The Cronbach's alpha is the most widely used method for estimating internal consistency reliability. This procedure has proved very resistant to the passage of time, even if its limitations are well documented and although there are better options as omega coefficient or the different versions of glb, with obvious advantages especially for applied research in which the ítems differ in quality or have skewed distributions. In this paper, using Monte Carlo simulation, the performance of these reliability coefficients under a one-dimensional model is evaluated in terms of skewness and no tau-equivalence. The results show that omega coefficient is always better choice than alpha and in the presence of skew items is preferable to use omega glb coefficients even in small samples.

In the context of multidimensional structures, with the presence of a common factor and multiple specific or group factors, estimates of reliability require specific estimators. The use of classical procedures such as the alpha coefficient or omega total that ignore structural complexity are not appropriate, since they can lead to strongly biased estimates. Through a simulation study, the bias of six estimators of reliability in multidimensional measures was evaluated and compared. The study is complemented by an empirical illustration that exemplifies the procedure. Results showed that the estimators with the lowest bias in the estimation of the total reliability parameter are omega total, the two versions of greatest lower bound (GLB) and the alpha coefficient, which in turn are also those that produce the highest overestimation of the reliability of the general factor. Nevertheless, the most appropriate estimators, in that they produce less biased estimates of the reliability parameter of the general factor, are omega limit and omega hierarchical.

School climate is related to a wide variety of positive results at the school level; however, its relationship with the construct of values has received little attention, despite being a key variable in the development of personality. This study aimed to examine the direct and indirect relationships between school climate, attitudes towards authority, and values. The participants in this study were 2683 students (51.2% men and 48.8% women) from 32 schools aged between 12 and 20 years (M = 15.78 years, SD = 1.35). Two models of structural equations were estimated, and the model that best fit the data confirmed that school climate was indirectly related to values through attitudes towards authority. The reciprocal and interactive relationships between school climate, attitudes towards authority, and values are also discussed.

School climate is a highly relevant construct in the educational field; however, most research adopts cross-sectional designs, which limits the understanding of its stability and development over time. Consequently, this study aimed to assess the degree of the longitudinal invariance of the SCASIM-St15 in a sample of adolescent students throughout their secondary education trajectory. A longitudinal panel design was used, with one-year intervals, covering the entire secondary education cycle and following the same cohort of 679 Chilean students across four measurements: wave 1 = 1st year of secondary school with a mean age of 14.53 Sd = 0.625; wave 2 = 2nd year with a mean age of 15.60 [Sd = 0.629]; wave 3 = 3rd year with a mean age of 16.55 [Sd = 0.602]; and wave 4 = 4th year with a mean age of 17.49 [Sd = 0.587]. The results from factorial invariance modeling across the four time points indicate that the SCASIM-St15 shows an overall good fit, with satisfactory goodness-of-fit indices, suggesting that the factorial structure of the SCASIM-St15 remains stable over time.

School climate is a relevant construct for understanding social relations at school. The SCASIM-St has been widely defined as a multidimensional construct; however, new factor structures have not been explored through evidence that allows for interpreting school climate scores from an approach that respects the multidimensionality of the scale and, at the same time, allows for identifying the degree of essential unidimensionality in the data. Consequently, the objective was to analyze the psychometric properties of the SCASIM-St from a bifactor model approach, evaluating the influence of a general school climate factor versus five specific factors. The study involved 1860 students of both sexes (42% males and 58% females), with an average age of 16.63 years (SD = 0.664), from 17 secondary schools in Chile. The results obtained by a confirmatory factor analysis provided evidence that the best model was the bifactor model for the 38 items, with one general factor and five specific factors. The Explained Common Variance (ECV) values and reliability levels by hierarchical omega accounted for a strong general school climate factor with high levels of reliability. Evidence of external criterion validity, assessed through the attitude toward authority scale (AIA-A), showed a theoretically expected and significant relationship between the factors of both instruments. This study confirmed the psychometric robustness of the SCASIM-St scale by means of a bifactor model, allowing for a new, essentially unidimensional interpretation of the scale scores and providing an instrument to measure school climate in Chile.

This study aims to evaluate the psychometric properties of the Authoritarian Attitude Scale in a sample of high school students from Chile. A total of 775 students (46.5% men; 53.5% women), with an average age of 15.99 years (Sd = 1.32), participated through non-probabilistic convenience sampling in 11 schools. Confirmatory factor analysis supported a three-factor structure with correlated factors and adequate fit indices. Criterion validity revealed positive and significant correlations with the violent behaviour dimension of the antisocial and delinquent behaviour scale. The factorial invariance analysis confirmed configural, weak, strong, and strict equivalence by gender, age and ethnicity, demonstrating model stability. The adoption of the Authoritarian Attitude Scale among Chilean adolescents provides a valid, culturally relevant tool for assessing authoritarian tendencies and understanding psychosocial dynamics in the educational context. The findings offer initial evidence of the scale’s reliability and validity.