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1 Imaging Data

Review the 3D/4D MRI imaging data discussion in Chapter 3. Extract the time courses of several timeseries at different 3D spatial locations, some near-by, some farther apart (distant voxels). Then, apply time-series analyses, report findings, determine if near-by or farther-apart voxels may be more correlated.

Example of extracting timeseries from 4D fMRI data 

<code>
  # See examples here: https://cran.r-project.org/web/packages/oro.nifti/vignettes/nifti.pdf
  
  library(oro.nifti)
  fMRIURL <- "http://socr.umich.edu/HTML5/BrainViewer/data/fMRI_FilteredData_4D.nii.gz"
  fMRIFile <- file.path(tempdir(), "fMRI_FilteredData_4D.nii.gz")
  download.file(fMRIURL, dest=fMRIFile, quiet=TRUE)
  (fMRIVolume <- readNIfTI(fMRIFile, reorient=FALSE))
  # dimensions: 64 x 64 x 21 x 180 ; 4mm x 4mm x 6mm x 3 sec 
  
  fMRIVolDims <- dim(fMRIVolume); fMRIVolDims
  time_dim <- fMRIVolDims[4]; time_dim
  
  hist(fMRIVolume)
  
  # To examine the time course of a specific 3D voxel (say the one at x=30, y=30, z=15):
  plot(fMRIVolume[30, 30, 10,], type='l', main="Time Series of 3D Voxel \n (x=30, y=30, z=15)", col="blue")
  
  x1 <- c(1:180)
  y1 <- loess(fMRIVolume[30, 30, 10,]~ x1, family = "gaussian")
  lines(x1, smooth(fMRIVolume[30, 30, 10,]), col = "red", lwd = 2)
  lines(ksmooth(x1, fMRIVolume[30, 30, 10,], kernel = "normal", bandwidth = 5), col = "green", lwd = 3)
</code>

2 Tabuar data

Use Google Web-Search Trends and Stock Market Data to:

  • Plot time series for variable Job
  • Apply TTR to smooth the original graph by month
  • Determine the differencing parameter
  • Decide the auto-regressive (AR) and moving average (MA) parameters
  • Build an ARIMA model and Forecast the timecouse over the next 365 days (for 2012).

3 Latent variables model

Use Hand written English Letters data to:

  • Explore the data and evaluate the correlations between covariates
  • Justify to apply latent variable model
  • Apply proper data convert and scale data
  • Fit SEM on the data by adding proper latent variable
  • Summarize and interpret the outputs
  • Use the model you find above to fit GEE and GLMM model setting latent variable as response and compare AIC.

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