I derived evidence for the validity of the internal structure of the TSE-ASDI Scale by examining the degree to which the items formed factors that conformed to structural expectations. Research questions one and two asked about the factor structure of the TSE-ASDI Scale and whether the factor structure differed for pre-service and in-service early childhood teachers. The main goal of a factor analysis is parsimony, summarizing
data in a simple way so that relationships and patterns can be understood. It is used to regroup variables into a limited set of factors based on shared variance (Costello & Osborne, 2005; Young & Pearce, 2013). There are two main factor analysis techniques: EFA and Confirmatory Factor Analysis (CFA). Researchers use EFA to uncover complex patterns within datasets and to test predictions, that is build theory; and use CFA to confirm hypotheses with respect to how items on a measure will function, as such test theory (Matsunaga, 2010). Given that the development of this measure and its theoretical basis are in the emergent stages, the use of EFA is most appropriate.
Exploratory factor analysis is used to estimate the unknown, latent structure of the observed data (Matsunaga, 2010). Of note, statistical scholars have commented on the ways that researchers have used the processes of exploratory factor analysis with
principal components analysis interchangeably despite the fact that these two procedures while similar are conceptually and mathematically distinct (Costello & Osborne, 2005; de Winer & Dodou, 2016; Matsunaga, 2010). In contrast to EFA, principal components analysis summarizes the information from a data set and reduces it into components. Principal axis factor analysis separates the shared variance from its unique variance and error variance to uncover the underlying factor structure however principal component analysis does not differentiate shared and unique variance (Costello & Osborne, 2005). I used principal axis factor analysis rather than principal component analysis since my aim was to identify the underlying structure of the latent variables while taking into account the shared and error variance.
For the purposes of this study, I conducted an EFA on the data collected during the pilot test to provide validity evidence regarding the internal structure of the TSE- ASDI Scale. I predicted, based on my literature review, that there were five dimensions or factors for the construct teacher self-efficacy for teaching students with ASD in inclusive early childhood classrooms. A multivariate statistical analysis such as the EFA was needed to test if the score variability for each item is attributable to just one
dimension or if it is also attributable to any other identified dimension (AERA, APA, NCME, 2014). I also used the EFA to make the methodological decision about how many items to retain or discard (Hayton, Allen & Scarpello, 2004).
To determine the suitability of the data for an EFA, I analyzed the Bartlett’s test of Sphericity and the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. Bartlett’s test of Sphericity was 2 (378) = 7091.57, p < .001, and the KMO statistic was .96, well above the recommended value of .6 and suggesting “marvelous” sampling adequacy (Kaiser & Rice, 1974).
In order to determine the number of factors to extract, I used Horn’s (1965) parallel analysis, a sophisticated factor extraction strategy that has greater merit than more traditional methods such as the eigenvalue greater than one rule or examination of scree plots (Thompson & Daniel, 1996). Horn’s parallel analysis begins with principal axis factoring performed on randomly generated data sets. The eigenvalues of the factors that emerge from the actual data are compared to mean eigenvalues from the random data. Factors with eigenvalues greater than those of the randomly generated data are considered viable and retained for analysis (i.e., these eigenvalues exceed what would be
expected by chance). In addition to Horn’s parallel analysis, I reviewed the more
traditional approaches to factor identification (i.e., scree plot and eigenvalues greater than 1) to fully explore the potential of the data collected.
After determining the number of factors to extract, I conducted a principal axis factor analysis with Promax rotation and examined the rotated factor matrix for all participants. Promax is an oblique rotation, which allows the factors to relate. I anticipated that the proposed factors were at least moderately correlated since they all comprised one construct, teacher self-efficacy for teaching students with ASD in inclusive early childhood classrooms. Therefore, using oblique rotation should “theoretically render a more accurate, and perhaps, a more reproducible solution” (Costello & Osborne, 2005, p.3).
To assign items to factors, I used the following decision rules: items with pattern coefficients greater then |.40| were retained; items with pattern coefficients greater than |.40| on two or more factors were assigned to factors based on their theoretical alignment with other items on the factor and the size of the coefficients.
I conducted separate parallel analyses and EFA’s on the in-service (n = 156) and pre-service (n =133) teacher responses, following the steps described above, to determine if there was a difference in the factor structure of the TSE-ASDI for these two sub-
groups. I examined the emergent factor structures for each group for qualitatively different structures.