INTERNATIONAL JOURNAL OF PSYCHOLOGY, 2003, 38 (6), 390–400

Correspondence should be addressed to Stéphane Vautier, CERPP, UFR de Psychologie, Université de Toulouse Le Mirail,5 allées A. Machado, F-31058 cedex 9, France (E-mail: vautier@univ-tlse2.fr).

This work was supported by the CERPP and the LTC. We thank Julia Kogan for useful remarks on the manuscript.

© 2003 International Union of Psychological Sciencehttp://www.tandf.co.uk/journals/pp/00207594.html DOI: 10.1080/00207590344000222

Dimensionality of the Revised Life OrientationTest and the status of filler items

Stéphane Vautier, Eric Raufaste, and Magali Cariou

Université de Toulouse Le Mirail, France

D ispositional optimism was originally construed as unidimensional (Scheier & Carver, 1992). However, LOT-Rdata (Scheier, Carver, & Bridges, 1994) generally appeared bidimensional as a number of studies suggest a two-

correlated-factor model representing optimism and pessimism. Attempts at corroborating one-factor models suggest thatcorrelated errors between positively worded items are required for an adequate account of the data. This article explainsbidimensionality by the influence of social desirability (i.e., being positive is desirable). Namely, in the present study,correlated errors are interpreted as the presence of individual differences related to the tendency to present oneself in apositive manner. Moreover, response styles can be corroborated by appropriately modelling the entire covariance matrix(i.e., including fillers), by checking that fillers with positive meaning correlate with the faking-good group factor. Stu-dents (N = 442) responded to a French adaptation of the LOT-R. The data were submitted to SEM analyses. The tradi-tional two-correlated factor model (optimism–pessimism) was outperformed by a model including a common factor(“optimism”) plus a factor grouping positive items only (“faking positive”). In addition, reliability analyses showed thatthe choice of the model clearly impacts the reliability estimates based on the model. The entire dataset was modelled forexploring the relationships between the fillers and the measurement model (i.e., the set of all relationships between factorsand their indicators). The specific correlations of fillers whose meaning is positive with the faking-good group factorcorroborated its substantial interpretation. It is concluded that there is no empirical necessity for hypothesizing that thedispositional optimism construct must be split into optimism plus pessimism.

L’optimisme dispositionnel a été initialement conçu comme unidimensionnel (Scheier & Carver, 1992). Néanmoins,les données recueillies avec le LOT-R (Scheier, Carver, & Bridges, 1994) sont généralement apparues

bidimensionnelles, un modèle à deux facteurs corrélés d’optimisme et de pessimisme étant suggéré par de nombreusesétudes. Les tentatives pour corroborer les modèles unifactoriels suggèrent que corréler les erreurs entre items positivementformulés est nécessaire pour rendre compte adéquatement des données. Cet article explique la bidimensionalité parl’influence de la désirabilité sociale (i.e., il est désirable de paraître positif). Ainsi, dans la présente étude, la corrélationdes erreurs est interprétée comme le signe de l’existence de différences individuelles dans la tendance à se présenter demanière positive. L’existence de styles de réponse peut de plus être corroborée en modélisant correctement la matrice decovariances entière (y compris les items servant de leurre), en vérifiant que les leurres ayant une signification positivecorrèlent avec le facteur ayant trait à la désirabilité des réponses. Des étudiants (N = 442) ont rempli une adaptationfrançaise du LOT-R. Les données ont été analysées par modèles d’équations structurelles. Le modèle traditionnel à deuxfacteurs corrélés (optimisme et pessimisme) s’est révélé moins performant que le modèle comprenant un facteur commun(«optimisme») et un facteur de groupe lié aux items positifs («faire bonne figure»). En outre, les analyses de fidélité ontmontré que le choix d’un modèle affecte nettement les estimations de fidélité basées sur ce modèle. La matrice de covari-ances entière a été modélisée pour explorer les relations entre les leurres et le modèle de mesure (i.e., l’ensemble desrelations possibles entre les facteurs et leurs indicateurs). Les corrélations entre les leurres à signification positive et lefacteur de désirabilité ont corroboré l’interprétation proposée. En conclusion, il n’y a pas de nécessité empirique à supposerque le concept d’optimisme dispositionnel doive être scindé en deux concepts d’optimisme et de pessimisme.

E l optimismo disposicional se conceptuó originalmente como unidimensional (Scheier & Carver, 1992). Sin embargo, los datos del LOT-R (Scheier, Carver, & Bridges, 1994) generalmente han aparecido como bidimensionales, ya que

un número de estudios ha sugerido un modelo de dos factores correlacionados que representan optimismo y pesimismo.

DIMENSIONALITY OF LOT-R 391

In order to assess individual differences in optimism, afirst version of the Life Orientation Test (LOT) wasdeveloped (for a review, see Scheier & Carver, 1992).Later, a revised version was developed (LOT-R;Scheier, Carver, & Bridges, 1994). In the revised ver-sion, raters assess their degree of agreement with 10statements, 4 of which are fillers excluded from the fi-nal composite score. The LOT-R is a brief measure thatcan easily be included in more extensive projects. Thispaper addresses the question of the dimensionality ofthe LOT-R questionnaire, taking into account the struc-tural status of fillers.

According to Lai, Cheung, Lee, and Yu (1998), theLOT-R was proposed by Scheier and Carver (1985) tomeasure a one-dimensional bipolar construct ofdispositional optimism as a response to intensifyingcontroversies about the issue of one- vs. two-dimensionality of dispositional optimism. Dispositionaloptimism was defined as positive outcome expectancyand was thought of as a single trait. Previous empiricalstudies reviewed by Lai et al. suggest two correlatedfactors predicting answers to the positively worded itemsand the negatively worded items, respectively. Thismodel will be labelled the “2CF model.” Concludingfrom the Scheier et al. (1994) paper that “Confirmatoryfactor analysis further indicated that the single-factorsolution was superior to a two-factor one,” Lai et al.(1998, p. 46) conducted confirmatory factor analysesto compare the goodness of fit of the single- and thetwo-factor solutions for modelling data from Hong KongChinese students. Lai and colleagues argued that theLOT-R better supports a one-factor than a two-factormodel: one-factor, c2(38) = 316.39, p < .001, Bentler-Bonnett normed fit index = 0.69; two-factor,c2(37) = 526.24, p < .001, Bentler-Bonnett normed fitindex = 0.34 (p. 51).

Starting from a discussion of a point made by Lai etal. (1998), it will be argued that:

1. Their results cannot be taken as supportive evi-dence for the idea of unidimensionality of the LOT-Rdata.

2. The one-factor model of Scheier et al. (1994), la-belled the 1FCE (one-factor plus correlated errors)model, is actually formally equivalent to a two-orthogonal factor (2OF) model because error terms ofthe positively worded items are intercorrelated;therefore,the 1FCE provides evidence againstunidimensionality of the LOT-R measures. In addition,the (traditional) 2CF (two-correlated factor) model canbe replaced by the 2OF model, which is theoreticallycompatible with both unidimensionality of dispositionaloptimism and bidimensionality of the LOT-R data.

3. Including the fillers in the analysis should help toexplain both unidimensionality of the optimism con-struct and bidimensionality of the data.

As regards LOT-R data dimensionality, additionalto the three models presented above, the “congenericmodel” (one factor with no correlations between errorterms) also serves as an important contrast to the 1FCEmodel: the former corroborates whereas the latter re-futes unidimensionality of the data (see McDonald,1981). In order to illustrate these points, the four alter-native models will be fitted to empirical data. For thesake of clarity, Figure 1 depicts the congeneric, 1FCE,2OF, and 2CF models.

The present paper is organized as follows. In the firstsection, it is shown that Lai et al. (1998) goodness-of-fit statistics cannot be based on the analyses they re-ferred to. The second section turns to the modelling ofthe target measures. The hypothesis thatunidimensionality does not hold, as can be expectedfrom previous research, was tested, and the 1FCE, the2OF, and the 2CF models were assessed. The 2OFseems to be the best model. The third section returns tothe issue of fillers, which raises interesting questions:

Los intentos encaminados a corroborar los modelos de un factor sugerían que, para lograr una explicación adecuada de losresultados, se requería de errores correlacionados entre los reactivos positivos. Este artículo explica la bidimensionalidadpor medio de la influencia de la deseabilidad social (es decir, ser positivo es deseable). En el presente estudio, los errorescorrelacionados se han interpretado como la presencia de diferencias individuales relacionadas con la tendencia a presentarsea sí mismo en una forma positiva. Además, los estilos de respuesta pueden corroborarse, si se modela adecuadamente labase de datos completa (es decir, si se incluyen los reactivos de relleno). Se verifica que los reactivos de relleno consignificado positivo correlacionen con el factor del grupo que simula una apariencia positiva. Cuatrocientos cuarenta ydos estudiantes respondieron a la adaptación francesa del LOT-R. Los datos se analizaron mediante el modelo de ecuacionesestructurales. El modelo que incluye un factor común (“optimismo”) más un factor que agrupa sólo los reactivos positivos(“positivos simulados”) superó al modelo tradicional de dos factores correlacionados (optimismo-pesimismo). Asimismo,los análisis de fiabilidad mostraron que la elección del modelo impacta claramente los cálculos de fiabilidad basados en elmodelo. Se modeló la base de datos completa para explorar las relaciones entre los reactivos de relleno y el modelo demedición (es decir, la serie de todas las relaciones entre los factores y sus indicadores). Las correlaciones específicas delos de relleno, cuyo significado fuera positivo, con el factor del grupo que simula una apariencia positiva corroboró suinterpretación. Se concluye que no hay necesidad empírica de hipótesis que propongan que el constructo de optimismodisposicional deba dividirse en optimismo más pesimismo.

392 VAUTIER, RAUFASTE, CARIOU

How would the fillers work if added to a correct meas-urement model of dispositional optimism (i.e., the setof all relationships between factors and their indica-tors)? What can the fillers teach us about optimismdimensionality? In order to put forth some possibleanswers to these questions, the relationships betweenfillers and the measurement model from the best model,the 2OF, are explored.

WHY SO MANY DFS IN THE LAI ET AL.STUDY?

The c2 statistics of Lai et al. (1998) are hard to explain.The measurement models that should have been speci-fied are based on a 6 ́ 6 input covariance matrix formedby the six target items, which entails 6 ́ (6 + 1) / 2 = 21sample variances and covariances (see Bentler &Bonett, 1980). As shown in Figure 1, the congenericmodel requires the estimation of six loadings plus sixuniquenesses (or error terms in a broad sense), lead-ing to degrees of freedom (dfs). By itself, the 2CFmodel involves 8 dfs. Lai et al. (1998) reported 38 and37 dfs for the test of their models. Despite their claim,the dfs reported by Lai et al. (1998) thus suggest thatmodels other than the congeneric or 2CF models havebeen tested in their study.

How can such a discrepancy be explained? If onedoes not remove the fillers from the analysis, the ob-served covariance matrix provides 10 ́ (10 + 1) / 2 = 55

input values. The question is: How have the fillers beenmodelled? Lai et al. (1998) reported 38 dfs for the testof what they called the “one-factor model.” Thus, theirmodel contains 55 – 38 = 17 parameters to be estimated.It can be conjectured that the four fillers have beenmodelled as an independent covariance submatrix, lead-ing to 4 ´ (4 + 1) / 2 = 10 parameters to be estimated.Then the measurement model could have been speci-fied using one common parameter for the error variances(an equality constraint) and six loadings, or six errorvariances and one common parameter for the sixloadings (another kind of equality constraint). The sameconjecture works if one considers the two group fac-tors (i.e., two factors grouping two different subsets ofitems), as the correlation between both factors elimi-nates one df.

It cannot be claimed that Lai et al.’s analyses wereconducted in this way, however. What rationale couldbe used to justify an equality constraint for the loadingsor the error variances? The lack of a detailed reportabout the models merely allows for the suggestion thatusing an equality constraint may explain why 38 and 37dfs were reported in their study, instead of 9 and 8 dfs,respectively.

The estimated value of the Bentler-Bonnett normedfit index (NFI) strongly suggests that their so-called“one-factor model” could be improved substantially(NFI = .64). The NFI measures the relative improve-ment of fit caused by switching from a “null model,”

Figure 1. Four alternative measurement models for the target tems of the LOT-R.

DIMENSIONALITY OF LOT-R 393

or baseline model, to a more complex model (the esti-mated model). As the fit becomes perfect this indexapproaches 1. According to Bentler (1995, p. 93),“Values of NFI greater than .9 are desirable.” A valueof .64 is far below .9. Clearly, the goodness-of-fit in-dices allow for comparing the models with 38 vs. 37dfs, but not for concluding that the “one-factor model”accounts acceptably for the data.

It seems that among the published psychometricstudies devoted to the LOT-R, only Lai et al. (1998)took the fillers into account in the factorial analyses.As will be argued later, modelling all the LOT-Rdata including fillers could be useful for addressingthe issue of dimensionality of the optimism data. Thenext section goes back to the issue of dimensionalityof dispositional optimism as measured using targetitems only.

MODELLING DISPOSITIONALOPTIMISM

What are the psychological dimensionsbehind optimism data?

It is proposed that empirical bidimensionality of theLOT-R data and theoretical unidimensionality of theoptimism trait can be reconciled, remembering that dataare gathered using self-ratings. Self-ratings may conveyindividual differences in response styles, e.g., the ten-dency to present oneself in a positive manner (e.g.,Paulhus, 1986). This idea can easily be operationalizedusing a 2OF model. Moreover, the 2OF model allowsfor solving some theoretical concerns with the 1CFE andthe 2CF models, namely the issues of correlated errorsin measurement models and of defining the basic dimen-sions required for modelling true variance.

Admitting that the linear factorial framework is suit-able for modelling optimism, bidimensionality of thedata is strongly supported by the factorial evidenceavailable. Among a selection of 11 studies investigat-ing the factorial structure of the LOT or the LOT-R,only the study by Lai and Yue (2000) reported evi-dence for unidimensionality. No reason why this se-lection would be biased towards two-factor modelscould be found. The Lai and Yue exception will bediscussed later in the paper. Remaining findings areoutlined below. Evidence can be categorized by dis-tinguishing studies supporting one-factor vs. two-fac-tor models.

One-factor models

Scheier et al. (1994) and Steed (2002) presented aone-factor model, yet with correlated errors. However,

specifying correlated errors within a one-factor modelby definition tells us that unidimensionality is lost. Morespecifically, the 1FCE model is formally equivalent tothe 2OF (two-dimensional) model, within which thecorrelated errors are replaced by a group factor (seeFigure 1), i.e., by a factor that contributes to a subset ofthe measured items. The group factor explicitly repre-sents a systematic source of variance, hypothetically akind of response style attribute. For example, in Scheieret al. (1994) the group factor relates to the three posi-tive items, which are interpreted as a social desirabilitybias concomitant to the desire to emphasize positiveappearance.

One concern with the 1FCE model is the use of cor-related errors: Why would errors correlate? In factorialmodels, error terms are actually uniquenesses thatadditively combine (1) a specificity (e.g., a source ofvariance genuinely bound to the effect of formulationof the question that triggers the rating), and (2) a purelyrandom error component (e.g., Bollen, 1989, pp. 218–221). The specific component is thought of as a truecomponent, because it is not random error. Correlateduniquenesses can be interpreted as reflecting correlatedspecificities, that is, a part of true variance. This part oftrue variance may as well be formalized using a groupfactor, thus reframing the 1FCE model into a 2OFmodel.

Despite their formal equivalence, the choice of the1FCE vs. 2OF model has important consequences onreliability estimation. In classical test theory, the com-posite reliability of the data is defined as the ratio ofthe true variance to the total variance. This ratio can becomputed using the parameter estimates of the measure-ment model (McDonald, 1999; Raykov, 1997), insteadof coefficient alpha, which is based on the input matrix.The numerator will be smaller in the 1FCE model thanthat in the 2OF model because, by definition, variancemodelled as correlated errors (1FCE model) cannot bequalified as true variance, whereas the same variancemodelled as a group factor (2OF) is naturally qualifiedas true variance. Since total variance remains the samein the two models, the composite reliability calculuswill provide a value larger for the 2OF than for the1FCE. An interesting issue was how reliability wouldbe affected by the modelling of the input matrix in the1FCE vs. 2OF models, comparing their respective 90%confidence intervals. The literature about two-factormodels is now considered.

Two-factor models

Turning to the second category of empirical evidence,a 2CF model was selected in six studies related to the firstLOT (Chang & McBride-Chang, 1996; Cheng & Hamid,

394 VAUTIER, RAUFASTE, CARIOU

1997; Lai, 1994; Marshall & Lang, 1990; Marshall,Wortman, Kusulas, Herving, & Vickers, 1992; Robinson-Whelen, Kim, MacCallum, & Kiecolt-Glaser, 1997).Concerning the LOT-R, Creed, Patton, and Bartrum(2002), Lai and Yue (2000), and Sultan and Bureau(1999) also provided evidence for a 2CF model.

Despite its compelling empirical support, the 2CFmodel is not entirely satisfactory because it lacks aclear theoretical background. If optimism and pessi-mism are not exact empirical opposites, how is theirdifference theoretically grounded? The 2CF model ac-counts for the imperfect negative correlation betweenthe optimism and pessimism group factors, but doesnot account for their conceptual difference. Measuresof dispositional optimism were intended to capture asense of good-bad expectancy (Carver & Scheier,1998). Recently, Carver and Scheier (2001) pointedout the bidimensionality of the LOT(-R) measures. Totake the empirical evidence into account, they sug-gested that “It may be that one component of the meas-ure reflects confidence about attaining positiveoutcomes, and the other component reflects confidenceabout avoiding undesired outcomes” (p. 41). This viewraises the issue of the unspecified correlation betweenboth factors. This feature is undoubtedly helpful forfitting a confirmatory model to a given sample, capi-talizing on chance (MacCallum, Roznowski, &Necowitz, 1992), but theory underlying the 2CF modelshould be able to explain why the correlation is al-lowed to change across samples.

A radically different explanation is based on astrong structural approach: LOT-R data would con-tain more than good-bad expectancies, because theyare produced through a self-rating technique. System-atic artifactual variance, then, may have polluted thedata. Marshall and Lang (1990) have suggested thatthe bidimensionality of their LOT data could be ex-plained as a “simple method bias” (p. 134). Impor-tantly, Chang and McBride-Chang (1996) showed thatthe bidimensionality disappeared when items were re-worded in such a way that only one direction was ap-parent. The issue of response styles has not stronglyemerged in the debate of dimensionality of the LOT-R measures. Admitting artifactual variance leads tothe hypothesis of two distinct sources of variance inthe data. Moreover, this second source of variance maybe assumed to be orthogonal to the target construct.Thus, in this view, bidimensionality of the data is com-patible with unidimensionality of dispositional opti-mism. There is no need to admit variability of thestructural relationship between the basic dimensionsunderlying the data.

Concentrating the artifactual variance on the posi-tively worded items is suggested for two reasons: First,

correlated errors have previously been treated this wayby Scheier et al. (1994); indeed, they did not modelthem as a factor but simply as a collection of correla-tions. Second, the positively worded items may elicitindividual differences related to the tendency of fakingpositive.

Summarizing the relationships between compet-ing hypotheses and competing factorial structures, itappears that the only one-dimensional one-factormodel is the congeneric model and that the 2OFmodel provides a plausible alternative to the 1FCEand 2CF models. This new alternative is appealing,since: (1) it replaces unexplained correlations of er-rors by a factor with a clear psychological meaning—the desire to have a positive appearance; and (2) itprovides a stable structural view for modelling thedata, by avoiding the use of an unspecified and un-stable correlation between the hypothetical optimismand pessimism factors.

Method

Participants

A French translation of the LOT-R was developed(see Appendix A) and tested with 450 volunteer studentsfrom three French universities. The respondents were149 males, 288 females, and 13 persons who did notprovide gender information. The mean age was 21.8years (SD = 3.5). The LOT-R items were completelyfilled in 442 questionnaires, allowing the factorial struc-ture of the LOT-R to be tested.

Analyses

The statistical analyses used in this study are based onthe structural equation modelling (SEM) methodologicalframework (for an introductory textbook, e.g., see Kline,1998). The researcher specifies a structural model thatcan include latent variables and fits the model to the data.Goodness-of-fit indices allow for testing the adequacyof the model, using null hypotheses such as “not closefit” or “poor fit,” as elaborated below.

The congeneric model was tested, using EQS(Bentler, 1998). Paraphrasing MacCallum, Browne, andSugawara (1996, p. 139), power analysis in SEM ad-dresses the following question of interest here: If themodel fit is actually very good, the Root Mean SquareError of Approximation (RMSEA) is well below .05,say .02, and if the null hypothesis of poor fit is tested,say RMSEA ³ .08, what is the likelihood of rejectingthe null hypothesis? The statistical power p for testingthe null hypothesis of poor fit (RMSEA ³ .08) for analpha = .05 level and RMSEA = .02 (that is, a small butnon-null noncentrality) was p = .92 for 9 dfs and p = .80

DIMENSIONALITY OF LOT-R 395

for 6 dfs, N = 442 (computed with STATISTICA,StatSoft, 2001); i.e., sufficient under the light of usualconventions (p ³ .80).

To investigate the presence of correlations betweenthe errors of positively worded items found by Scheieret al. (1994) in their 1FCE model, the Lagrange Mul-tiplier (LM) test (Bentler, 1995, chapter 6) was usedfor evaluating the statistical necessity of constrainingindependence between errors. It was assessed whetherthe 1FCE model significantly improves the fit of thedata, as compared to the congeneric model. Then, the2CF and 2OF models were compared. Here, as inScheier et al. (1994), the group factor in the 2OF modelrelates to the three positive items so it has threeloadings and the number of dfs of the model equalsthe number of dfs of the 1FCE model. Logically, good-ness of fit is identical in the two models because esti-mated parameters reproduce the input covariancematrix in the same way.

Finally, the 90% confidence intervals of the reli-ability estimates provided by the 1FCE and 2OF mod-els were assessed.

The models were specified using standardized fac-tors and were estimated using robust maximum likeli-hood (ML) and the covariance matrix as input. Insteadof merely using the c2 test of the null hypothesis of per-fect fit (which is uninteresting because it almost neverhappens with moderate to large sample sizes, howevergood the model may be) and NFI, it was more relevant torely on the more realistic two-index strategy presentedby Hu and Bentler (1999), using the recommended cut-off values close to .08 for the standardized root mean

squared residual (SRMR) and to .06 for the RMSEA,which (Steiger, 1990) corrects a measure of populationnoncentrality by compensating for model parsimony. Thetwo-index strategy is useful for assessing whether themodel has an acceptable, although not perfect, fit. In ad-dition, the 90% confidence interval of RMSEA (CI

RMSEA)

was used to evaluate whether the null hypothesis of poorfit could be rejected at the .05 level (for the similar butmore stringent null hypothesis of “not close fit” seeMacCallum et al., 1996, Table 1). The Satorra-Bentlerscaled c2 is also provided in order to compare the nestedmodels, and also the NFI to keep some consistency withthe previous comments on Lai et al. (1998) models.

Reliability analyses were conducted using theRaykov and Shrout (2002) model-based approach toreliability of a composite score, which extendsMcDonald’s omega coefficient (1999). Like Cronbach’salpha, omega requires positive loadings. To obtain posi-tive loadings, the scores of the negatively worded itemswere reversed.

The 90% confidence intervals for omega were ob-tained using bootstrapping (1000 times, as suggestedby Raykov & Shrout, 2002). The bootstrapping tech-nique consists of considering the sample as the popula-tion, sampling a data set of size N with replacement,estimating the measurement model, sampling and esti-mating the model again, and so on until the necessarynumber of samplings is reached, i.e., 1000. All esti-mates are registered and 1000 reliability estimates arethen computed. The 90% confidence interval of thepopulation parameter is approximated by the 5th and95th percentiles of the distribution. STATISTICA

TABLE 1Descriptive statistics for the items (N = 442)

Fill02 Fill05 Fill06 Fill08 P01 P04 P10 N03 N07 N09 M SD Sk. Ku.

Fill02 .007 .007 .007 .014 .022 .009 –.004 .053 –.061 .004 3.11 1.54 –0.13 –1.07

Fill05 .122 .001 .002 .001 –.067 .014 .059 .082 –.053 –.023 4.52 0.47 –1.76 4.64

Fill06 –.112 .245 .000 .003 .047 .013 –.004 –.008 –.017 –.003 3.68 1.34 –0.63 –0.47

Fill08 .307 .129 –.076 .000 –.061 .037 .027 –.109 –.063 –.005 2.77 1.48 0.11 –1.00

P01 .202 –.004 .047 .033 .002 .006 .020 .082 –.017 –.010 2.64 1.26 0.19 –0.69

P04 .400 .133 .013 .217 .288 .010 .005 .000 –.016 –.013 3.26 1.37 –0.18 –0.64

P10 .286 .131 –.004 .136 .219 .472 .007 –.011 –.013 –.004 3.19 1.24 –0.19 –0.82

N03 –.057 .082 –.008 –.109 .021 –.190 –.209 .000 .001 .013 2.61 1.25 0.26 –0.68

N07 –.241 –.053 –.017 –.063 –.116 –.328 –.339 .285 .000 –.009 2.61 1.14 0.23 –0.60

N09 –.159 –.023 –.003 –.005 –.099 –.295 –.415 .269 .412 .000 2.67 1.34 0.23 –0.93

Fillnn = Fillers, Pnn = positively keyed items, Nnn = negatively keyed items, where nn indicate the serial position in the questionnaire.The four right columns provide single item statistics (M = mean; SD = standard deviation; Sk. = skewness; Ku. = kurtosis). The left lowertriangle shows pairwise item correlations. Numbers in the upper right triangle (above the diagonal) and in the diagonal display standardizedresiduals related to the model in Figure 2.

396 VAUTIER, RAUFASTE, CARIOU

(StatSoft, 2001) bootstrapping facilities were used forconvenience.

Results

Testing the congeneric and 1FCEmodels

Table 1 shows the descriptive statistics of the items.Using the criteria set forth by the Hu and Bentler (1999)rules of thumb (SRMR < .08 and RMSEA < .06), thecongeneric model exhibited a mediocre fit, c2(9, N = 442)= 35.53, p < .001, NFI = .84, SRMR = .06, RMSEA =.10, CI

RMSEA = (.07, .13). In addition, the NFI was under

the .90 cut-off. Interestingly, the LM test suggested thatindependence between two error pairs of positivelyworded items could be relaxed. This respecification ledto a significant improvement of fit, c2

difference(2) = 20.92,

the respecified model having c2(7, N = 442) = 14.61, p =.04, NFI = .94, SRMR = .04, RMSEA = .06, CI

RMSEA =

(.03, .10). This also implied the inclusion of the third er-ror covariance to complete the cluster of error covariancesbetween the positive items, leading to a new significantimprovement of fit, c2

difference(1) = 6.80, the new indices

of fit being c2(6, N = 442) = 6.81, p = .34, NFI = .98,SRMR = .02, RMSEA = .04, CI

RMSEA = (.00, .08). In

addition, the null hypothesis of poor fit could be rejectedat the .05 level (the entire confidence interval being be-low .08). However, it should be noted that respecified thisway, the model holds but it is no longer a congenericmodel: It is the 1FCE model.

Comparing the 2OF and 2CFmodels

As expected, and logically, the 2OF model has ex-actly the same goodness-of-fit summary as the 1FCEmodel. The 2CF model was also well fitted, c2(8, N =442) = 15.29, p = .05, NFI = .94, SRMR = .04, RMSEA= .06, CI

RMSEA = (.00, .09). Since both models are not

nested, the c2 difference test was not employed for com-parison. Because the 2CF model has 2 dfs more than the2OF model, it has a higher probability of rejecting thenull hypothesis of poor fit (RMSEA ³ .08) if this hypoth-esis is false. Strictly speaking, however, the 2CF modeldid not allow for rejecting the null hypothesis of poorfit (i.e., the superior limit of the CI

RMSEA exceeds the .08

cut-off) whereas the 2OF did. Thus, the 2OF modelappears to slightly outperform the 2CF model.

Reliability estimates for 1FCE and 2OFmodels

For the 2OF model, the 90% bootstrapped confi-dence interval for omega was (.68, .76). Conversely,

using the 1FCE model, the reliability estimate dropped,the corresponding 90% bootstrapped confidence inter-val being (.53, .68). As can be seen, the two intervalsdo not overlap, which suggests that the way of model-ling the input matrix has a non-negligible impact on re-liability estimation. It could be instructive to notice thatthe proportion of variance due to the group factor to totaltrue variance ranged from .12 to .23 (90% confidenceinterval). This share represents variance attributable toindividual differences that relate to the hypothetical ten-dency of faking positive.

Summary

In summary, the unidimensional (congeneric) model didnot hold whereas the various versions of the two-dimen-sional model held. Among the two-dimensional mod-els, the 2OF and 1FCE slightly outperformed the 2CF.In addition, the 2OF model exhibited more reliabilitythan the 1FCE model. These results will be consideredin the general discussion.

MODELLING THE ENTIRE LOT-RCOVARIANCE MATRIX

Rationale

Now consider the status of fillers in the LOT-R. None ofthe 11 reviewed studies, including Scheier et al. (1994),explicitly addressed the issue of the status of fillers. EvenLai et al. (1998) provided no rationale for including thefillers in their analyses. Filler items have normallynothing to do with dispositional optimism. Nevertheless,they were introduced in the questionnaire because theyare supposed to have a beneficial effect on target itemmeasures. For example, fillers could attenuate potentialmeasurement artifacts such as assimilation effects due toproximity of items (Schwarz, 1996, 1999; Schwarz &Strack, 1999; Vautier, Mullet, & Jmel, in press). Now, ifthe fillers have any role in enhancing the ability of theLOT-R to measure dispositional optimism, then they mustprevent something that would otherwise pollute targetitems. What is the nature of this polluting factor? Vari-ance related to assimilation and/or contrast effects mustbe distinguished from variance related to faking positive.In a measurement model, the former can be modelledusing auto-regressions or correlated errors, as shown byGreen and Hershberger (2000). Importantly, fillers canbe expected to reduce the former, but not the latter. Ex-plicitly modelling the relationships between the fillers onone hand and the measurement model (i.e., the optimismconcept plus the construct of faking positive) on the otherhand might help to corroborate the nature of the hypo-thetical faking-positive factor.

DIMENSIONALITY OF LOT-R 397

Two competing hypotheses were compared.

1. Using the 2OF model as a correct measurementmodel for dispositional optimism (i.e., all target itemsbeing indicators of the common factor “optimism,” plusall positive items being indicators of the group factor“faking positive”), the null hypothesis that no filler hasanything to do with the measurement model can easilybe tested. This null hypothesis simply means that nocorrelation should be found between the group factorand the filler items.

2. On the contrary, the alternate hypothesis claimsthat since the group factor in the 2OF model will capturea systematic variance related to individual differencesabout faking positive, and it will correlate with fillershaving desirable meanings, like items #2 or #8 (seeAppendix A or the English items in Carver, 2002).

Method

The LM test can seek potential covariances (1) betweenfactors and observed variables, (2) betweenuniquenesses, and (3) between uniquenesses and ob-served variables. A structural model including the 10items was specified as the juxtaposition of the 2OFmodel and the covariance matrix formed by the fill-ers. Thus, the whole model assumes independencebetween the fillers on the one hand and the measure-ment model components on the other hand. Techni-cally, the elements of the 6 ´ 4 submatrix wereconstrained to nullity. The model was estimated usingEQS, the 10 ́ 10 covariance matrix as input data, andthe robust ML method.

As the “independent model” has 30 dfs, its statisti-cal power for rejecting the null hypothesis of poor fit(RMSEA ³ .08) with alpha = .05 and RMSEA = .02 ismaximal, 1≈π . In other words, if the hypothesis ofpoor fit is wrong, it can be rejected with almost totalcertainty. It is noteworthy that the LM test is explora-tory in essence and capitalizes on chance. It must beclear that by respecifying the model this way, it cannotbe intended to provide a proof of the generalizability ofthe hypothesis, but rather to provide inductively a ra-tionale for further replications.

Results

The “independent model” exhibited poor fit, c2(30, N= 442) = 136.06, p < .001, NFI = .82, SRMR = .10,RMSEA = .09, CI

RMSEA = (.07, .11). Obviously, the

respecified model fitted the data closely, c2(25, N = 442)= 30.84, p = .19, NFI = .97, SRMR = .03, RMSEA =.03, CI

RMSEA = (.00, .05). The respecified model is de-

picted in Figure 2. To facilitate interpretation, standard-ized estimates are provided. Standardized residuals aregiven in Table 1, in and above the diagonal. The readermay be surprised that dispositional optimism (the DOfactor) negatively loads positive items and positivelyloads negative target items. This is simply because thefactor is negatively oriented.

Summary

This section has provided the rationale for testing thestatus of filler items with regard to the factorial struc-ture of the LOT-R. The exploratory application of the

Figure 2. A bi-factor view (2OF model) of the optimism construct (DO = dispositional optimism, RS =response style) extended to include the context of fillers. The DO factor is negatively oriented. Labels ofthe manifest variables correspond to codes explained in Table 1.

398 VAUTIER, RAUFASTE, CARIOU

LM test clearly shows that they are correlated with posi-tive target items, thus corroborating the response stylehypothesis.

DISCUSSION AND CONCLUSION

This study tackled the problem of the factorial struc-ture of dispositional optimism as measured using theLOT-R: Most studies found bidimensionality whereasLai et al. (1998) and Lai and Yue (2000) reportedunidimensionality. In addition to solving this prob-lem, it aimed to show that some theoretical ground-ing remains to be provided for the competingstructural models. The methodology used by Lai etal. to assess the factorial structure of the LOT-R wasfirst criticized. Four alternative measurement modelswere tested, providing strong support forbidimensional models. With regard to the theoreticalgrounding question, at least two approaches of theLOT dimensionality exist in the literature: One con-siders dispositional optimism as a single factor com-mon to all target items, and more or less explains theremaining correlations between positive items. Asecond approach considers two correlated group fac-tors that relate to approach and avoidance systems.The first factor would explain positive items and thesecond negative items. However, the second approachdoes not define how the factors should correlate. Thispaper proposes a third explanation: LOT-R wouldactually capture two constructs. Only one factorwould be dispositional optimism (DO); the other one,response styles (RS), would reflect individual differ-ences linked to self-rating, and would be sensitive toa kind of social desirability bias, “faking positive.”RS would load positive items only, whereas DOwould load all target items. The competingbidimensional models, plus the congeneric model thatrepresents unidimensionality, were empirically tested.The faking positive hypothesis is compatible with theneed to recognize bidimensionality of the data. Filleritems were then introduced in a new analysis, in or-der to explore how fillers would correlate with theoptimism and faking-positive factors.

Several points emerged from the theoretical andempirical analyses. First, it was demonstrated that theLai et al. (1998) confirmatory analyses were likely tohave been conducted on all LOT-R items, including thefillers. However, by itself, this does not eliminate thecongeneric (unidimensional) model.

Second, it was argued that it is necessary not to con-fuse a congeneric model with a 1FCE model. The firstcomprises one common factor plus uncorrelateduniquenesses (or errors in a broad sense) and supportsunidimensionality, whereas the second refutes

unidimensionality of the data. Actually, the 1FCE modelcan be replaced by a 2OF model, replacing the clusterof correlated uniquenesses by a group factor orthogonalto the common factor. The 2OF model is better suitedfor representing two theoretically distinct sources ofvariance in the data, one of them being dispositionaloptimism as a bipolar one-dimensional trait, in line withthe concept of the good-bad sense of expectancy ofCarver and Scheier (1998, 2001). The other might be aresponse style construct that is independent ofdispositional optimism and would be linked to the posi-tively worded items: faking positive. An asset of the2OF model is its structural stability: It needs no un-specified correlation between the basic dimensions un-derlying the data, which would be a theoretical weaknessif a confirmatory approach is used.

Third, the reliability of data described using the 2OFmodel is logically higher than that of the 1FCE model.This is algebraically explained because reliability is com-puted as the ratio of explained variance to total (explainedplus error) variance. The variance related to the cor-related uniquenesses is qualified as error variance in the1FCE model, whereas this variance is qualified as truevariance in the 2OF model. Nevertheless, it is notewor-thy that the discrepancy was non-negligible, because therespective 90% confidence interval did not overlap. It isa positive function of the amount of artifactual variancethat represents from 12 to 23% of the true variance. Inother words, explaining the source of correlations bet-ween positive items appears to be important.

Fourth, using data gathered with a French transla-tion of the LOT-R, it was found that congenericitycould not be assumed and that bidimensionality couldbe accounted for satisfyingly by the 2OF model. Thisdemonstrates that there is no empirical necessity fortwo correlated optimism and pessimism constructs. Asa consequence, further studies will be required to de-cide between competing hypotheses, probably usingmore experimental manipulations. The LOT-R mightactually capture individual differences in bipolardispositional optimism and in the tendency to exhibitpositive appearance (the response style factor). Inte-restingly, the fact that the optimism factor descriptivelypredicts the negative items better than the positive ones(as shown by higher absolute values of the loadings)is compatible with the well-known literature showingthat negative affect outweighs positive affect (Ito,Larsen, Smith, & Cacioppo, 1998; Kahneman &Tversky, 1979). Strictly speaking, this asymmetry ofabsolute loadings suggests that the optimism constructcould be renamed as dispositional pessimism.

Fifth, it was explored how the whole covariance ma-trix can be modelled to account for the structural rela-tionships of fillers with the components of the 2OF

DIMENSIONALITY OF LOT-R 399

measurement model. Apparently, this topic is a primerin the literature dedicated to the LOT-R. The presentfindings support the idea that the group factor of the2OF model captures a kind of response style construct,and suggest that the submatrices formed by the targetoptimism items and the fillers are not independent. Thesignificant positive correlations that appeared betweenthe group factor and fillers #2, #5, and #8 are compat-ible with the substantial interpretation of response style(faking positive): All these items mean something de-sirable. The correlation between filler #2 and the com-mon factor (optimism) was not expected. Post hoc, itseems reasonable that optimism and relaxation covarypositively. The DO factor being negatively oriented, itlogically loads the filler #2 negatively. Further researchwould be useful for testing that the “relaxation filler” ismoderately related to dispositional optimism. Never-theless, the whole structural model that was fitted sug-gests that fillers can be neglected when modelling thetarget matrix because the quasi-absence of linear rela-tionships between the target and the filler matrices sug-gests no hidden factor that would create amisspecification of the measurement model. It is notcertain, however, that fillers play a specific role withinthe questionnaire.

Finally, an intriguing question remains, which shouldbe addressed by future research. Why does a unidimen-sional space sometimes appear adequate to model em-pirical data using a linear factorial model (see Lai & Yue,2000)? A possibility is hypothesizing that the variancedue to response styles might sometimes be statisticallynegligible. In other words, the variance due to responsestyles would sometimes be too small relative to the over-all variance. This view assumes that individual differencesare hard to detect statistically, but it does not indicate thatthere is no response style. Could cross-cultural differencesaccount for this fact? The dataset was collected within aFrench cultural context whereas Lai and Yue’s (2000)dataset was collected within a Chinese cultural context.Perhaps Chinese people are more careful not to appearovertly positive and therefore exhibit fewer individualdifferences along this trait than occidental people? Nev-ertheless, it seems hard to find a clear argument to justifywhy the respective samples differed when producing theirratings, and specifically, why Chinese respondents shouldexhibit negligible individual differences along the hypo-thetical response style dimension.

As a conclusion, if there is little doubt as to the fac-torial bidimensionality of the LOT-R data in most ofempirical studies, the question of the definition of thebasic psychological dimensions underlying the data isstill wide open.

Manuscript received December 2002Revised manuscript accepted July 2003

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A French translation of the LOT-R

Indiquez le degré avec lequel, pour chaque item, lecode suivant représente votre sentiment :

1 = Pas d’accord du tout2 = Pas d’accord3 = Je ne suis ni d’accord ni pas d’accord4 = D’accord5 = Fortement d’accord

1. Dans des périodes incertaines, je pensegénéralement que ce qui va arriver est le mieuxpour moi.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

2. Il est facile pour moi de me relaxer.pas d’accord du tout 1 2 3 4 5 fortement d’accord

3. Si quelque chose peut tourner mal pour moi, çatournera mal.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

4. Je suis toujours optimiste à propos de mon futur.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

5. J’apprécie beaucoup mes amis.pas d’accord du tout 1 2 3 4 5 fortement d’accord

6. Il est important pour moi de rester occupé.pas d’accord du tout 1 2 3 4 5 fortement d’accord

7. Je ne m’attends presque jamais à ce que les chosesaillent dans mon sens.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

8. Je ne me sens pas bouleversé si facilement.pas d’accord du tout 1 2 3 4 5 fortement d’accord

9. Je compte rarement sur les bonnes choses quipourraient m’arriver.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

10. D’une façon générale, je m’attends à ce que lesmeilleures choses m’arrivent plutôt que lesmauvaises.

pas d’accord du tout 1 2 3 4 5 fortement d’accord

APPENDIX A