Perfectionism is measured at one time point before any measures of the CAR take place. The details of these metrics are not important at this stage, but take note they both provide an index of stress. The CAR is expressed in two different metrics: AUCi and AUCg. To assess whether athletes are experiencing a change in CAR before a competition, the CAR is measured on a baseline day and the day of a competition (i.e., at multiple time points). One might expect that an athlete higher in perfectionism would get more stressed before a competition. In other words, the study is trying to see if levels of perfectionism in athletes can predict how stressed they get before a competition (of course, it is a little more complicated than that). The study is investigating whether athletes experience a change in their cortisol awakening response (CAR) the morning of a competition (the CAR is essentially a measure of stress), and whether perfectionism (a multidimensional personality trait) can predict these changes. Therefore, we must use an alternative solution: multilevel models. This is because we have a nested data structure. In this case, the assumption would be violated, as student scores are not independent of their class. If we were to model the prediction of student test scores, as was done above, using ordinary least squares (OLS) regression we would run into a problem: OLS regression requires independence of observations.
![spss 16 student edition spss 16 student edition](https://demo.fdocuments.in/img/378x509/reader022/reader/2020052122/5e4e30f1400f9719831861a0/r-1.jpg)
In this scenario, the effect of the higher-level class variable will be minimal or non-significant (more on this later). Indeed, there will be variability in students scores within classes, and it may be that different students in different classes still achieve similar scores. That is not to say that the class is the only predictor of student grades, rather, it must be modeled into the data.
![spss 16 student edition spss 16 student edition](https://img.informer.com/p5/spss-statistics-viewer-v19.0.png)
![spss 16 student edition spss 16 student edition](https://image.slidesharecdn.com/spssstudentoutlinecourse-150905165144-lva1-app6891/95/spss-student-outline-course-1-638.jpg)
The explanation for this is intuitive: the pupils in class 1 will be exposed to different teachers and different environments, etc., in comparison to the students in class 2, and so on. So extending the student-class example above, if the test scores of students 1-9 were to be predicted, it would be reasonable to assume that the scores of students 1-3 will be similar, as will the scores of students 4-6, as will the scores of students 7-9, as nested (grouped) by the higher-level class variable. Nonetheless, the most common nested structure is a two level structure, (i.e., students with classes), which is the type of nesting we will be exploring later.Įssentially, a nested data structure is one where the variables at one level (e.g., student) cannot be considered independent of the variables at another level (e.g. class). To extent of this nesting structure is only limited by the nature of the data collected.