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Criteri dell'Informazione e Selezione dei Modelli in Misurazione Funzionale
Full text linkThe processes of evaluation of environmental stimuli and decision are common in everyday life and in many social and economic situations. These processes are generally described in scientific literature using multi-attribute choice models. These models assume that evaluation of a stimulus described by several attributes results from a multi-stage process (Anderson, 1981; Lynch, 1985): evaluation of the attributes, integration of the values of the attributes and explicit evaluation of the stimulus. Commonly, in this field, experimental settings require the evaluation of a set of stimuli built combining some attributes. A subject evaluator examines the attributes of each stimulus; using her “mental” model of choice (Oral & Kettani, 1989), it assigns a value to attributes and formulate an overall judgment. Finally, subject expresses his opinion in terms of order-ranking, pairwise preference comparisons, values in a rating scale, and so on.
This so-called multi-attribute evaluation suffers of a fundamental difficulty to measure the values of each attribute of a stimulus starting by the overall evaluation of each subject. Basically, the problem is to derive each value decomposing the overall judgment (i.e. the response output). This difficulty in measuring is typical in most of the often complementary multi-attribute models traditions, as those of Conjoint Analysis (Luce & Tukey, 1964; Krantz & Tversky, 1971; Green & Rao, 1971) or Information Integration Theory (IIT: Anderson, 1970, 1981, 1982).
According to Anderson’s IIT, cognitive system give a subjective value to each characteristic of a stimulus, and the values are put together in a overall judgment using a specific integration function. IIT describe integration modalities using different mathematical rules, and functional measurement is the methodology proposed to determine and measure the integration function. Functional measurement use factorial experiments, selecting some attributes of a stimulus and combining them in factorial plans. Usually, subject’s evaluations for each cell of experimental design are reported on a category scale, and each subject replicates each evaluation for more trials. Starting from subject’s evaluations, functional measurement aims to quantify the value of each level of factors and its importance in the global judgment, for each subject evaluator or group of subjects.
Anderson’s theory suggests that the most widely used integration rules are of three fundamental and simple kinds: additive, multiplicative and weighted average. Statistical techniques as the analysis of variance can be used to detect the integration rule on the basis of the goodness of fit.
The averaging rule in particular can account for interaction effects between factors, splitting evaluation in two components: scale value and weight, which can be identified and measured separately (Zalinski & Anderson, 1989). If scale value represents the location of the level of attribute on the response scale, the weight represents his importance into global judgment. Averaging model provides a useful way to manage interaction between factors, surpassing the assumption of independence on which most applications of multi-attribute choice models are based. However, the model presents some critical points about the estimation issue, and for this motivation it potential is not fully exploited up until now. In this research work, a new method for parameter estimation for averaging model is proposed. The method provides a way to select the best set of parameters to fit data, and aims to overcome some problems that have limited the use of the model.
According to this new method, named R-Average (Vidotto & Vicentini, 2007; Vidotto, Massidda & Noventa, 2010), the choice of optimal model is made according to so-called “principle of parsimony”: the best model is the “simplest” one which found the best compromise between explanation of phenomenon (explained variance) and structural complexity (number of different weight parameters). Selection process use in combination two goodness-of-fit indexes: Akaike Information Criterion (AIC; Akaike, 1974) and Bayesian Information Criterion (BIC; Schwarz, 1978). Both indexes are derived starting from the logarithm of the residual variance weighted for the number of observations, and by penalizing the models with additional parameters. AIC and BIC differ in penalty function - since the BIC imposes a larger penalty for complex models than the AIC does - and are very useful for model comparison.
In this research work, two version of R-Average method are presented. This two versions are one evolution of the other, and both methods are structured in some procedures to perform estimation. Basically, R-Average consists of three procedures: EAM Procedure, DAM Procedure and Information Criteria (IC) Procedure. EAM, DAM and IC differ in constraints imposed on weights during the optimization process.
EAM Procedure constrains all the weight within each factor to be equal, estimating an Equal-weight Averaging Model. This model is the optimum in terms of parsimony, because it presents the smallest number of parameters (one single weight for all levels of each factor). In fact, it is defined as “parsimonious” a simple model, in which the weights are equal. Differently, DAM Procedure does not impose constraints on the weights, leaving their free to vary. Thus, this procedure may converge to a complete Differential-weight Averaging Model, which is the less parsimonious model (i.e. all the weights of each level of each factor are different).
The core of R-Average method is the Information Criteria Procedure. This procedure is based on idea that, from a psychological point of view, a simple model is more plausible than a complex model. For this reason, estimation algorithm is not oriented to search parameters that explain the greater proportion of variance, but search a compromise between explained variance and model complexity. A complex model will be evaluated as better than a simpler one only if the allows a significantly higher degree of explanation of phenomenon.
IC Procedure search the model, trying to keep (in the “forward” version) or to make (in the “backward” version) all the weights equal. In the forward version, the procedure starts from the EAM model and spans all the possible combination of weights, modifying it: initially one by one, then two by two, then three by three and so on. For each combination, the procedure tries to diversifies weights. From time to time, using BIC and AIC indexes, the procedure selects the best set of parameters and assume the selected model as reference for the following step (if an evidence of improvement is found). In the backward version, the procedure starts from the DAM model and spans all the possible combinations of weights, trying to equalize them. BIC and AIC are used to compare the new models with the reference model: if a new model is detected as better than the reference one, it will used as new reference for following steps.
Finally, all the estimated models by the procedures are compared, and the best model based on information criteria is preferred.
The original formulation of the averaging model was modified in the evolution of the basic R-Average method. This reformulation considers the weight not as simply w parameters but as w = exp(t). This exponential transformation leads to a solution for classical problem of uniqueness which affect averaging formulation (Vidotto, 2011). Furthermore, this reformulation justifies the application of cluster analysis algorithms on weight values, necessary for the clustering procedure of experimental subjects on the basis of their similarity. In fact, the distance between two t values can be evaluated in terms of simply difference. Differently, the distance between two w values can be evaluated only in terms of ratio between them. This allows to use clustering algorithms of subjects based on matrices of proximity between parameters.
The performance of R-Average was tested using Monte Carlo studies and practical applications in three different research fields: in marketing, in economic decision theory and in interpersonal trust.
Results of Monte Carlo studies show a good capability of the method to identify parameters of averaging model. Scale parameters are in general well estimated. Differently, weight estimation is a bit more critical. Punctual estimation of the real value of weights are not precise as the estimation of scale values, in particular as the standard deviation of the error component in observed data increases. However, estimations appears reliable, and equalities between weights are identified. The increasing of the number of experimental trials can help model selection when the errors present a greater standard deviation. In summary, R-Average appear as an useful instrument to select the best model within the family of averaging models, allowing to manage particular multi-attribute conditions in functional measurement experiments.
R-Average method was applied in a first study in marketing field. In buying a product, people express a preference for particular products: understanding cognitive processes underlying the formulation of consumers’ preferences is an important issue. The study was conducted in collaboration with a local pasta manufacturer, the Sgambaro company. The aims of research were three: understand the consumer’s judgment formulation about a market product, test the R-Average method in real conditions, and provide to Sgambaro company useful information for a good marketing of its product. Two factors was manipulated: the packaging of the Sgambaro’s pasta (Box with window, Box without window and Plastic bag) and the price (0.89€, 0.99€, 1.09€).
Analyses started considering evaluations of the product express by participants: for each subject, parameters of averaging model was estimated. Since the consumers population is presumably not homogeneous in preferences, the overall sample has been split in three clusters (simply named A, B and C) by an cluster analysis algorithm. For both Price and Packaging factors, different clusters showed different ratings. Cluster A express judgments that are positioned on the center of scale, suggesting as participants are not particularly attracted by this products. By contrast, Cluster B express positive judgments, and Cluster C express globally negative with the exception of the package “box with window”. For packaging, it observes that the box with window, although is not the preferred one in the three clusters, has always positive evaluations, while judgments on other packaging are inconsistent across groups. Therefore, if the target of potential consumers for the product is the general population, the box with window can be considered the most appreciated packaging.
Moreover, in Cluster C ANOVA shows a significant interaction between Price and Packaging. In fact, estimated parameters of averaging model show that Cluster C is greatly affected by a high price. In this cluster the highest price had a double weight in the final ratings, therefore the positive influence on the judgment of the “box with window” packaging could be invalidated. It’s important to notice that the group which is more sensitive to the high price is also that one which gave the lowest ratings compared to the other clusters.
In a second experiment, the R-Average method has been applied in a study in the field of economic decision marking under risk. The assumption that moved the study is that, when a person must evaluate an economic bet in a risky situation, person integrates cognitively the economic value of bet and the probability to win. In the past, Shanteau (1974) shown that integration between value and probability is made according a multiplicative rule. The study, as Lynch (1979), highlighted that when the situation concern two simultaneous bets, each one composed from a value and a probability, judgments for double bet is different to the sum of judgments for single bets. This observation, named subadditivity effect, violate the assumptions of Expected Utility Theory.
The proposed study analyze the convenience/satisfaction associated with single and duplex bets. The study proposed to participants two kind of bets. A first group of bets involved a good (Mobile Phones), and the other one, a service (free SMS per day); to each good/service was associated the a probability to obtained him. Two experimental conditions was defined. In the first condition, subjects judge bets considering that phones come from a good company, and SMS service came from a untrustworthy provider. In the reverse condition, subjects judge bets considering that phones was made with low-quality and come from a untrustworthy company, and SMS service come from a strong and trustworthy provider.
For duplex bets, the presence of averaging integration model was hypnotized, and the parameters of model was estimated using R-Average on each subject. Results show that the integration in presence of a duplex bet is fully compatible with an averaging model: the averaging and not adding appear the correct integration rule.
In the last experiment, averaging model and R-Average methodology were applied to study trust beliefs in three contexts of everyday life: interpersonal, institutional and organizational. Trusting beliefs are a solid persuasion that trustee has favorable attributes to induce trusting intentions. Trusting beliefs are relevant factors in making an individual to consider another individual as trustworthy. They modulate the extent to which a trustor feels confident in believing that a trustee is trustworthy. According to McKnight, Cummings & Chervany (1998), the most cited trusting beliefs are: benevolence, competence, honesty/integrity and predictability.
The basic idea under the proposed study is that beliefs might be cognitive integrated in the concept of trustworthiness with some weighting processes. The R-Average method was used to identify parameters of averaging model for each participant. As main result, analysis shown that, according to McKnight, Cummings & Chervany (1998), the four main beliefs play a fundamental role in judging trust. Moreover, agreeing with information integration theory and functional measurement, an averaging model seems to explain individual responses. The great majority of participants could be referred to the differential-weight case. While scale values show a neat linear trend with higher slopes for honesty and competence, weights show differences with higher mean values, still, for honesty and competence. These results are coherent with the idea that different attributes play a different role in the final judgment: indeed, honesty and competence seem to play the major role while predictability seems less relevant. Another interesting conclusion refers to the high weight of the low level of honesty; it seems to show how a belief related to low integrity play the most important role for a final negative judgment. Finally, the different tilt of the trend for the levels of the attributes in the three situational contexts suggests a prominent role of the honesty in the interpersonal scenarios and of the competence in the institutional scenarios.
In conclusion, information integration theory and functional measurement seem to represent an interesting approach to comprehend the human judgment formulation. This research work proposes a new method to estimate parameters of averaging models. The method shows a good capability to identify parameters and opens new scenarios in information integration theory, providing a good instrument to understand more in detail the averaging integration of attributesI processi di valutazione degli stimoli ambientali e di decisione sono comuni nella vita quotidiana e in tante situazioni di carattere sociale ed economico. Questi processi sono generalmente descritti dalla letteratura scientifica utilizzando modelli di scelta multi-attributo. Tali modelli assumono che la valutazione di uno stimolo descritto da più attributi sia il risultato di un processo a più stadi (Anderson, 1981; Lynch, 1985): valutazione degli attributi, integrazione dei valori e valutazione esplicita dello stimolo. Comunemente, in questo campo, le situazioni sperimentali richiedono la valutazione di un set di stimoli costruiti combinando diversi attributi. Un soggetto valutatore esamina gli attributi di ogni stimolo; usando il solo modello “mentale” di scelta (Oral e Kettani, 1989), assegna un valore agli attributi e formula un giudizio globale. Infine, il soggetto esprime la sua opinione in termini di ordinamento, preferenze a coppie, valori su una scala numerica e così via.
Questa cosiddetta valutazione multi-attributo soffre di una fondamentale difficoltà nel misurare i valori di ogni attributo di uno stimolo partendo dalle valutazioni complessive di ogni soggetto. Fondamentalmente, il problema è derivare ogni valore decomponendo il giudizio complessivo (cioè la risposta in output). Questa difficoltà di misurazione è tipica di molte delle spesso complementari tradizioni dei modelli multi-attributo, come la Conjoint Analysis (Luce e Tukey, 1964; Krantz e Tversky, 1971; Green e Rao, 1971) o la Teoria dell’Integrazione delle Informazioni (IIT: Anderson, 1970, 1981, 1982).
Secondo la IIT di Anderson, il sistema cognitivo fornisce un valore soggettivo a ogni caratteristica di uno stimolo, e tali valori vengono combinati in un giudizio complessivo utilizzando una specifica funzione d’integrazione. La IIT descrive le modalità d’integrazione utilizzando differenti regole matematiche, e la misurazione funzionale è la metodologia proposta per determinare e misurare la funzione d’integrazione. La misurazione funzionale si serve di esperimenti fattoriali, selezionando alcuni attributi di uno stimolo e combinandoli in piani fattoriali. Solitamente, le valutazioni dei soggetti per ogni cella del disegno sperimentale sono riportate su una category scale, e ogni soggetto ripete la valutazione per più prove. Partendo dalle valutazioni soggettive, la misurazione funzionale mira a quantificare il valore di ogni livello dei fattori e la sua importanza nel giudizio complessivo, per ogni soggetto valutatore o gruppo di soggetti.
La teoria di Anderson suggerisce che le regole d’integrazione più ampiamente utilizzate sono di tre fondamentali e semplici tipologie: additiva, moltiplicativa e di media ponderata (averaging). Tecniche statistiche come l’analisi della varianza possono essere utilizzare per individuare la regola d’integrazione sulla base della bontà dell’adattamento.
La regola averaging in particolare è in grado di tenere in considerazione gli effetti d’interazione tra i fattori, scindendo la valutazione in due componenti: valore di scala e peso, che possono essere identificati e misurati separatamente (Zalisnki e Anderson, 1989). Se il valore di scala rappresenta il posizionamento del livello del fattore sulla scala di risposta, il peso rappresenta la sua importanza nel giudizio complessivo. Il modello averaging fornisce una via molto utile per gestire gli effetti d’interazione tra i fattori, superando l’assunto d’indipendenza sul quale molte applicazioni dei modelli di scelta multi-attributo sono basate. Tuttavia, il modello presenta alcuni punti critici relativi alla questione della stima, e per questo motivo il suo potenziale non è stato pienamente sfruttano fin’ora. In questo lavoro di ricerca viene proposto un nuovo metodo per la stima dei parametri del modello averaging. Il metodo consente di selezionare il miglior set di parametri per adattare i dati, e mira a superare alcuni problemi che ne hanno limitato l’uso.
Secondo questo nuovo metodo, chiamato R-Average (Vidotto e Vicentini, 2007; Vidotto, Massidda e Noventa, 2010), la scelta del miglior modello è fatta in accordo al cosiddetto “principio di parsimonia”: il miglior modello è quello più “semplice”, che trova il miglior compromesso tra spiegazione del fenomeno (varianza spiegata) e complessità strutturale (numero di parametri di peso diversi). Il processo di selezione usa in combinazione due indici di bontà dell’adattamento: l’Akaike Information Criterion (AIC; Akaike, 1974) e il Bayesian Information Criterion (BIC; Schwartz, 1978). Entrambi gli indici sono ricavati partendo dal logaritmo della varianza residua pesata per il numero di osservazioni, e penalizzando i modelli con parametri aggiuntivi. AIC e BIC differiscono nella funzione di penalizzazione – dato che il BIC impone una penalità maggiore ai modelli con più parametri – e sono molto utili per la comparazione fra modelli.
In questo lavoro di ricerca vengono presentate due versioni del metodo R-Average. Queste due versioni sono una l’evoluzione dell’altra, ed entrambi i metodi sono strutturati in diverse procedure per eseguire la stima. Fondamentalmente, R-Average consta di tre procedure: procedura EAM, procedura DAM e procedura Information Criteria (IC). EAM, DAM e IC differiscono nei vincoli imposti sui pesi durante il processo di ottimizzazione.
La procedura EAM vincola tutti i pesi all’interno di ogni fattore a essere uguali, stimando un modello a pesi uguali. Questo modello è il migliore in termini di parsimonia, perché presenta il minor numero di parametri (uno unico per ogni fattore). Infatti, si definisce come “parsimonioso” un modello semplice, nel quale i pesi sono uguali. Diversamente, la procedura DAM non impone alcun vincolo sui pesi, lasciandoli liberi di variare. Così, questa procedura può potenzialmente convergere verso un modello averaging a pesi completamente diversi (dove cioè tutti i pesi dei livelli di ogni fattore sono dive
Influenza della memoria di lavoro visuo-spaziale sullo sviluppo delle abilità matematiche.
No full textNella ricerca sono stati seguiti in longitudinale 43 bambini misurando le loro abilità di memoria di lavoro spaziale e visiva all’inizio (T1) e fine (T2) della prima primaria e alla fine della seconda primaria (T3), mettendole in relazione con le prestazioni nella pre-matematica e nella prima matematica.
I risultati mostrano che i migliori predittori delle prestazioni nella pre-matematica al T1 sono le abilità di memoria di lavoro visiva (manipolazione visiva di immagini) e spaziale simultanea (Corsi indietro), mentre non troviamo implicate le abilità di memoria di lavoro spaziale sequenziale (matrici sequenziali con doppio compito). Al T2 troviamo che le conoscenze di pre-matematica sono la variabile più importante nel definire le performance aritmetiche, mentre alla fine della seconda primaria (T3) le abilità di pre-matematica perdono importanza e riemerge l’influenza della memoria di lavoro visiva e di quella spaziale simultanea mentre, come al T1, non si trova implicazione della memoria spaziale sequenziale
Assertività e soddisfazione degli studenti nelle transizioni scolastiche: Una ricerca nella scuola secondaria superiore
No full textThe present study investigates the relationship between assertiveness and satisfaction of students in school transitions in and out of the secondary school. Method. 250 high school students (first and fifth classes) completed the questionnaires: "Come mi comporto con gli altri" [How do I behave with others?] and "La Mia vita da Studente" [My life as a student] (Soresi and Nota, 2003). Through path analysis a model was tested designed to evaluate the influence of factors related to assertiveness on students' satisfaction Results. Some model paths differ significantly depending on the relative school transition: among first-class students some social skills (eg. expressing disagreement, having social initiative) influence satisfaction in the relationship with peers, while among fifth-class students these social skills affect satisfaction with regards to school experience and the awards received. Moreover, for fifth-class students facing post-degree choices, accepting and manifesting one's own limitations can lead to lower levels of satisfaction in the relationship with family members. In any case, among the students examined, the frequency in asking for help and support is a good predictor of overall satisfaction. Conclusions. The study suggests that actions of satisfaction promotion should be differentiated according to age and relative school transition
An open source software application to study numerical representations in children and adults
No full textInformation technologies have strongly improved psychological research, contributing to speed up the progress of knowledge in this field. Unfortunately, for many years, most part of software solutions for psychological research were very expensive and distributed with proprietary licenses, but open source applications may solve these difficulties. This work applies an open source software developed in Python using the module PyshcoPy, with the aim to study numerical representations in children and adults: we transformed in a computer-based test the paper-and-pencil version of the Number Line Task (NLT), which requires to estimate the position of several digits along a line. Paper-and-pencil and computer versions of the NLT were compared submitting the task to different ages groups, analyzing individuals’ performances and response’s variability: results indicated that there were not significant differences between the two versions of NLT task in children’s and adults’ percentage of absolute errors (PAE) and in responses’ variability. We concluded that there were not significant differences between the classical NLT version and the open source NLT software to assess the cognitive representation of numerical magnitude; however, differently to the paper-and-pencil task, the computer program allows to record data with a great decimal precision, to record reaction times, to decrease monetary and environmental costs (paper) and to avoid human errors in data entry
Fattori predittivi della prestazione al Number Line Task in bambini prescolari
No full textINTRODUZIONE
Gli studi di Dehaene (2003) hanno messo in evidenza che i numeri vengono rappresentati lungo una virtuale Linea Numerica Mentale e grazie a questa rappresentazione riusciamo a manipolarli mentalmente. Per studiare la rappresentazione della grandezza numerica, Siegler (2003) ha messo a punto il compito di linea numerica (il Number Line Task - NLT) mettendo in luce l’importanza della performance al NLT come indicatore dell'adeguato sviluppo delle abilità matematiche, importanza confermata da molti studi che trovano che il NLT è buon predittore, in età scolare, delle competenze matematiche (Geary, 2008). Per quel che riguarda il collegamento tra prestazione al NLT e conoscenze di pre-matematica, la letteratura è invece molto carente. In questo lavoro abbiamo voluto studiare la relazione tra prestazione al NLT e pre-matematica chiedendoci quali competenze numeriche precoci predicano la prestazione al NLT.
METODO
Hanno partecipato alla ricerca 34 bambini prescolari (F=18; media età in mesi: 69.24; DS: 3.3) a sviluppo tipico. Le abilità pre-matematiche sono state valutate con la Batteria BIN 4-6 (Molin et al., 2007) e a queste misure è stata affiancato il compito di linea numerica (NLT) 0-100 somministrato al PC. Da una prima analisi di correlazione è emerso che le abilità significativamente correlate con il NLT sono: il confronto tra numeri arabici, la seriazione di numeri arabici e la enumerazione indietro. Successivamente si è approfondita la relazione tra abilità pre-matematiche e NLT adattando un modello di regressione nel quale i predittori sono stati individuati attraverso una forward selection basata sull’utilizzo dell'indice BIC che ha permesso di selezionare il modello migliore in ottica bayesiana.
RISULTATI
I risultati mostrano che il miglior modello finale selezionato attraverso il BIC è dato dalla seriazione di numeri arabici (area del conteggio) con un B = -.53, t(31) = -3.95, p < .001 e dal confronto di numeri arabici (area semantica) con un B = -.33, t(31) = -2.46, p = .019 che insieme spiegano il 46% della varianza della prestazione al NLT mentre le altre abilità indagate non risultano predittive. Il valore del BIC è 88.28 e la F(2,32) = 13.5, p < .001.
CONCLUSIONI
I risultati suggeriscono che la prestazione all’NLT a 5 anni è strettamente legata non tanto alle conoscenze relative alle quantità (per es. confronto di dots) o alle conoscenze relative al nome dei numeri (per es. conoscenze di area lessicale) ma esclusivamente a conoscenze che hanno a che fare con la semantica del numero nel suo formato arabico. I bambini sembrano inoltre utilizzare, per risolvere il NLT, le loro conoscenze di conteggio e seriazione di numeri arabici. Questi risultati sembrano confermare le conclusioni di ricerche molto recenti (Lyons et al., 2014) che trovano che la funzione predittiva del successo matematico del NLT è in relazione con l’abilità di ordinamento di simboli numerici più che con abilità relative alla stima intuitiva di grandezze pre-simboliche
The Italian version of the Dutch Workaholism Scale (DUWAS): A study on a group of nurses
No full textIntroduction: The risk for nurses to be exposed to workaholism is widely demonstrated in the relevant international literature; however, this does not seem to be paid sufficient study and analysis in Italy. The Italian adaptation of the Dutch Workaholism Scale (DUWAS) comprises the working excessively (WE) and working compulsively (WC) scales. Method: A group of 485 Italian nurses, balanced in terms of gender and seniority, compiled the DUWAS questionnaire. The Rasch model was used to analyse the retrieved data, which helped to identify nurses at risk of workaholism. Results: The WE and WC scales within the DUWAS show low internal consistency, some points of contact, and appear to relate to each other. About 18% of the group of subjects shows a workaholic profile, and approximately 29% are at risk of becoming workaholic. Conclusions: This study contributes to improve the validation of the Italian version of the DUWAS, and helps to assess workaholism in nursing, a crucial healthcare profession
Integrating different factorial solutions of a psychometric tool via social network analysis: The case of the mood disorder questionnaire
No full textEvaluating the factorial structure of a psychometric test is crucial to capture the complexity of a psychological phenomenon. Indeed, for the same test, several studies may find different factorial solutions which, in turn, may be explained by within and/or between sample variability. In this paper we introduce a novel quantitative approach to combine different factorial solutions of the same test. We propose to use a method based on Social Network Analysis to create and statistically evaluate an integrated factorial structure based on the information provided by previous researches. We present an application to the Mood Disorder Questionnaire by considering different factorial structures reported in the literature. The integrated factorial solution indicates the presence of three factors supporting the multidimensionality of the test. The role of single items in the composition of factors is also evaluated and discussed in terms of differences and similarities between the five original studies and the new integrated model. From an applied perspective, our approach may be useful to assist researchers in summarizing different factorial solutions for the same test efficiently. Furthermore, the resulting integrated factor solution could serve as baseline model to validate the structure of the test by applying confirmatory factor techniques to new data
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