Locus of Control (LOC) is a variable which is frequently evaluated in psychology and education owing to the important role it plays in different contexts (Cheng, Cheung, Chio & Chan, 2012; Muñiz, Suárez-Álvarez, Pedrosa, Fonseca-Pedrero, & García-Cueto, 2014; Severino et al. 2011; Aiello, Cascio, Ficarra & Messina, 2011; Suárez-Álvarez, Campillo-Álvarez, Fonseca-Pedrero, García-Cueto & Muñiz, 2013; Urbig & Monsen, 2012). There is no unanimous agreement on how many dimensions make up the factorial structure of LOC (Ferrando, Demestre, Anguiano-Carrasco & Chico, 2011; Kormanik & Rocco, 2009; Levenson, 1981; Niles, 1981; Paulhus & Van Selst, 1990; Rotter, 1966, 1975), although the most commonly accepted theoretical models tend to reject the unidimensional structure (Levenson, 1981; Paulhus & Van Selst, 1990; SuárezÁlvarez, Pedrosa, García-Cueto & Muñiz, in press; Thompson & Prendergast, 2013). In other words, the locus of control is not a continuum between two poles as originally proposed (Rotter 1966); a person may simultaneously have an external attributional style and an internal attributional style (Suárez-Álvarez et al., in press). Therefore it is reasonable to think that the cause of a behaviour may be attributed to what one does (internal LOC), while at the same time, accepting that the situation may also be influenced by events outside one's control (external LOC).

In a recent meta-analysis, Cheng, Cheung, Chio and Chan (2012) found that external LOC was not related to anxiety and depression in the same way in all cultures. That is, the significance of LOC is cultural and, hence, different depending on the population. The roots of these differences may be found in the cultural values in each society (Hofstede, 2001; Triandis & Suh, 2002). For example, individualistic societies, such as those in the West, tend to place the responsibility on an individual for his or her actions, whereas collectivist societies, like those in Asia are generally more sensitive to external influences (Cheng et al., 2012). This might explain the fact that differences between Europeans and Americans are small whereas when comparing Americans and Asians they are much bigger (Yamaguchi, Gelfand, Ohashi & Zemba, 2005).

Studying LOC across cultures means being able to ensure equivalence when measuring the construct (i.e. measurement invariance). Hence, if one wants to make multi-group comparisons, one has to demonstrate that the measurement instruments work in exactly the same way and that the construct under evaluation has both the same theoretical structure and psychological implications for the groups of interest (Byrne, 2008). In other words, it would not be acceptable to compare scores of people belonging to two cultural groups in a construct that did not have the same significance in both cultures. Neither would it make sense to interpret the results of a test if its application in two contexts is associated with different measurement errors (Elosua, 2005). Both questions are contingent on checking factorial invariance (Byrne, 2008; Dimitrov, 2010; Elosua & Muñiz, 2010; Supple, Su, Plunkett, Peterson & Bush, 2012; Zecca et al., 2012). Van de Vijver and Leung (1997) proposed three forms of factorial equivalence: configural invariance, in which the underlying psychological process is the same in the different groups since all the factors are shaped by the same items; metric invariance, in which the scaling metrics are the same; and scalar invariance, in which the origin of the scale is also the same for the different groups.

There is no unanimous agreement on the dimensionality of LOC, neither does there seem to exist any agreement on its measurement equivalence across cultures. The results are highly inconsistent. When Rotter's unidimensional scale is used, the results show a different factorial structure for Africans, Europeans and Indians (Furnham & Henry, 1980). Smith, Trompenaars and Dugan (1995) headed a transcultural investigation in 43 countries using Rotter's scale and identified three dimensions which were relatively close to those proposed by Levenson (1981): one dimension of internality and two of externality (powerful others and chance). Other authors have also confirmed Levenson's multidimensional structure between Scots, Spanish and Irish (Bonetti et al., 2001), and between US and Indian groups (Ghorpade, Hattrup & Lackritz, 1999). On the other hand, some researchers reject the equivalence of this multidimensional structure between Caucasian Americans, Filipino Americans and Latino Americans (Malcarne, Fernández & Flores, 2005), and across young, middle-age, and elderly age groups (Shewchuk, Foelker, Camp & Blanchard-Fields, 1992). Rossier, Dahourou and McCrae (2005) tested whether the bidimensional structure (internal and external LOC) was a better fit than the multidimensional one between Switzerland and Burkina Faso.

It is not clear if the discrepancies in these results are due to measurement problems or to cultural variations in LOC (Rossier et al., 2005). It seems as though one possible explanation might be found in the process of adapting the measuring instruments, because the process of translating an instrument from one language into another involves much more than mere back-translation (Hambleton, Merenda & Spielberger, 2005). In addition, it must be taken into account that the main interest in transcultural studies is usually the comparison of scores according to the home country and therefore an adequate translation and adaptation of the instrument is necessary. Any bias in the translation or adaptation (Van de Vijver & Hambleton, 1996), will directly affect the instrument's equivalence metrics and, therefore, the comparison of scores between groups (Byrne, 2008; Dimitrov, 2010).

The goal of this research was to add new evidence of validity in relation to the factorial invariance of LOC. More specifically, the research looked at the cross-cultural equivalence of the bidimensional structure of LOC (i.e. internal LOC and external LOC). In order to do this, a progressive evaluation of the factorial invariance between Spanish, Chilean and British groups was carried out using structural equation modelling (SEM) within the framework of a confirmatory factor analysis (CFA) model for ordered-categorical data. Once the cross-cultural equivalence of the measuring instrument was confirmed, a transcultural study of LOC was carried out according to home country.

The objective of this research was to add new evidence of cross-cultural validity in relation to factorial invariance of LOC. Cross-cultural equivalence of the instrument was carried out following the steps established by Byrne (2008): a) translation and adaptation of a test for a British population to evaluate LOC (Oviedo Locus of Control Scale; Suárez-Álvarez et al., in press) using the back-translation method and following international directives for the translation and adaptation of psychometric instruments (Hambleton, Merenda, & Spielberger, 2005; Muñiz & Bartram, 2007; Muñiz et al., 2013); b) checking that the original factorial structure of the instrument is the same in the new versions and c) checking the equivalence of the changes across groups.

Firstly, regarding the translation and adaptation of the instrument, one item was found to have low discriminative power in the British population (To be successful it is necessary to have good contacts). However, this item had a value of .31 in the the Spanish and .35 in the Chilean sample. This suggests that the lack of discriminative power for the British could be due to a problem with the translation (Muñiz et al., 2013). Spanish speakers interpret this item in a way which clearly corresponds to an external attributional style; it seems reasonable to think that the British do not consider having "good contacts" as an external or chance event, but instead more as a consequence of personal merit. This fact highlights the importance and complexity of adapting instruments to other cultures (Hambleton, Merenda, & Spielberger, 2005). On the other hand, the reliability coefficients were acceptable in all groups for both the internal LOC (α_Spain = .81; α_Chile= .96; α_UK = .93) and external LOC (α_Spain = .82; α_Chile = .93; α_UK = .88). Furthermore, these results reasonably approximate those obtained in the original test (α_internal = .87; α_external = .85). (Table 4.)

Table 4

Note. χ2 = chi-square test; df = degrees of freedom.*The differences were statistically significant (p < .05) between groups

Secondly, the configural invariance of the instrument was confirmed in all three groups. Hence it is reasonable to conclude that the bidimensional structure is confirmed in the Spanish, Chilean and British populations. Hence it can be concluded that the original factorial structure of the instrument is the same in the new versions.

Thirdly, a strong measurement invariance assumption was confirmed by the progressive factorial invariance analysis (Table 3). This means that not only factor loadings and thresholds are invariant across Spain, Chile, and United Kingdom, if not that error variances and factor variances are invariant too. This implies that similar levels of precision are performed when the construct is measured across these groups.

Finally, there were statistically significant differences between the nationalities in both subscales (p < .001). As can be seen in Table 4, the British and Chileans had the highest score in external LOC and the lowest in internal LOC, while this was the inverse in the case of the Spanish. These results coincide with the general tendency to observe differences in LOC according to nationality (Cheng et al., 2012; Malcarne, Fernández & Flores, 2005; Rossier, Dahourou, & McCrae, 2005; Yamaguchi, Gelfand, Ohashi & Zemba, 2005). On the other hand, it seems reasonable that, nowadays, people from changing economies such as Spain tend to make internal attributions to a greater extent than those from more well off countries such as Britain. The reason is that people might be expected to attribute the cause of change to what one can do. On the contrary, in countries with a social welfare system and a better economy one would expect that the inhabitants would tend to trust in community or welfare systems for support. Furthermore, the differences between Spanish and Chileans were smaller in both constructs than when they were compared with British. Interestingly, Chile and Spain have similar scores for power distance, uncertainty avoidance, and individualism (Hofstede, 2001). Regardless, the effect size was considerably low implying that the differences found are not relevant. In sum, the differences found must be taken as a tendency, and if it wants to support crosscultural differences, more empirical evidence should be provided.

In summary, the progressive evaluation of factorial invariance allows us to confirm a strong measurement invariance assumption. This provides evidence that the items were measured with the same precision in each group, so the group differences on any item are due only to group differences on the common factors (Dimitrov, 2010). These results add new evidence for the theses that a bidimensional structure represents the most realistic form of LOC in cross-cultural studies (Rossier et al., 2005).

The following limitations must be borne in mind when interpreting these results. Firstly, it would be useful to increase the sample size to improve the representativeness of the data. Secondly, it would be interesting to have convergent measures with LOC at transcultural level to improve the evidence of validity. Lastly, all the data were collected via self-reporting methods; in the future, it would be useful to administer other measuring instruments such as interviews or situational tests.