Maartje Boer

CHAPTER 2 36 Reliability and Item Performance Given the dichotomous nature of the nine items, reliability of the scores was calculated using the ordinal alpha based on the tetrachoric correlationmatrix (Gadermann et al., 2012), which indicates the level of internal consistency. Reliability was further analyzed using Item Response Theory (IRT). IRT models describe the relation between observed item scores and their underlying unobserved latent trait ( ϴ ) by means of difficulty (i.e., threshold) and discrimination (i.e., loading) parameters (Baker, 2001). The difficulty parameter of an item indicates at which value of ϴ respondents have a 50% probability of endorsing that item. The discrimination parameter of an item denotes the item’s ability to discriminate between respondents with high versus low values on the continuumof ϴ , with higher values suggesting better discrimination (Baker, 2001). The difficulty and discrimination parameters were used to generate information curves, that graphically illustrate the amount of information that was provided by single items and the total scale across the continuum of ϴ . The higher the information, the higher the reliability (Toland, 2014). Measurement Invariance Multigroup CFAs were conducted to examine whether the factor structure of the SMD-scale was measurement invariant across gender, educational level, age, and ethnic background. First, configural invariance wasmodelled by fitting a multigroup CFA where all item loadings and thresholds were freely estimated acrossgroups (e.g., acrossboys andgirls). Second, scalar invariance wasmodelled by fitting amultigroup CFA where item loadings as well as item thresholds were constrained to be equal across groups. The models were estimated according to specific guidelines for invariance testing of dichotomous variables, which do not allow for a separate test of metric invariance (i.e., multigroup CFA with equal factor loadings and free thresholds) due to model non-identification (L. K. Muthén & Muthén, 2017c). Measurement invariance was established when adding the equality constraints did not substantially deteriorate model fit in terms of CFI, RMSEA, andSRMR (F. F. Chen, 2007). Thesefit indices are commonly used in measurement invariance analyses on large samples as an alternative to χ ²-difference tests (F. F. Chen, 2007).