I am studying teacher-student relationships using a survey. This survey consists of parallel versions for teachers and students. Thus, in a classroom of 20 students, each student will complete the survey once about his/her teacher and the teacher will complete the survey 20 times (once for each student). I have clustered the data by "Teacher ID" to account for this nesting.
I would like to conduct a test of configural invariance, so I set up a file for the teacher data and one for the student data and used the method described by Byrne (2012). However, when I did this, I received an error stating "CLUSTER option cannot be used with multiple data files."
How can I conduct this test of invariance given that I need to account for the nesting in my data?
I don't see your data as being appropriate for a multiple group analysis. Multiple group analysis requires the groups to be independent and the students and teachers are not independent. I would suggest a multilevel model for these data where the cluster variable is teacher. Your data set would have a set of student items for each student and a set of teacher items for each student. The teacher items would be the average of the teacher ratings for each student. As a first step, you might want to do a TWOLEVEL EFA to examine the factor structure at both the student and teacher levels. It is often the case that the same number of factors are not found at each level. Please note that you need from 30-50 teachers for this analysis to work well.
Thank you for your reply! I am a bit unclear about your statement: "The teacher items would be the average of the teacher ratings for each student." I have raw data (a response on each item) from each student about one teacher and then responses to the same parallel items from that teacher about that student. I have organized the data such that each student line has the student's responses to the items and the corresponding teacher's responses to parallel items. I did not average any scores. Is that what you were suggesting?
Given this setup, I have clustered the data by "Teacher ID" to account for nesting of students within teachers and created models using Type = Complex and Parameterization = Theta.
I did try to create two-level models, as you suggested, but the only data that are actually at the cluster level are teachers' demographics. The teachers' responses to the items about their students are different for each student - so, although these are completed by the teacher, they are measured at the individual student level. In addition, I am only attempting to model outcomes at the student-level (i.e., students' homework completion, grade in class, feelings of self-efficacy, etc.). I do not have any outcomes at the teacher-level.
Given my data and the outcomes I'm trying to predict, does my approach seem appropriate?
I think you do have an outcome at the teacher-level. Each student in a class rates the teacher. You can average these student ratings of the teacher to create a classroom-level variable. The teacher ratings of each student is a student-level variable.