Optimizando las cinco categorías de calif icación par a ... · La personalidad es uno de los...

| Universitas Psychologica | Colombia | V. 15 | No. 4 | Octubre-Diciembre | 2016 | ISSN 1657-9267 |

**Strictu Sensu Post Graduate Program inEducational Psychology. FIEO-University Center- UNIFIEO/SP, Brasil. Correo Electrónico:[email protected]

Optimizing rating scales of the big fivesocialization scale in athletes by Rasch

model*Optimizando las cinco categorías de calificación para una escala de

socialización de atletas bajo el modelo Rasch

Received: 18 June 2015 | Accepted: 14 July 2016

Daniel BartholomeuFundação Instituto de Ensino para Osasco, Brasil

**

José Maria MontielFundação Instituto de Ensino para Osasco, Brasil

Afonso Antonio MachadoUniversidade Estadual Paulista, Brasil

ABSTRACTPersonality is one of the main psychological aspects that influenceathletes’ performance in competition and one of the most studied subjectsin sport psychology. We aimed to optimize item scales in a socializationtest based on the big-five model, assessed by means of adjectives andadministered to a sample of 225 athletes of both genders, with 56.9%male. Age ranged from 14 to 45 years with a mean of 20 (SD = 5.21).Participants attended to basketball (11%), football (21.8%), handball(17.3%), jiu-jitsu (10.2%), tennis (5.60) and volleyball (16 %) sportmodalities. The results indicated that the four point scale was the bestitem scale structure regarding validity evidences. Hence, this structurecould be adopted in this scale aiming to better socialization assessmentin athletes.Keywordspsychological assessment, human performance, personality.

RESUMENLa personalidad es uno de los principales aspectos psicológicos queinfluyen en el rendimiento de los atletas en la competencia y uno de lostemas más estudiados en la psicología del deporte. El objetivo de esteestudio consistió en optimizar los ítems de las escalas en una prueba desocialización basada en el modelo de los Cinco Grandes, estableciendoasociaciones a partir de adjetivos y aplicando una muestra de 225 atletasde ambos sexos, donde el 56.9 % eran hombres. El rango de edad oscilabaentre 14 y 45 años, con una media de 20 (DE = 5.21). Los participantesse distribuyeron en las siguientes modalidades: baloncesto (11 %), fútbol(21.8 %), balonmano (17.3 %), jiu-jitsu (10.2 %), tenis (5.6 %) y voleibol(16 %). Los resultados indicaron que la escala de cuatro puntos ofrece losmejores resultados sobre la estructura de la escala evidencia de validez.Por lo tanto, esta escala se podría adoptar para una mejor evaluación dela socialización en los atletas.Palabras claveevaluación psicológica, rendimiento humano, personalidad.

Daniel Bartholomeu, José Maria Montiel, Afonso Antonio Machado.

| Universitas Psychologica | V. 15 | No. 4 | Octubre-Diciembre | 2016 |

To cite this article: Bartholomeu, D., Montiel, J.M., & Machado, A. A. (2016). Optimizationrating scales for an athletes’ socialization scale byRasch model: Scales of socialization. UniversitasPsychologica, 15 (4). http://dx.doi.org/10.11144/Javeriana.upsy15-4.orsa

Introduction

Personality is one of the most importantpsychological aspects that affects athletes’performance in competition and one of the moststudied subject since the emergence of SportPsychology after the World War II. From 1950to 1970 there was a tendency to measure thisvariable in athletes mainly to compare theirresults with groups of non-athletes, or betweendifferent sports (Cratty, 1984). This manuscriptfocuses on the Five-Factor Model of personality(FFM). This model does not provide an a prioritheoretical explanation of the five factors ofpersonality but derives then based on the factoranalysis of numerous instruments such as the 16PF (Cattell & Cattell, 1995), MMPI (Butcheret al., 1992), Murray Needs, among others thatprovide similar solutions to the FFM, regardlessof the underlying theory (Hutz et al., 1998).

Numerous authors, such as Goldberg (1982),studied the factorial solutions found betweenpersonality tests and contributed to thecurrent understanding of the factors to explainpersonality. Research during the past 10 yearshas demonstrated the solidity of such factors.Thus, this model has been considered by manyauthors as the best alternative for the descriptionof personality. It is suggested that these are basicdimensions of personality desirable to ascertainin any people with whom one will interact (Hutzet al., 1998; McCrae, Costa, & Piedmont, 1993).Whereas the FFM has its origins in the analysisof language used to describe people, using traitsdescriptors (adjectives) can help identify thesepersonality factors. In the opinion of Goldberg(1982), if a personality feature is evident, a wordcould be enough to describe it.

In Brazil, the study of Hutz et al. (1998)investigated the adequacy of a list of adjectivesused to describe personality on a big fivefactor model. Factor analysis demonstrated theexistence of five factors as expected. Thefirst factor was "Socialization" ("agreableness"),followed by "Extraversion", "Scrupulosity","Neuroticism", and "Openness to Experience",with Cronbach’s alpha coefficients rangingbetween 0.78 and 0.88. The total varianceexplained by factors was approximately 44% andmultivariate analyzes of variance (MANOVA)indicated significant gender differences in allfactors except neuroticism.

Despite this study, no researches were madewith athletes with this scale as well as no teston the items rating scale. In Brazilian athletes,this fact assumes greater importance sinceno personality test has specific psychometricproperties to this context, especially in the FFM.The present research focuses on Socializationitems once we used Rasch model that supposesunidimensionality to run. Regarding polytomousscales meanings, specifically in the case ofsocialization, each consecutive number in thescale represents a higher amount of socializationand the increase in scale points indicates a higherincidence of this aspect. As a person moves inthe continuum of these variables, each successivepoint becomes the most likely response (assumingthat subjects were able to distinguish between alllevels of the scale).

Among the various models of item responsetheory available, we analyzed the item fit toRasch model. This system considers only theitem difficulty parameter and people ability as afunction to determine the probability to scorean item. This model is the most popular withinthe item response theory due to its greatermathematical simplicity (Muñiz, 1990). Also, itassumes data additivity, defined as measurementunits (logits) that have the same size in thecontinuous (interval data), if the data fit to themodel. Thus, these parameters are estimated andused to determine the response patterns expectedfor each item. The adjustment is derived from acomparison of these with the observed patternsthat provide validity evidences for the test. In

Optimizing rating scales of the big five socialization scale in athletes by Rasch model*


turn, the standard errors associated with itemcalibration and people ability estimate are usedin the reliability estimates in this model. Theseerrors can be used to describe the confidenceinterval in which the true item difficulty andpeople ability are found (Wright & Stone, 1988).

Rasch model can be used in optimizing thenumber of scale categories in a test without theneed to administer different versions of the samescale. Some ways of observing the number ofresponse categories appropriate to the items of atest can be proposed (Bartholomeu, Montiel, &Machado, 2013). The thresholds parameters canbe also observed to determine which categoriesare not effective in measuring the variableunder investigation. Ordered thresholds implythat as a person moves along the continuumof socialization, each category becomes themost likely answer. The disorder occurs inthe responses for the same reasons previouslymentioned and can be best seen through theprobability curves graph.

Finally, an outfit analysis can detect the useof random categories (Linacre, 1997, 1999).Some possible solutions to these mismatchesmay be combining adjacent categories, changethe location of adjacent categories, or treatingthe missing responses as if the name is notappropriate or does not share the same traitthat the other (Linacre, 1997, 1999). It isworth noting that the diagnosis should bemade taking into account these three criteria,besides visual inspection of the probabilityplot of categories agreement. In this context,considering the lack of studies with personalitytests in Brazilian athletes and that no research,were found analyzing item category optimizationin personality tests to athletes, this study aimedto optimize item rating scales in a socializationfactor assessed by means of adjectives.

Method

Participants

Two hundred and twenty-five athletes of bothgenders, with 56.9% male and ages ranging from

14 to 45 years, mean of 20 (SD = 5.21), werestudied. Regarding the modalities, these werebasketball (11%), football (21.8%), handball(17.3%), jiu-jitsu (10.2%), tennis (5.60) andvolleyball (16%). The survey was conductedin several clubs in the state of São Paulo,Brazil. The educational level was also varied,ranging from elementary school (4.7%) tothe doctoral level (0.6%), and most subjects(62.8%) had incomplete university level. 58.7%of the participants worked and practiced sports,although most have had a routine of intensetraining, mostly three to five days a week (78%)as well as two to three hours a day (76.2%).Regarding competition, 90.7% reported that theyhad attended in competitions.

Instruments

Big Five Adjectives (Hutz et al., 1998)

This test presents a list of 64 adjectivesand participants should indicate the agreementwith that item as a good descriptor of itspersonality in a five-point Likert scale. Theanswers are arranged from 1, Strongly Disagreeto 5, Strongly Agree. In relation to the factorsattained by the instrument, Factor I assessesSocialization and adjectives are affable, sociable,docile, nice, generous, romantic, gentle, kind,understandable, friendly, cold, kind, passionate,friendly, sentimental, and delicate, making atotal of 16 items in this subscale. Factor IIconcerns the Extraversion and its items areshy, extroverted, communicative, resourceful,introverted, embarrassed, quiet, inhibited, andshut, totaling 10 items. In turn, Factor IIIhas information on Realization (Scrupulosity)and adjectives that characterize it arehonored, responsible, dedicated, hardworking,studious, honesty, disorganized, efficient, careful,methodical, organized, meticulous, devoted, andpervaded, forming a total of 14 items for thissubscale. Factor IV concerns the Neuroticismand comprises adjectives such as pessimistic,happy, bored, affirmative, selfish, unhappy,



depressed, insecure, obnoxious, lonely, anxious,and sad, totaling 12 items on this scale.

Finally, Factor V informs aboutOpening and adjectives are curious,funny, creative, philosophical, courageous,energetic, adventurous, audacious, imaginative,intellectual, artistic, and impulsive composingthe total of 12 items. The result for each scalewas obtained by summing the scores given toeach item divided by the total number of items ineach corresponding subscale. Some psychometricproperties of the instrument were taken byHutz et al. (1998). Factor analysis provided atotal variance explained by these five factorsof 43.91%. Beside this, the Cronbach's alphavalues for the dimensions are 0.88, 0.88, 0.84,0.89, 0.78, respectively, and can be consideredsatisfactory.

Procedure

Data collection was collective and madeafter participants’ acceptance by completing anauthorization term of free and informed consent.The project followed all ethical principlesfor research with human subjects and wasapproved by the Research Ethics Committeeof Anhanguera University under the number810/2011. The evaluation was held at the Clubin a meeting room with chairs and appropriateconditions for application of the instruments.We distributed an answer sheet of the testfor the participants. The application of theinstrument was part of an intervention projectthat aimed collecting information to be used laterfor determining the techniques to be employedand communicated to the participants that thedata would be kept confidential and would alsolater used in a research. Following the objectivesof the study, the analyzes were performed by theprogram Winsteps .

Results and Discussion

In spite of classical tests theory, which usestotal scoring by summing the items in a scale,the item response theory (IRT) allows different

interpretation of test scores according to personalabilities assessed in each response. A comparisonof the three IRT models made by Wright (1992)pointed out some advantages of the Rasch modelover the other two models. The Rasch modelwas derived for defined measures specifyingthe measure requirements. Its mathematicalformulation is solid and provides statisticsthat enable reaching linear and objectivemeasurement. Also, in the Rasch model guessingis not accepted for being considered as unreliable.Not everyone makes use of guessing, let alonefor the same items. Moreover, variations on itemdiscrimination are rejected by the Rasch modelfor being considered a symptom of item bias. Theitems discrimination variance is affected by itemsbias or by extra dimensions.

In terms of Socialization, the difficultyparameter reveals that the more difficult an itemis, the less agreement is displayed on it, andthe less incidence of that trait is presented.That is, a subject presenting high levels ofagreement on items that extreme, some trait willprobably present a higher incidence of this sortof characteristics, also enhancing the probabilityof presenting a high level of agreement on itemsthat measure lower levels on that personality trait(easier items).

The accuracy assessed by this model providedan index of 0.97 for items and 0.70 for persons,which favors the interpretation that subjectsprovided more data about the items than theydid about their behaviors. Despite this, it isprecise both for items and for people. The averagemeasurement error was 0.15 for items and 0.06for persons. The subject’s precision indicates thepossibility of finding similar results in the samesample whether submitted to another group ofitems with same characteristics and that assessthe same underlying construct. This fact is morelikely to happen in cases with less significantmeasurement errors, as was the case in thepresent study. The items precision informs thereplicability of the items if the same indicatorswere employed in another sample with similarlevels of ability in the latent trait (Bond & Fox,2001). This, as well as additional information, isfeatured in Table 1.



TABLE 1Summary statistics of Rasch model for theSocialization items with 5-point scale .

Source: own work

Concerning the fit to Rasch model, twoprocedures must be observed: (a) the infit,which informs the discrepancy between theobserved and expected data in the area ofthe item characteristic curve (ICC), in whichthe probability of a high level of agreementwith the item is close to 50% and (b) tooutfit, which corresponds to the unexpectedpattern of response at the extreme regions ofthe same curve, with high and low probabilitiesof agreement with the item. This adjustmentis performed to the items as to the persons,and Bond and Fox (2001) considered that1.00 would be an expected value for each ofthese measures. However, our study followedthe Linacre (2002) suggestion that the 1.50level would be considered the maximum limit ofacceptance for an item. Only two items presentedinfit and outfit problems, above 1.5 (items Shy andCold), suggesting that higher agreement rates onthese are unexpected considering the latent traitSocialization. Indeed, this amount of fit problemsmay be considered small. Regarding persons fitto Rasch model (in terms of infit and outfit), ithas generally been above the expected values.About 10% of people presented infit and outfitindicators above 1.50 that can be considered avery small amount.

A detailed analysis of people’s Socializationand the items difficulty (level of agreement on thetrait assessed by the indicators) suggested that allitems have measured mean levels of Socialization(Figure 1). All items ranged within –1 and 1,which assess persons with more accuracy (Bond& Fox, 2001). The mean scores of item measuresis higher than the persons mean measures scoreswhich suggests that items assess higher levels ofSocialization than the athletes sample actually

has. The items with the higher agreement wereFriendly and Gentle adjectives and the item withlower agreement was the adjective Cold.

Figure 1Map of Item and Person.

Source: own work

We examined the differential item functioningby gneder. In this analysis the intensity of thecharacteristics in persons are estimated andsubtracted by group. Then, it is supposed thatthe intensity of each item must be statisticallyequivalent in the studied groups (gender, in thiscase). This procedure estimates the quantityof DIF measure added to item positively ornegatively and calculates the probability of thisdifference to be aleatory and furnishes a Studentt measure. Draba (1977) considers that 2 is agood point to determine statistical significancein analyzing less than 20 items (as in this case).Table 2 presents these results.



TABLE 2DIF analysis criteria to the Big Five Socializationscale items .

Size of Mantel-Haenszel slice = 0.100 logitsSource: own work

Three items from 16 (18%) yielded t scoresabove the suggested point, revealing that someitems favored one of the groups and are biasedby characteristics of one of the genders that areindependent of Socialization level. The itemsSentimental and Delicate favored females andare easier to agree in this group than for males.The item Cold favored male athletes.

We investigated whether the number of itemcategories is representative of socialization (Table3, Figure 2). The progression of Rasch measureindicated an increased ability of people in eachresponse categories. The Outfit level, suggestedgood fits in all categories, except for category1 (totally disagree). Finally, by analyzing thethresholds graph, there was a discontinuity incategories 2 and 3 (neither agree nor disagree andpartially agree, respectively). In this context, onesolution would be to combine the responses ofcategories 2 and 3.

TABLE 3Tables structure of categories of the five-pointstructure .

Source: own work

Figure 2Probability chart categories for the socializationscale in the 5-point model

Source: own work

These results revealed more appropriate datawith better outfit and continuity of the proposedcategories as suggested in the graph. However,it has not been satisfactory since categories 2and 4 did not discriminate well the participant’sanswers yet. To ensure that this number ofcategories are good to represent data assessedwith this test, validity evidences with this testformat are necessary (Bond & Fox, 2001; Wright& Masters, 1982). So we performed Raschanalysis again and checked the adjustment ofitems with this new format in the Rasch scale toprovide further validity evidences of the internalstructure of the items (Table 4, Figure 3).

TABLE 4Categories structure for the socialization scale withfour categories

Source: own work



Figure 3Probability chart categories for the socializationscale with four categories

Source: own work

The validity evidences for these items withfour category format were slightly better thanwith the five category format. Indeed, thefour category format provided almost the samereliability results as well as the same amountof items with infit and outfit problems andsimilar standard errors. The same is applicable forpeople. As no significant differences were foundin difficulty level and persons’ abilities betweenthe two items format, no important differencescould be found in the item-person map. Table 5presents the summary of the Rasch model of theitems and persons with this format.

TABLE 5Summary statistics of Rasch model for theSocialization items with 4-point scale

Source: own work

Also, the same DIF items with other formatpresented DIF again. Hence, the only advantagewith this format is better information of eachcategory. It does not make sense to include acategory in the items that does not yield anybetter information on the latent trait (Bond &Fox, 2001; Smith, Wakely, de Kruif, & Swartz,

2003; Wright & Masters, 1982). Since the resultswith four categories were slightly better than thefive-point format, we constraint another categoryto ascertain if better validity results are obtained.Then we combined categories two and four andthe results are presented in Table 7. This itemscale showed the best discrimination betweenthe categories with better outfit and continuityof the proposed categories, as indicated in thegraph. Nevertheless, validity evidences showedworst results with lower levels of reliability andmore items and persons with infit and outfitproblems (Table 6, Figure 4). Despite only twoitems (loving, cold) have presented such aspect,infit and outfit indices were higher than withother scales.

TABLE 6Structure of categories and probability chartcategories for the socialization scale with treecategories

Source: own work

Figure 4Probability chart categories for the socializationscale with three categories

Source: Own work.

Within this item scale, 33% of peoplepresented infit and outfit higher than 1.5,suggesting a larger amount of misfits than with4 or 5-point scale. Also, the same items thatpresented DIF with other scales did so, butwith one more item (Romantic, t=2.88, favoring



women). The other tendencies were the samebut with higher t values, suggesting greatermisfits (Table 7). It is important to note thatsome adjectives in the socialization scale weremisfits, presented DIF problems, or both suchas Cold, Shy, and Delicate. These items showedunexpected agreement with higher categorieswhen lower athletes’ socialization was evidenced.Hence, they should be removed from this scaleto assess such traits in athletes. Despite thethree-category structure in the items was the onewith better thresholds, outfit level, progressionof socialization mean and most discriminativecurves, its validity evidences were worse than theother two structures (with four and five levels)regarding DIF, model fit, and reliability makingit unfeasible (Bond & Fox, 2001; Lopez, 1996;Wright & Masters, 1982).

TABLE 7Summary statistics of Rasch model for theSocialization items with 3-point scale

Source: own work

Indeed, the four-point scale was the bestregarding validity evidences, despite similaramount of misfits, the coefficients werebetter than with the five-point scale aswell as the category information with moreadequate thresholds, outfit levels, progressionof socialization mean, and good discriminativecurves. Hence, this structure could be adoptedin this scale aiming towards better socializationassessment in athletes. Category 4, partiallyagree, is the one that yielded worst thresholds anddiscrimination level but the level of socializationof the sample was low and this fact can besomehow expected. New studies could focuson higher athlete samples with higher levels ofsocialization to assure that this category can beadjusted aiming test standardization.

It is important to note that, although thisanalysis provides some guidelines regarding

which categories have potential problems, itshould be emphasized that the final decisionto merge or delete a given category should bemade not only based on statistical criteria buton assumptions provided in the variable underinvestigation. Furthermore, the optimizationdepends on the scales and sample to be testedagain with a fresh sample of the same population(Smith et al., 2003). These preliminary evidencesmust be set into the Brazilian context, whereno adequate instruments with good psychometricproperties to assess athletes’ personality arefound (Bartholomeu et al., 2013; Brandão, 2007;Moraes, 2007). Further studies with this test(not only with the socialization scale, but allother five factors) can make it proper for usein the Brazilian context. Also, this test wasfirst developed to assess personality traits incollege students, and comparisons on the Likertscale structure between these two samples canbe valorous, since personality expression variesbetween contexts (Sinn & Moltschaniswskyj,2005).

One possible explanation to these data can bethat the use of adjectives to describe personality,despite being easier and quicker to use, they canbe less informative than the use of phrases withcontext information of behaviors. Hence, newstudies can investigate differences on categoryquantity in personality assessment by adjectivesand phrases.

Final Considerations

The objectives of this study were to optimizescales of items in a scale of five great factors,socialization, assessed by means of adjectives, andadminister them to a sample of athletes. Theresults showed that, although the structure ofthe items of three levels of response have betterstatistical properties shown with a progression ofaverages and thresholds, top anxiety, as well asoutfit values and probability plot curves presentthe most discriminative for each of the categories.Wright and Masters (1982) point out that whencomparing various forms of assessment items youmust demonstrate an improvement in Indices of



reliability and validity by means of adjustmentmeasures, InFit, outfit, and differential itemfunctioning. In other words, the new structurelevels of the items should show a betterfunctioning, which show as a reduction of errorsand biases in the measurement and improvementin validity evidence. In this sense, it may pointto the need to characterize and differentiategroups of responses in this type of instrumentfor this population and, thus, differentiate thedifferent levels of performance that can bringa difference for this type of analysis, especiallyregarding personality characteristics.

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