The tool validated in this study is the Preschool Social Behavior Scale-Teacher (PSBS-T). It evaluates physical and relational aggression in preschoolers corresponding up to six years (Crick et al., 1997). This scale was validated and adapted from the tool designed to assess aggression and prosocial behavior in school-age children (Children´s Social Behavior Scale-Teacher Form; CSBS-T; Crick, 1996 ).

PSBS-T has previously been used in other studies to compare different contexts of aggression (Ostrov & Keating, 2014), evaluate prevention programs (Kim et al., 2011), determine the continuity of physical and relational aggression (Ostrov, 2010) and validate scales in preschool population (Fehr & Russ, 2014) as well as assess the effects of violent media and video games on aggressive behaviors. However, there is currently no version of this scale that has been adapted for the Chilean context. Therefore, the purpose of this study is to adapt and provisionally validate the Preschool Social Behavior Scale-Teacher (PSBS-T) scale to evaluate physical and relational aggression in preschools in kindergartens and local schools in an urban commune in Chile.

The final sample was 538 children from 3 to 6 years old, as described in Table 1. The sample was selected from one urban community in Santiago of Chile using a convenience sampling design from public elementary schools and kindergartens in the community. The inclusion criteria were to belong to that urban community, from the public system, and be willing to participate in the study. Therefore, we collected data from five Elementary schools and four Kindergartens using 12 teachers as student informants. Teachers were selected considering more than 3 months in the job, and students more than two months attending to classes.

Table 1

			Age
	3 years	4 years	5 years	6 years	Total
Boys	62	75	112	35	284
Girls	44	86	93	31	254
Total	106	161	205	66	538

PSBS has a version for teachers and another for parents. In this study, the version for teachers was used exclusively. This version uses a Likert scale with 5 types of answers: 1: “never or almost never”, up to 5: “ always”. The scale contains 25 items grouped into 6 subscales: (1) Relational aggression, with 8 items (4, 8, 11, 13, 15, 19, 21, and 22), including “The child tells a classmate that he/she will not play with him/her unless he/she does what he/she wants”; “The child tries to make his/her classmates dislike another partner by saying bad things about him/her behind his/her back”; (2) Physical aggression, with 8 items (2, 5, 7, 12, 14, 17, 20, and 23), including: “Child kicks or punches peers”; “Child pushes peers”; (3) Pro-social behavior, with 4 items (1, 3, 6, and 10), including “Child is good at sharing and respecting turns”; and (4) Depressive affection, with 3 items (9, 16, and 18), e. g. “Child doesn’t have much fun”. The last two subscales are composed of a single item each: (5) Acceptance of the child by peers of the same gender (“The child is very well liked by peers of the same gender”, item 24); (6) Acceptance of the child by peers of the opposite gender (“The child is very well liked by peers of the opposite gender”, item 25).

The first step in the validation procedure was the linguistic adaptation of the instrument through the back-translation approach (English-spanish-english) of the language by bilingual professionals (Hambleton et al., 2004). Based on this Spanish version of the instrument we developed a content validation of the instrument based on the expertise of three judges with an academic background on the topic in Chile. Two of them are academics from Chilean universities and the other is a practitioner from the Minister of Education. Experts’ judge suggestions were focused on a few grammatical gender distinctions, keeping all the rest of the items from the original instruments. Subsequently, a pilot study was carried out with a sample of two classes from a single educational establishment, with 30 students in each class. In general, no problems were reported with the comprehension of the items, except for one (item 15: “This child tells a peer they won’t be invited to their Birthday party unless he/she what the child wants”). Based on the pilot application, we edited item 15 related to birthday party invitations that were hard to understand for the Chilean sample.

Moreover, informed consent was obtained from each student. Finally, the application of the scale took place between August and September 2014 by one professional running the study.

To evaluate the factor structure of the PSBS-T, a Confirmatory Factor Analysis (CFA) was carried out comparing the original structure of four factors (defined by items 1 to 23). However, two original factors were defined by only one item; therefore, only four factors from the original scale were compared.

Given that the scale items are answered with ordinal-type response options, and the assumption of multivariate normal distribution is not fulfilled, the polychoric correlation matrix was obtained and the parameters of the models were estimated using the Weighted Least Squares Mean and Variance adjusted method (WLSMV). The previous procedure allows obtaining a robust modification of the quality statistics of the fit of the analyzed model, as well as adequately estimating the parameters and their standard errors. Since the study participants belonged to different courses, the standard error produced by the grouping (intraclass correlation) was controlled by means of an adjustment obtained by including the students’ course as the Cluster variable. The quality of fit of the analyzed models was carried out based on the following statistics: a) χ2, b) CFI, c) TLI d) RMSEA and its 90% confidence interval. As indicative criteria of a good fit for a model, a non-significant χ2 statistic, values of 0.95 or higher for CFI and TLI, and a value less than 0.08 for RMSEA have been proposed (Hu & Bentler, 1999). These analyzes were carried out using the Mplus 8.4 software.

Once the model that best fit the data was identified, the invariance of the scale measurement between men and women was analyzed. For this, a Multi-Group Confirmatory Factor Analysis (MGCFA) was performed and it required the comparison of a sequence of three models. Model 1: Configural invariance. This model specified the same factor structure for each group, but the estimation of thresholds and factor loadings were freely estimated in both groups. Model 2: Metric invariance. In this model, all factor loadings were constrained to be equal across groups, while thresholds were freely estimated excepting those that required constraining to be equal across groups to allow identification of the model. Model 3: Scalar invariance. All factor loadings and thresholds were constrained to be equal across the two groups. To assess the measurement invariance hypothesis, the sequence adjustment level of the previously described models was compared. A statistically significant reduction in the quality of fit between two models indicates the existence of differences in some parameters between the compared groups. Given that each model in the sequence was nested in the previous model, two comparisons were made, Configural vs Metric, and Metric vs Scalar. To assess the statistical significance of the differences in fit quality, the Difftest option of the Mplus 8.4 software was used. A non-significant result in these comparisons supported the measurement invariance hypothesis.

The fit quality results for the four-factor model were c2(224) = 496.158, p < 0.001, CFI = 0.963, TLI = 0.958, RMSEA = 0.048 (90% CI: 0.042-0.054). For the factor loadings, absolute values in the range 0.57 to 0.96 were observed, all statistically significant (p <0.001). Taken together, these results provide evidence regarding the adequacy of the four-factor model. The reliability Omega coefficients were: F1: 0.88; F2: 0.93; F3: 0.84; and F4: 0.63. The estimated parameters for this model are presented in Figure 1.

Figure 1 Figure 1 Four Factor PSBS-T Scale Model Note. Factor 1: Relational aggression; Factor 2: Over/Physical aggression; Factor 3: Prosocial behavior; Factor 4: Depressed affect. *: p < 0.05; ***: p < 0.001.

Once the factor structure for the PSBS-T scale was established, an analysis of the invariance of the measurement according to gender was performed. For this, the adjustments of a sequence of three models were compared, each one more restrictive than the previous one in terms of the invariance of its parameters. The results of these analyzes are presented in Table 2.

Table 2

	(gl) p-value	a (gl) p-value	RMSEA (90% CI)	CFI	TLI
Configural	808.021 (448)p < 0.001	¾	0.055 (0.049, 0.061)	0.966	0.962
Metric	827.462 (467)p < 0.001	22.974 (19)p = 0.24	0.054 (0.048, 0.060)	0.966	0.963
Scalar	861.978 (531)p < 0.001	67.024 (64)p = 0.37	0.049 (0.043, 0.054)	0.969	0.970
Note: A comparison of the fit quality of the model sequence was performed using the Difftest option in Mplus.

As seen in Table 2, the comparison of the fit of the Configural and Metric models ( =22.974, p = 0.24) provides evidence in support of the hypothesis of equality of factor loadings for men and women. Thus, these results support the hypothesis of sex. Similarly, the results of the comparison in the adjustment of the Metric and Scalar models ( = 67.024, p =0.37) provide evidence for the hypothesis of equality of the factor loadings and thresholds between men and women. Thus, these results support the hypothesis of scalar invariance across sex. Taken together, these results provide evidence for the measurement invariance hypothesis between men and women for the PSBS-T scale.

Once the existence of measurement invariance between men and women (particularly scalar invariance) was established, the differences in the means of the four factors for these groups were estimated. The results indicated that men exhibited lower levels in Factor 3 ( = -1.248, p = 0.03). No statistically significant differences were observed in the remaining three factors.