Participants

1518 subjects participated in the study, 815 women and 703 men, all university students of Mexico. The subjects' age ranged between 18 and 26 years, with an average of 20.56 and a standard deviation of 1.88 years.

The sample was randomly divided into two parts using the Statistical Package for Social Sciences (SPSS) version 18.0; in order to perform parallel studies to corroborate and verify the obtained results (cross validation).

The first half (subsample 1) was composed of 787 subjects; 449 women and 338 men. The ages range between 18 and 26 years, with an average of 20.48 and a standard deviation of 1.87 years.

The second half (subsample 2) was composed of 731 subjects; 366 women and 365 men. The ages range between 18 and 26 years, with an average of 20.66 and a standard deviation of 1.89 years.

Instrument

Self-Concept Questionnaire (AUDIM) Likert scale of 33 items related to the person itself; where the respondent answers on a scale of 1 to 5 (1 = False, 2 = Rather false 3 = neither true nor false, 4 = Rather true and 5 = True) their level of agreement with each of the aspects proposed (choosing the answer that best fits their person). The questionnaire items are grouped into four specific factors: academic self-concept (8 items), social self-concept (4 items), physical self-concept (8 items), personal self-concept (8 items) and one General, General self-concept (5 items).

For our study, three adaptations to the original version of ^{Goñi, Madariaga, Axpe and Goñi (2011)} were made: First adaptation, in the original version is scored five response options: (0) false, (1) almost always false, (2) sometimes true sometimes false, (3) almost always true and (4) true; in the version used in this research the subject chooses between 11 possible answers. We combine the original scale with our version to make it as follows: false (0), almost always false (1, 2 and 3), sometimes true, sometimes false (4, 5 and 6), almost always true (7, 8 and 9) and true (10). This first adaptation is justified because the subjects as students are used to the scale of 0 to 10, since like that they have been evaluated by the education system in our country (Mexico).

The second adaptation was to change some terms used in the items of the original version in order to use a language appropriate to the context of the Mexican culture and summarizing the content of the 8 items of academic self-concept factor, in only 3 items (I'm good with subjects of grammar and Spanish; I'm good at math and in science subjects); reason why we refer to the AUDIM questionnaire as questionnaire AUDIM-M.

The third adaptation was to apply the instrument through a computer (Figure 1); this in order to allow the storage of data without prior encoding stages, with greater precision and speed.

Figure 1 Sample answer to the questionnaire items. 

Procedure

Students of the degrees offered at the Faculty of Physical Culture (FCCF) of the Autonomous University of Chihuahua were invited to participate. Those who agreed to participate signed the consent letter. Then, the instrument described above was applied using a personal computer (administrator module of the instrument of the scales editor of typical execution), in a session of about 30 minutes in the computer labs of the FCCF. At the beginning of each session students were given a brief introduction on the importance of the study and how to access the instrument; they were asked the utmost sincerity and they were guaranteed the confidentiality of the data obtained. Instructions on how to respond were in the first screens; before the first instrument item. At the end of the session they were thanked for their participation.

Once the instrument was applied, data was collected by the results generator module of scales editor, version 2.0 (^{Blanco et al., 2013}).

Finally the results obtained are analyzed using SPSS 18.0 and AMOS 21.0.

Data analysis

The psychometric analysis was conducted in two steps: 1) Exploratory factor analysis and 2) confirmatory factor analysis and factorial invariance; in order to obtain proof that presents the best properties for the conformation of body image scores in college students.

Classic Analysis of the Psychometric properties of the scale

The first step in analyzing the psychometric properties of the questionnaire was to calculate the mean, standard deviation, skewness, kurtosis and discrimination indexes of each item. Then remove of the scale those who obtain a kurtosis or extreme asymmetry, or a discrimination index below .30.

Then, to determine the minimum number of common factors capable of reproducing, in a satisfactory manner, the observed correlations between the instrument items (with good discrimination), two separate exploratory factor analysis with sub-samples 1 and 2 were made, from the method of maximum verisimilitude, based on the criterion of Kaiser-Guttman (^{Costello y Osborne, 2005}), plus to ensure an adequate representation of variables (items), only those whose initial communality was higher than .30 were kept; after a varimax rotation (^{Costello y Osborne, 2005}).

Subsequently, the reliability of each of the factors of the models obtained in both subsamples was calculated through the Cronbach's alpha coefficient (^{Elosua y Zumbo, 2008}; ^{Nunnally y Bernstein, 1995}) and the Omega coefficient (^{Revelle y Zinbarg, 2009}; ^{Sijtsma, 2009}).

Confirmatory factor analysis and factorial invariance

Were submitted to comparison two measurement models: Model 1 (M5), five-factor model according to the original distribution of the items in the questionnaire and Model 2 (M4) four-factor model according to the results of exploratory factor analyzes, removing the items that were not sufficiently well explained and / or obtained an index of low discrimination.

To conduct the confirmatory factorial analysis, AMOS 21 software was used (^{Arbuckle 2012}), variances in terms of error were specified as free parameters, in each latent variable (factor) a structural coefficient was set associated to one, so that scale was equal to one of the observable variables (items). The estimated method used was the maximum likelihood method; following the recommendation of ^{Thompson (2004)}, so when the confirmatory factorial analysis is used, it is necessary to verify not only the fit of the theoretical model but it is recommended to compare the fit indexes of some alternative models to select the best.

To evaluate the adjustment model, statistical chi-squared, the Goodness-of-fit index (GFI), the standardized root mean square residual (SRMR) and the root mean square error of approximation (RMSEA) were used as absolute adjustment measures. Adjusted goodness of fit index (AGFI) the Tucker-Lewis Index (TLI), the comparative fit index (CFI) as measures of increasing adjustment. The chi-squared fit index divided by degrees of freedom (CMIN/GL) and the Akaike Information Criterion (AIC) as adjusting measures of Parsimony (^{Byrne, 2010}; ^{Gelabert et al., 2011}).

Subsequently, following the recommendations of ^{Abalo et al. (2006)} was made an analysis of the factorial invariance of the questionnaire for the subsamples, taking as a base the best measurement model obtained in the previous stage.

Finally was calculated the reliability of each of the dimensions, of the measurement models obtained in each subsample, through Cronbach's alpha (^{Elosua y Zumbo, 2008}; ^{Nunnally y Bernstein, 1995}) and Omega coefficient (^{Revelle y Zinbarg, 2009}; ^{Sijtsma, 2009}).

Exploratory factor analysis (first and second factorial solutions)

In Table 1 are summarized the results of the descriptive analysis and the discrimination indexes (total-item correlation corrected) of each of the 28 items on the questionnaire in the subsample 1 and 2.

In the subsample 1, responses to all items reflect mean scores that oscillate between 4.97 and 9.31, and the standard deviation provides, in all cases, higher values than 1.50 (within a response range between 0 and 10). With the exception of the items 2 and 9, all values of skewness and kurtosis are within the range ± 2.00 and ± 7.00 respectively; so it is inferred that the variables are reasonably fit a normal distribution. As for the discrimination indexes most items satisfactorily discriminate with discrimination indexes above .30 (^{Brzoska y Razum, 2010}).

In the subsample 2, responses to all items reflect mean scores that oscillate between 5.01 and 9.29, and the standard deviation provides, in all cases, higher values than 1.50 (within a response range between 0 and 10). With the exception of the items 2 and 9, as in the subsample 1, all values of skewness and kurtosis are within the range ± 2.00 and ± 7.00 respectively; so it is inferred that the variables are reasonably fit a normal distribution. As for the discrimination indexes most items satisfactorily discriminate with discrimination indexes above .30 (^{Brzoska y Razum, 2010}).

After a varimax rotation (^{Costello y Osborne, 2005}) the exploratory factor analysis of the items, in both subsamples, revealed a four-factor structure; leading to eliminate 13 of the 28 items analyzed. The set of the selected factors explained 66.06% of the variance in the first subsample and 66.85% of the variance in the second subsample (Tables 2 and 3).

Congruence between the factors of the two factorial solutions (cross-validation)

The values of the Congruence coefficients and Pearson correlation coefficients between the factor weights of the factors obtained in the exploratory factor analyzes conducted with subsamples 1 and 2; indicate, according to suggested by ^{Cureton and D'Agostino (1983)}, ^{Mulaik (1972)} and ^{Cliff (1966)}, a high congruence between pairs of factors (Table 4).

Reliability of the subscales (internal consistency)

The subscales (factors) resulting in the exploratory factor analysis, of both subsamples, possess mostly, internal consistency values above .70 in both samples demonstrating adequate internal consistency for these type of subscales, particularly when you consider the reduced number of items (Table 5).

Confirmatory factor analysis for subsamples 1 and 2

The overall results of the confirmatory factor analysis in the subsample 1 (GFI .746; RMSEA .097; CFI .694) and the subsample 2 (GFI .792; RMSEA .089; CFI .725) for the M5 model indicate that the measurement model, in both subsamples is acceptable (Table 6).

The set of the four factors of the model M5 account approximately 53% of the variance in both subsamples. Furthermore according to the results of Table 7; only 8 of the 28 items in both subsample, have saturations equal or greater than .70 in its intended dimension (items 5, 9, 13, 14, 20, 25, 26 and 27). Also observed in both subsamples, high intercorrelations among the factors of personal self-concept and general self-concept showing a poor discriminant validity among them.

The overall results of the confirmatory factor analysis in the first (GFI .964; RMSEA .049; CFI .971) and second subsample (GFI .951; RMSEA .061; CFI .952), the second model tested (M4) that corresponds to a four-dimensional structure according to the results of the exploratory factor analysis of the questionnaire items, indicate that this measurement model is better than the previous model and its setting is optimal (Table 6). The four factors of this model explain together approximately 62% of the variance in both subsamples.

Furthermore according to the results of Table 8; 10 of the 15 items have saturations equal or greater than .70 in its intended dimension (items 8, 9, 12, 13, 15, 20, 23, 25, 26 and 27) in the first subsample and 9 in the second subsample (items 8, 9, 12, 13, 15, 20, 25, 26 and 27). Also observed in both subsamples, low to moderate intercorrelations between factors evidencing an adequate discriminant validity between them.

Invariance of the factor structure between subsamples

The fit indexes obtained (Table 9) allow to accept the equivalence of the basic measuring models between the two subsamples. Although the value of Chi-squared exceeds to that required to accept the hypothesis of invariance, the CFI=.962, RMSEA=.039 y AIC=681.583 indexes contradict this conclusion allowing us to accept the base model invariance (unrestricted model).

Adding to the base model restrictions on factorial loads the metric invariance was characterized. The values shown in Table 9 allow to accept this level of invariance. The goodness of fit index (GFI .956) and root mean square error of approximation (RMSEA .038) continue to provide convergent information in this direction. Also, the Akaike Information Criterion (AIC 676.968) and Bentler comparative fit index (CFI .961) do not suffer large variations over the previous model. Using the criteria for the evaluation of the nested models proposed by ^{Cheung and Rensvold (2002)}, who suggest that if the calculation of the difference of the CFI of both nested models diminish in .01 or less, the restricted model is taken for granted therefore the compliance of the factorial invariance; the difference of the CFIs obtained allows to accept the metrical invariance model. We can conclude up to this point that factorial charges are equivalent in the two subsamples.

Having demonstrated the metric invariance between the subsamples, we evaluate the equivalence between intercepts (strong factorial invariance). The Indices (Table 9) show a good adjustment of this model, evaluated independent as well as analyzed toward nesting with the metric invariance model. The difference between the two comparative indices of Bentler is less than .002; and the general adjustment index is .953 and the root mean square error of approximation is .038. Accepted then the strong invariance, the two evaluated models are equivalent toward the factorial coefficients and the intercepts.

The factors obtained in the confirmatory factor analysis, mostly all reached values above o equal to .70 of internal consistency in both samples; demonstrating adequate internal consistency for these type of subscales, particularly if it is considered the small number of items (Table 10).