Data was collected from a sample of participants recruited through social media and e-mail snowballing. Previous studies have shown that these sampling methods are effective and cost-efficient (for systematic reviews see Thornton et al., 2016; Topolovec-Vranic & Natarajan, 2016). We recruited a total pool of 2,698 respondents (67.6% of the respondents were women). To balance the sample by gender, a random sample from the total pool of respondents that maintained a similar ratio of male and female participants was used.

The final sample was composed of 1,800 participants (92.7% with Spanish nationality), aged from 18 to 75 years old (M_age = 34.24, SD_age = 14.41) of whom 52.8% were women. We divided the sample into two subsamples of 900 participants with similar ratios of gender, age, nationality, and educational level categories. The socio-demographic information of the sample is displayed in Table 1.

We also recruited a second sample of 50 male IPVAW offenders who had been court-mandated to attend an intervention program. The mean age of the sample was 39.84, and their ages ranged from 21 to 69 years old. Most of the offenders had completed compulsory secondary education (86%).

Victim-Blaming Attitudes in cases of IPVAW (VB-IPVAW). A pool of 60 items referring to victim-blaming attitudes was selected from a review of European surveys on violence against women (Gracia & Lila, 2015). These items were translated into English from their original language by European experts in the field of IPVAW who provided the survey data for the review. A panel of six IPVAW experts was asked to assess the relevance of each item in the pool (Lynn, 1986; Polit & Beck, 2006). The experts rated the relevance of the items on a 5-point Likert-type scale (i.e., “Is this item relevant to measure victim-blaming attitudes in cases of IPVAW?”; 1 = strongly disagree, 5 = strongly agree). We selected those items with an average rating of 4 (i.e., the agree category) or above to construct a 13-item measure. The items were translated into Spanish by the authors of the review. Respondents were asked to indicate their level of agreement with the item statements on a 4-point Likert-type scale (1 = strongly disagree, 4 = strongly agree). The complete VB-IPVAW is shown in Appendix 1.

Acceptability of IPVAW (A-IPVAW; Martín-Fernández et al., 2018). The A-IPVAW scale is composed of 20 items in which respondents rate the acceptability of a set of men’s behaviors towards their female partners (e.g., “It is acceptable for a man to hit his partner if she has been unfaithful”). Responses were gathered on a 3-point Likert-type scale (0 = not acceptable, 1 = somewhat acceptable, 2 = acceptable). This instrument was cross-validated in the general Spanish population and showed an adequate internal structure, as well as validity evidence based on its relationship with other variables, such as perceived severity of IPVAW or ambivalent sexism (Martín-Fernández et al., 2018). The A-IPVAW showed a good internal consistency in the general sample (Cronbach’s α = .89).

Perceived Severity of IPVAW (PS-IPVAW; Gracia, García, & Lila, 2009). The PS-IPVAW scale posits eight IPVAW scenarios (e.g., “A couple is having a quarrel; he insults her and threatens to beat her up”). Respondents were asked to rate the severity of each scenario (ranging from 1 = not at all severe, to 10 = extremely severe). This scale presents adequate psychometric properties and has been validated in the general Spanish population and also with police officers and IPVAW offenders (Gracia et al., 2011, 2014). The scale has been related not only to attitudes toward IPVAW, such as victim-blaming attitudes and acceptability of IPVAW (Gracia & Tomás, 2014; Martín-Fernández et al., 2018), but also to sexism, personal responsibility, and empathy (Lila, Gracia, & García, 2013; Vargas, Lila, & Catalá-Miñana, 2015). This instrument showed a good internal consistency in the general sample of this study (Cronbach’s α = .89).

Ambivalent Sexism Inventory (ASI; Glick & Fiske, 1996). We used the Spanish version of the ASI (Expósito, Moya, & Glick, 1998). This instrument includes two subscales, hostile and benevolent sexism, each composed of 11 items. Hostile sexism is conceptualized as attitudes of discrimination and prejudice against women based on the assumption of women’s inferiority (e.g., “Women are too easily offended”). Benevolent sexism reflects men’s views of women as week and needing protection (e.g., “Women should be cherished and protected by men”). The ASI has been adapted and validated in more than twenty countries (Glick et al., 2000; Glick, Sakall, Urgurlu, Ferreira, & Aguilar de Souza, 2002) and has also shown to be strongly related to IPVAW responsibility attribution, with attitudes towards intervention in IPVAW cases among police officers, and with acceptability of IPVAW (Gracia, et al., 2014; Lila et al., 2013; Martín-Fernández et al., 2018). The internal consistency of both subscales was good in the general sample (Cronbach’s α = .88 and .89 for hostile and benevolent sexism, respectively).

The online survey included the VB-IPVAW scale, the PS-IPVAW scale, and the ASI. The survey remained open for a recruitment period of four weeks in November and December 2016. A message providing information about the study and calling for participation was posted on various social media groups. Informed consent information was provided and was implicit in the agreement to participate in the on-line survey. Participation was anonymous.

The following analyses were conducted to evaluate the psychometric properties of the VB-IPVAW. Descriptive statistics of the items, corrected item-test correlations, and internal consistency were computed for the whole sample. The latent structure of the scale was assessed following a cross-validation approach by splitting the general sample in two subsamples, each of 900 participants. An exploratory factor analysis (EFA) was carried out to identify a latent variable model for the scale items in the first subsample. This model was then replicated in the second subsample using confirmatory factor analysis (CFA).

Before conducting the EFA, we tested the suitability of the dataset with the Bartlett’s sphericity test and the Kaiser-Meyer-Olkin (KMO) statistic. Then a parallel analysis based on minimum rank factor analysis using polychoric correlations was computed (Timmerman & Lorenzo-Seva, 2011). This method has performed well in testing the number of factors to extract for a categorical EFA (Garrido, Abad, & Ponsoda, 2013, 2016). The parallel analysis uses Monte Carlo simulation to generate randomized datasets similar to the empirical dataset. Ranked factor analysis is used to compute the percentage of variance explained by a series of different factorial models (i.e., one-factor model, two-factor model, three-factor model, etc.) in the random datasets; the mean and the 95^th percentile are obtained. When the percentage of variance explained by a given factor model in the empirical data is below the percentage expected for that model in the simulated datasets, the model is adding more factors than needed. We therefore looked for the minimum number of factors needed to explain more variance in the empirical data than in the random datasets.

We conducted an EFA using weighted least squares with adjusted means and variances (WLSMV) as the estimation method, since it is more robust for ordinal and categorical data (Asparouhov & Muthén, 2010). Model fit was assessed using a combination of fit indices: the comparative fit index (CFI), the Tucker Lewis index (TLI), the root mean square error of approximation (RMSEA), and the standardized root mean square residual (SRMR). CFI and TLI values greater than .95 are indicative of good model fit (Hu & Bentler, 1999), whereas SRMR values lower than .08, and RMSEA values lower than .06 are considered good fitting models (MacCallum, Browne, & Sugawara, 1996).

We replicated the results yielded by the EFA by conducting a CFA. The WLSMV was again used to estimate the CFA model, and model fit was evaluated using the same fit indices and their cut-off values (CFI & TLI ≥ .95, RMSEA ≤ .06).

After evaluating the latent structure of the scale, we fitted an item response theory (IRT) model for the whole sample. IRT provides improved factor score estimates and does not assume constant measurement precision. These two aspects of IRT allow researchers to identify which levels of the latent trait are better assessed by an instrument (Chernyshenko, Stark, Chan, Drasgow, & Williams, 2001). Given the ordinal nature of the data, the graded response model was selected (Samejima, 1969). The model was estimated using the MHRM algorithm (Cai, 2010) and model fit was assessed with the same combination of fit indices and their aforementioned cut-off values (CFI & TLI ≥ .95, RMSEA ≤ .06). Maydeu’s M₂ statistic for ordinal variables was used to compute these indices instead of other chi-square approximations for ordinal variables, as this statistic was developed specifically to assess the overall fit for IRT models (Maydeu-Olivares & Garcia-Forero, 2010; Maydeu-Olivares & Joe, 2006). The test information function was obtained and the IRT scores (i.e., the person parameters of the model) were used for the validity analyses.

To establish whether the VB-IPVAW is invariant across gender, we conducted a differential item functioning (DIF) analysis for polytomous data using the logistic regression method (Choi, Gibbons, & Crane, 2011; French & Miller 1996). DIF occurs when the probability of endorsement of an item category is not the same for male and female respondents with an equivalent IRT score, meaning that men and women respond differently to the item. If DIF is detected for an item, then the item parameters should be recalibrated for each subgroup in order to obtain a comparable IRT score.

We assessed the VB-IPVAW scale validity for the whole sample. To this end, we first correlated the IRT scores (i.e., estimates of victim-blaming attitudes) with the A-IPVAW scores, the PS-IPVAW scores, and the hostile and benevolent sexism scores from the ASI. We then compared the VB-IPVAW scores between age groups and gender for the general sample, and between men from the general sample and from the male offenders sample.

Finally, we used the automated test assembly (Diao & van der Linden, 2011) procedure to create a shortened version of the scale with the most informative items measuring higher levels of the latent trait. Through this procedure, a minimum number of items that meet criteria established by the researchers are selected for inclusion in the shortened version. We selected the items that most accurately measure higher levels of victim-blaming attitudes.

Descriptive statistics, classical internal consistency, and IRT analyses were computed with the statistical package R (R Core Team. 2017). Specifically, we used the psych (Revelle, 2016), the mirt (Chalmers, 2012), the lordif (Choi et al., 2011), and the lpSolveApi libraries (Konis, 2016). The parallel analysis was conducted with the factor package (Lorenzo-Seva & Ferrando, 2006), whereas the EFA and CFA analyses were carried out with Mplus 7.1 (Muthén & Muthén, 2010).

The mean, standard deviation, range, skew and kurtosis statistics, and item-total corrected correlations are displayed in Table 2. All items present a mean centered in the lower category (i.e., strongly disagree), with standard deviations around 0.50, positively skewed and with high values of kurtosis. This implies that most of the respondents disagree with the statements. Regarding item-total corrected correlations, all items were strongly related with the scale raw scores, except the last item, which was removed from the scale for this reason. The scale showed good internal consistency (Cronbach’s α = .89).

We carried out an EFA with the first subsample. Bartlett’s sphericity test was significant (p < .001) and the KMO index was acceptable (KMO = .939), indicating that the matrix was suitable to perform a factor analysis. The parallel analysis based on minimum rank factor analysis showed that a one-factor solution accounted for 74.2% of the variance, above the expected 20.8% for the simulated datasets. However, a two-factor solution accounted for only 6.9% of the variance, below the expected 14.5% for the simulated datasets. A one-factor solution was therefore considered for the EFA. We then extracted one factor using the polychoric correlation matrix and the WLSMV estimation method. The model converged normally and the model fitted the data well (CFI = .99, TLI = .98, RMSEA = .051, SRMS = .038).

We conducted a CFA with the second subsample. To this end we specified a one-factor model and estimated it using the WLSMV method. As shown in Figure 1, all standardized loadings were greater than .70, with standard estimation errors around .02. The comparative fit indices of the model were good (CFI = .99, TLI = .99), with well-fitted residuals (RMSEA = .051), replicating the EFA results in a different subsample and yielding an overall good fit to the data. We kept the one-factor solution as the latent structure of the VB-IPVAW.

Once the dimensionality of the VB-IPVAW had been determined, we used the full sample to fit the IRT graded response model (Samejima, 1969).

Item parameters are displayed in Table 3. The threshold parameters (b₁, b₂, and b₃) are in the same metric as the IRT scores (i.e., estimates of victim-blaming attitudes), indicating the point on the latent trait continuum where the probability of endorsement between two adjacent categories is .50 for any respondent with an IRT score equal to the threshold parameter value. Respondents with IRT scores lower than the b₁ parameter would be more likely to endorse the lowest category (i.e., strongly disagree), whereas those respondents with IRT scores higher than the b₃ parameter would tend to endorse the upper category (i.e., strongly agree). Respondents with IRT scores between the b₁ and b₂ parameters would be more likely to endorse the second category (i.e., somewhat disagree), whereas respondents with IRT scores between the b₂ and b₃ parameters would more likely endorse the third category (i.e., somewhat agree). The b₁ threshold parameters were in general moderate (i.e., around 1), whereas the b₂ and b₃ parameters presented high (i.e., above 2) and very high values (i.e., above 3), indicating that the instrument is sampling moderate to high levels of victim-blaming attitudes.

The discrimination parameters (a), in turn, provide information about the accuracy of each item. In particular, the greater this parameter, the less likely a given respondent will endorse a category above or below their IRT score. The discrimination parameters of the VB-IPVAW were high, with values above 2 for almost all the items, with the exception of item 8, which presented a moderate a value.

To assess differential item functioning (DIF), we conducted a series of logistic regression models (e.g., Choi et al., 2011). These models tested for any effect of belonging to each group (i.e., men or women) on the latent trait continuum (i.e., estimates of victim-blaming attitudes), and whether this effect is constant (uniform) or varies across the continuum (non-uniform). These models were compared using a χ² test. Nagelkerke’s pseudo-R² was also computed to assess the size of the DIF effect. This pseudo-R² indicates the improvement from the base model (i.e., non-DIF model) to the fitted model (i.e., uniform or non-uniform DIF model). We found uniform DIF for items 1, 2, and 8 (p < .001, R²_Nagelkerke = .010, .007, and .018, respectively), and non-uniform DIF for item 3 (p = .002, R²_Nagelkerke = .010), all with small Nagelkerke’s pseudo-R² values. This implies that adding the DIF effect to the model improved the fit of the model by less than 2%, which could be considered a negligible effect size for this statistic (Choi et al., 2011; Cohen, 1988).

Figure 2 shows the test information function and the standard error of estimation (SE) for men and women when the flagged items are taken into account. The VB-IPVAW scale was especially informative for moderate, high, and very high levels of the latent trait continuum (i.e., estimates of victim-blaming attitudes), especially among men. In the same line, the SE showed the precision of the scale for the latent trait levels; the lower the SE result, the higher the accuracy of the scale for a given latent trait level. In particular, SE values below 0.3 are equivalent to a Cronbach’s α of .91 or higher, and SE values between 0.5 and 0.3 are equivalent to an α around .75 and .90 for their respective IRT score. The test information function was very similar for men and women.

The overall fit of the model was tested using the ordinal version of the M₂ statistic. This statistic can be used to compute an approximation of the most common fit indices from the factor analysis (CFI, TLI, and RMSEA). The model showed a good fit to the data when the DIF was taken into account, M₂(92) = 373.50, p < .001, CFI = .98, TLI = .98, RMSEA = .04.

We used the IRT scores (i.e., estimates of victim-blaming attitudes) for validity analyses, since the items of the scale are not tau-equivalent (i.e., equally discriminative). IRT scores were on logistic metric, with an expected mean value of 0 and a standard deviation of 1 (Chalmers, 2012).

The correlations between the VB-IPVAW and the variables measuring related constructs were in the expected direction (see Table 4). Estimates of victim-blaming attitudes were positively related to the A-IPVAW scores, and to both subscales of the ASI, particularly the hostile sexism subscale, and negatively related to PS-IPVAW scores. Therefore, those participants scoring higher on the VB-IPVAW tended to score higher on acceptability of IPVAW, hostile and benevolent sexism, and were more likely to perceive the cases described in the PS-IPVAW as less severe.

We then compared the VB-IPVAW scores by gender and age. We found significant differences between men (M = 0.23, SD = 0.94) and women (M = -0.09, SD = 0.83), t(1711.9) = 7.63, p < .001, d = 0.36, with a moderate effect size. We also found significant differences between male respondents from the general sample and those from the offenders sample (M = 0.70, SD = 1.35), t(52.48) = -3.31, p = .002, d = 0.44, with a moderate effect size. There were significant differences between age groups, F(2) = 5.48, p = .004, η² = .006; however, the effect of age on the VB-IPVAW scores could be considered negligible, since the size effect was below the low cut-off value of .01 for the partial eta-squared (Miles & Shevlin, 2001).

To build the short version of the scale we computed an automatic test assembly algorithm. Two criteria were used: finding which items were more informative to assess moderate and high levels of the IRT scores for men and women (i.e., ≥ 0), and using the minimum number of items to ensure that those levels were measured accurately (i.e., SE ≤ 0.5). The items 1, 2, 6, 9, and 11 were selected (see Appendix 1).

The internal consistency of the resulting short version was good (Cronbach’s α = .77), and the correlation between the full and the short version was strong (r = .95). The correlations between the short version and the validity measures were in the same direction as the full VB-IPVAW (r = .46 with acceptability of IPVAW, r = -.36 with perceived severity of IPVAW, r = .36 with hostile sexism, and r = .33 with benevolent sexism).