This author has an interesting discussion of diagnostics in an exploratory model. But some of his comments are unclear to me. This discussion occurs in page 114 to 116 in the link below.
The author says
What does the vertical spread mean? The slope of the line, the difference between the high and low point of each line? I don't understand this.
Similarly on 115-116 the author says
I am not sure how he determines this. To me the difference is that at the top the slopes are downwards, but at the bottom they are largely upwards which suggest slope is the key. But I am not at all sure what the author is stressing here, it might also be a change in the vertical difference between the boy and girl side of the line.
http://courses.education.illinois.edu/EdPsy587/GLM_GLMM_LMM.pdf
The author says
The vertical spread between the lines indicates between classroom variation in terms of intercepts and is consistent with a random intercept model
Similarly on 115-116 the author says
The variability in the level of the classroom means differ between girls and boys; that is, the intercept variance may not be constant for gender. Most noticeable is the appearance of possibly two groups of boys—those with high segregation indices and those with lower values
http://courses.education.illinois.edu/EdPsy587/GLM_GLMM_LMM.pdf