A study collected data annually on 200 boys and 200 girls aged between 13 (wave 1) to 16 (wave 4), measuring their BMI and their level of physical exercise, assessed using data from an actigraphy watch that was worn during waking hours for one week (activity of a certain type and of a certain level was classified as ‘exercise’ and the total number of hours classified as exercise for the week of evaluation was totalled per individual). Using data recorded from this study, recorded in the file BMI_Actigrapgy.csv, answer the following research questions using the methods outlined below:
How are BMI and weekly exercise related amongst children aged 13 to 16 years?
What is a hypothetical causal relationship between these longitudinal measures?
What is the evidence in the data you are given that supports this causal hypothesis?
To address this research question, undertake initial descriptive analyses and explore both separate and joint latent growth curve models for each longitudinal measure:
• Provide appropriate summary descriptives of your data. • Produce a separate chart for each longitudinal measure (BMI & weekly Activity) showing the differences by Sex. • Explore a latent growth curve model for each measure separately, modelling explicitly the role of Sex and accounting for autocorrelation as an AR(1) function. • Draw an SEM or DAG, hypothesising on the causal relationship amongst all latent variables – you may draw multiple versions, indicating speculation, but ultimately you must settle on one as your ‘preferred’ causal model. • Jointly model the two longitudinal measures, exploring plausible models as described by your DAG(s); settle on one preferred model that tallies with your preferred DAG. • Summarise the results of your preferred joint model, attributing causal interpretation to model estimates, discussing any caveats. • Discuss the strengths and weaknesses of the investigation you have undertaken, making recommendations for future studies.
Write up your findings in a semi-formal structured report: marks are awarded primarily for scientific content, not polish of presentation, but clarity of communication is important to assess your grasp of the methods used and to assess your ability to undertake a complex analysis and interpret the findings appropriately. Your report should not exceed 1500 words. You should assume a statistically technical audience, but describe carefully all the analyses and interpretations of your findings with reference to technical details, where appropriate. The only appendix permitted is your annotated STATA or R code, which must be included. The word limit applies to the main text only, as tables, figures, bibliography, and the annotated software code is not counted.
Marks out of 50 will be awarded as per the following criteria: (a) clarity and understanding in the development and application of your models; (b) clear, well-reasoned interpretation of all your models, including a discussion around caveats, strengths, weaknesses, and possible improvements for future research; (c) overall clarity of presentation and clear language, including appropriate use of (Harvard style) citations and the appendix outlining your analytical code.