Education for all in action: Measuring teachers’ competences for inclusive education

Plan of analysis. To validate the factor structure underlying the DISCO-instrument, we combined exploratory (EFA) and confirmatory factor analyses (CFA) in a stepwise approach. In order to maximize power for the analyses and following the full information maximum like- lihood (FIML) on missing data theory [53], all available data was used for the factor analyses. Hence, respondents were not a priori list-wise deleted from the dataset for having missings on some survey-items. In the first step, using the data from pre-service teachers, exploratory fac- tor analysis using SPSS 25 was chosen to identify a (set of) latent constructs underlying the measured items without strong theoretical assumptions on how many factors existed [54]. Because teachers’ competences in handling diversity were expected to correlate [54,55], Princi- pal Component Analysis (PCA) with oblique rotation technique (direct oblimin) was used. The assumptions to perform EFA were checked: data distributions were checked to ensure that variables were roughly normally distributed [54] and the correlation-matrix was inspected to identify scale items that correlated below |.30| with all other variables or above |.80|. The suitability of the data for the exploratory analysis were checked by considering the Kaiser– Meyer–Olkin test (KMO) which should exceed the recommended value of .60, and the Bart- lett’s test of sphericity which should be significant. Furthermore, the anti-image correlation matrix was checked for negative correlations, low communalities or high partial correlations

[54]. To determine the number of factors, both the scree plots’ point of inflexion and Kaiser’s criterion (eigenvalue >1) were checked [54]. Items were eliminated if they had inadequate (partial) correlations or high cross-loadings (>|.40|), if their variance was not well explained as suggested by low communalities, or if the loading on their designated factor was weak (<|.35|). When a choice for being dropped or retained had to be made between items, the the- oretical interpretability and alignment with EfA tenets spurred the decision besides psycho- metric considerations. Factors with a minimum of three items and Cronbach’s alpha >.70 were retained for testing in the second step [54]. For the second step, the survey was adapted according to the insights from the first step and then presented to a new sample consisting of in-service teachers. The initial factor solution from step 1 was checked with data from these in-service teachers using confirmatory factor analyses in Mplus. This technique allows us to check to what extent a hypothesized model fits the data. An MLR estimation was used, and goodness of fit indicators were checked: CFI values larger than 0.95, X2/DF smaller than two, RMSEA values smaller than 0.05 and SRMR values smaller than 0.05 are considered good [56]. Where necessary, the model was optimized based on suggestions of the modification indices, standardized factor loadings, R-square estimates of the items, and theoretical interpretability of the factor. To compare models, we checked which

model had a lower AIC value. Note that X2 statistics are reported to increase transparency for the X2/DF calculation, but that the X2 statistics themselves are not discussed because the test is sensitive to large sample sizes [57]. Finally, based on these results, the scale scores for in-service teachers were obtained by computing a mean for each respondent with a maximum of 25% missing values on the scale- items. The final set of items for each scale can be seen in Tables 2 and 3. Repeated measures analysis of variance with a bonferroni post-hoc test was conducted to examine possible signifi- cant differences on scale scores for efficacy and beliefs. Results Step 1: EFA with pre-service teachers Professional beliefs about diverse students. Based on the data distributions, correlation matrix and anti-image correlation matrix, ten items were deleted (see Table 1). PCA on the remaining 27 items revealed satisfactory KMO-value, anti-image correlations and Bartletts’ PLOS ONE Measuring teachers’ competences for inclusive education PLOS ONE | https://doi.org/10.1371/journal.pone.0291033 November 8, 2023 7 / 22