The "Orthodont" data frame, available from the nlme package in R, has 108 rows and 4 columns

of the change in an orthdontic measurement over time for several young subjects. Investigators

at the University of North Carolina Dental School followed the growth of 27 children (16 males,

11 females) from age 8 until age 14. Every two years they measured the distance between

the pituitary and the pterygomaxillary fissure, two points that are easily identified on x-ray

exposures of the side of the head.

This data frame contains the following columns:

distance a numeric vector of distances from the pituitary to the pterygomaxillary fissure (mm).

These distances are measured on x-ray images of the skull.

age a numeric vector of ages of the subject (yr).

Subject an ordered factor indicating the subject on which the measurement was made. The levels

are labelled "M01" to "M16" for the males and "F01" to "F13" for the females. The

ordering is by increasing average distance within sex.

Sex a factor with levels "Male" and "Female"

You should

1. Appropriate plots of the data.

2. Regress distance on age and Sex and their interaction.

3. Is there any evidence that you should model heterogeneity in these data?

4. Is there any evidence that observations taken on the same subject are correlated with

each other and that this correlation should be modelled?

5. After taking possible heterogeneity/correlation into account, check whether the mean

structure (i.e. the fixed effects structure) of the model can be simplified.

6. In your final model, how does the fitted lines fitted to the data on males differ to the one

fitted to the data on females?

Finishing Off:

When you've finished, close down R by typing q(). Choose 'Save' when prompted as to whether

you want to retain your workspace. Remember to log off from your computer before leaving.

You are strongly advised to use R Markdown and submit a pdf. Include all R commands and output. The main foucs of the exercise is to model variance and correlation structures. You should fit several variance and correlation structures, and select the best, simplest model. Justify the model selection process.