I have measured students responses on a Likert scale, which measures their perceptions of their classroom teacher' characteristics. I have also gathered their writing samples in the fall and spring and want to predict how students' perceptions of the classroom teacher influence their their growth in writing. My hypothesis is that students' favorable perceptions of the teacher will predict greater growth in their writing over the school year. Should I use HLM, or do you have another suggestion? Thanks for your help.
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$\begingroup$ Do you have multiple writing samples for each student? How do you measure 'growth in writing' ? $\endgroup$– onestopCommented Jan 4, 2012 at 22:32
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1$\begingroup$ @onestop, presumably one or more people will grade the writing samples. Suzanne, the more detail you provide the more detailed the feedback can be. $\endgroup$– Michael BishopCommented Jan 4, 2012 at 23:50
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$\begingroup$ I think it would also be helpful to provide information about the number of classrooms that you have in your dataset. Assuming that you are interested in the clustering at the classroom level, if the number of available classrooms is small, it might be preferable to use a fixed effects approach. Additionally, if you are concerned about the clustering at the student level ( for instance you want to aggregate several writing samples into a single writing score ) then details about the instruments and number of persons would also be helpful. $\endgroup$– DavidCommented Jan 5, 2012 at 4:19
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2 Answers
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HLM, aka multi-level models, or mixed models, are a good idea here. The devil is in the details of how you setup such a model though. Consider the following questions:
Does each individual student's perception of their teacher affect their own growth in skills? Does the objective characteristics of their teacher affect students' growth in skills? Does the objective characteristics of their teacher affect students' perception of their teacher? Are student's perceptions of their teacher influenced by other students' perceptions? Does students' growth in skills affect their perception of their teacher's characteristics? How are students assigned to teachers?
answered Jan 4, 2012 at 23:48
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$\begingroup$ (+1) I agree - the direction(s) of causality is not at all clear. $\endgroup$– jbowmanCommented Jan 4, 2012 at 23:53
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Given the really complex causal relationships, as explained in Michael Bishop's answer, you might state your question non-causally and just compute a correlation between students' perception of the teacher and their change in writing scores. But even for this, it's crucial to have reliable and valid scores of the writing samples, which in itself is non-trivial.
answered Jan 6, 2012 at 5:33