

Conn, S. R., & Rieke, M. L. (1994). (Eds.) The 16PF fifth edition technical manual. Champagne, IL: Institute for Personality and Ability Testing, Inc.

Dancer, L .J. & Woods, S. A. (2006). Higher-order Factor Structures and Intercorrelations of the 16PF5 and FIRO-B. International Journal of Selection and Assessment, 14, 385-391.

French, B. F., & Finch, W. H. (2006). Confirmatory factor analytic procedures for the determination of measurement invariance. Structural Equation Modeling, 13, 378-402.

Gerbing, D.W., & Tuley, M.R. (1991). The 16PF Related to the Five-Factor Model of Personality: Multiple-Indicator Measurement versus the A Priori Scales. Multivariate Behavioral Research, 26, 271-289.

Hofer, S. M., Horn, J. L. & Eber, H. W. (1997). A Robust Five-Factor Structure of the 16PF: Strong Evidence from Independent Rotation and Confirmatory Factorial Invariance Procedures. Personality and Individual Differences, 23, 247-269.

Hopwood, C.J., & Donnellan, M.B. (2010). How should the internal structure of personality inventories be evaluated? Personality and Social Psychology Review, 14, 332-346.

Hu, L.-T., & Bentler, P.M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453.

Hu, L. T., & Bentler, P. M. (1999). Cut-off criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55.

Jöreskog, K. G. & Moustaki, I. (2006). Factor Analysis of Ordinal Variables with Full Information Maximum Likelihood. Available at

Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits. Structural Equation Modeling, 9, 151-173.

Marsh, H. W., Lüdtke, O., Muthén, B., Asparouhov, T., Morin, A. J. S., Trautwein, U. & Nagengast, B. (2010). A new look at the big-five factor structure through exploratory structural equation modeling. Psychological Assessment, 22, 471-491.

Matthews, G. (1989). The Factor Structure of the 16PF: Twelve Primary and Three Secondary Factors. Personality and Individual Differences, 10, 931-940.

McCrae, R.R., Zonderman, A.B., Costa, P.T., Bond, M.H. & Paunonen, S.V. (1996). Evaluating Replicability of Factors in the Revised NEO Personality Inventory: Confirmatory Factor Analysis Versus Procrustes Rotation. Journal of Personality and Social Psychology, 70, 552-566.

Meade A. W., & Kroustalis, C. M. (2006). Problems with item parcelling for confirmatory factor analytic tests of measurement invariance. Organizational Research Methods, 9, 369-403.

Muthen, L.K., & Muthen, B.O. (2010). Mplus User’s Guide. Sixth Edition. Los Angeles, CA: Muthen & Muthen.

Rossier, J., Meyer de Stadelhofen, F., & Berthoud, S. (2004). The Hierarchical Structures of the NEO PI-R and the 16PF5. European Journal of Psychological Assessment, 20, 27-38.

Sass, D. A., & Schmitt, T. A. (2010). A comparative investigation of rotation criteria within exploratory factor analysis. Multivariate Behavioral Research, 45, 73-103.

Saville, P. & Blinkhorn, S. (1981). Reliability, Homogeneity and the Construct Validity of Cattell’s 16PF. Personality and Individual Differences, 2, 325-333.

Schafer, J.L. & Graham, J.W. (2002). Missing Data: Our View of the State of the Art. Psychological Methods, 7, 147-177.

Schermelleh-Engel, K., Moosbrugger, H., & Muller, H. (2003). Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures. Methods of Psychological Research, 8, 23-74.

Sterba, S. K., & MacCallum, R. C. (2010). Variability in parameter estimates and model fit across repeated allocations of items to parcels. Multivariate Behavioral Research, 45, 322-358.

Vassend, O., & Skrondal, A. (2011). The NEO personality inventory revised (NEO-PI-R): Exploring the measurement structure and variants of the five-factor model. Personality and Individual Differences, 50, 1300-1304.

Westfall, P.H., Henning, K.S.S. & Howell, R.D. (2012). The effect of error correlation on interfactor correlation in psychometric measurement. Structural Equation Modeling: A Multidisciplinary Journal, 19, 99-117.

Yates, A. (1987). Multivariate exploratory data analysis: A perspective on exploratory factor analysis. Albany: State University of New York Press.

Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω H: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70, 123-133.

Footnote

1 Copyright© 1993 by the Institute for Personality and Ability Testing, Inc., Champaign, Illinois, USA. All rights reserved. Reproduced with special permission of the publisher. Further reproduction is prohibited without permission of IPAT Inc., a wholly owned subsidiary of OPP Ltd., Oxford, England.

Table 1

Second-Order Factor Solutions from 16 Analyses of the 16PF5

| |Extraversion |Anxiety |Tough-Mindedness |Independence |Self-Control |

Test Manual -

Conn & Rieke (1994) |A |F |H |N |Q2 | |C |L |O |Q4 | |A |I |M |Q1 | |E |H |L |Q1 | |F |G |M |Q3 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Chernyshenko et al. (2001) |A |F |H |N |Q2 | |C |L |O |Q4 | | |I |M |Q1 | |E | | | | | |G |M |Q3 | | |Rossier et al. (2004)a |A | |H |N |Q2 |L,Q1 |C |L |O |Q4 |I | | | | | |E |H | | |I |F |G |M |Q3 |Q1 | |Aluja et al. (2005) |A |F | |N |Q2 |M |C |L |O |Q4 | |A |I |M |Q1 |C,O |E |H | |Q1 |C |F |G |M |Q3 | | |Dancer & Woods (2006) |A |F |H |N |Q2 | |C |L |O |Q4 |M |A |I |M |Q1 | |E |H | |Q1 |O,C | |G |M |Q3 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |Note: Italicised scale labels indicate loadings which were not theorised by the test publishers. Scale loadings are included as per reported factor loading matrices. All loadings >0.30 are included.

a Rossier et al. located a fifth factor comprised of F & Q2.

Table 2

Primary Scale Dimensionality Analysis – Comparative Fit Statistics

Primary Scale |χ2SB |df |RMSEA |SRMR |CFI |NNFI | |Warmth(A) |1188.67 |44 |.071 |.080 |.95 |.94 | |Emotional Stability(C) |525.59 |35 |.052 |.050 |.99 |.99 | |Dominance(E) |445.65 |35 |.048 |.052 |.98 |.98 | |Liveliness(F) |794.09 |35 |.065 |.065 |.97 |.96 | |Rule Consciousness(G) |1004.48 |44 |.065 |.065 |.97 |.97 | |Social Boldness(H) |722.75 |35 |.062 |.044 |.99 |.99 | |Sensitivity(I) |1224.75 |44 |.072 |.064 |.97 |.96 | |Vigilance(L) |354.54 |35 |.042 |.043 |.99 |.99 | |Abstractness(M) |1111.62 |44 |.069 |.063 |.98 |.97 | |Privateness(N) |1604.85 |35 |.094 |.074 |.96 |.95 | |Apprehension(O) |878.43 |35 |.069 |.057 |.98 |.97 | |Openness to Change(Q1) |965.32 |77 |.047 |.055 |.96 |.96 | |Self-Reliance(Q2) |710.32 |35 |.061 |.054 |.98 |.98 | |Perfectionism(Q3) |1114.55 |35 |.078 |.073 |.96 |.95 | |Tension(Q4) |881.93 |35 |.069 |.060 |.98 |.97 | |

Table 3

Model Fit Statistics for Invariance Analysis of Sample 1 & 2 Testing the Conn & Rieke (1994) Structure of the 16PF5

Model |χ2SB |Df |RMSEA |SRMR |CFI |NNFI | |A: First Order Configural Invariance |14810.78 |1680 |.039 |.044

.044 |.97 |.97 | |B: First Order Metric Invariance |15994.49 |1710 |.040 |.048

.047 |.97 |.97 | |Δ Fit Statistics B vs A |3018.09

p< .001 |30 |.001 |.004

.003 |0 |0 | |C: First Order Scalar Invariance |19214.12 |1740 |.044 |.049

.047 |.97 |.96 | |Δ Fit Statistics C vs B |-7057.02a |30 |.004 |.001

.000 |0 |-.01 | |D: First Order Scalar Invariance with mean of F constrained. |19225.32 |1741 |.044 |.049

.047 |.97 |.96 | |Δ Fit Statistics D vs C |11.29

p< .001 |1 |0 | .000

.000 |0 |0 | |E: First Order Scalar and Second Order Configural Invariance |28590.92 |1888 |.052 |.074

.070 |.95 |.94 | |Δ Fit Statistics E vs D |11296.56

p< .001 |147 |.008 |.015

.013 |-.02 |-.02 | |F: First Order Scalar and Second Order Metric Invariance |28816.60 |1909 |.052 |.074

.072 |.95 |.94 | |Δ Fit Statistics F vs E |175.51

p< .001 |21 |0 |.000

.002 |0 |0 | |a Significance values cannot be computed when the χ2SB difference is negative.

Figure Captions

Figure 1. Second-order common factor structure of the 16PF5: standardized solution.

For scale labels please refer to Table 1. Parameter estimates in parentheses are from the validation sample.

Figure 1

[pic]

-----------------------

.59(.60)

C

.72(.72)

.83(.83)

.80(.80)

.82(.95)

.45(.43)

.25(.24)

.45(.45)

.86(.96)

.75(.76)

.74(.78)

-.46(-.44)

.66(.65)

.79(.79)

-.99(-1.00)

F

Q3

L

M

O

Q4

G

N

H

Q2

A

I

Q1

E

.31(.30)

.36(.36)

.47(.48)

.48(.47)

.50(.52)

.41(.38)

.48(.47)

.30(.30)

.42(.43)

.39(.37)

.46(.47)

.31(.29)

.32(.33)

.50(.54)

.44(.47)

.34(.36)

.48(.48)

.36(.36)

.43(.45)

.24(.26)

.48(.46)

.20(.18)

.24(.25)

.29(.27)

.45(.44)

.37(.40)

.51(.55)

.45(.48)

.49(.53)

.43(.39)

.36(.37)

.41(.42)

.38(.34)

.56(.55)

.39(.42)

.52(.49)

.29(.28)

.40(.41)

.42(.43)

.59(.60)

.42(.42)

.60(.59)

.42(.45)

.67(.68)

.50(.49)

ANXIETY

EXTRA-VERSION

SELF-

CONTROL

TOUGH

MINDED

INDEPENDENCE

L1

L2

L3

O3

O1

O2

Q4.1

Q4.2

Q4.3

G1

G2

G3

M1

M2

M3

N1

N2

N3

H1

H2

H3

F1

F2

F3

¨øºøÄøÎøØøâøêøòøôø$ù0ù@ùDùHùTù^ùbùfùhùâùôùþùúúú$ú,úóóóóóóóQ3.1

Q3.2

Q3.3

Q2.1

Q2.2

Q2.3

A1

A2

A3

I1

I2

I3

Q1.1

Q1.2

Q1.3

E1

E2

E3

C1

C2

C3

.76(.73)

.56(.55)

-.86(-.84)

.75(.77)

.63(.63)

-.59(-.61)

-.79(-.80)

.18(.22)

.77(.76)

.77(.79)

.72(.73)

.70(.69)

.72(.73)

.84(.84)

.76(.75)

.83(.84)

.78(.79)

.73(.73)

.75(.73)

.82(.82)

.71(.68)

.80(.80)

.81(.80)

.72(.72)

.76(.78)

.74(.72)

.72(.69)

.70(.67)

.74(.75)

.79(.78)

.84(.85)

.90(.91)

.87(.87)

.72(.73)

.75(.74)

.87(.86)

.79(.81)

.80(.79)

.77(.76)

.69(.71)

.66(.67)

.78(.76)

.76(.76)

.84(.85)

.77(.77)

.63(.64)

.64(.63)

.76(.76)

.71(.71)

.76(.74)

.57(.57)

.45(.47)

.22(.29)

.11(.15)

.55(.44)

.49(.47)

.40(.42)

-.09(-.21)

.48(.45)

.29(.25)

.27(.25)

................

................

#### To fulfill the demand for quickly locating and searching documents.

It is intelligent file search solution for home and business.

##### Related searches

- method of teaching in education
- baking soda method for drug test meth
- certo method instructions
- why is scientific method important
- examples of method of analysis
- effective interest method calculator
- effective interest rate method example
- best payment method for selling a car
- p value method formula
- race method for answering questions
- method study steps
- constant yield method excel