lixiongyang / maternspatialmodel-simulations

R Scripts for the simulation examples included in original research manuscript by Saqlain, Rönnegård, Alam, and Skarin

MaternSpatialModel-Simulations

R Scripts for the simulation examples included in original research manuscript by Saqlain, Rönnegård, Alam, and Skarin

Scripts to perform the simulations in Scenarios 1-5 in the paper are given here.

R packages used:

• Matrix
• lgcp (for circulant() function)
• spaMM

Scripts with functions:

• Functions_CreateZ.R: Source file where the functions to create Z with 3 nearest corners are
• Functions_CreateZ_4corners.R: Source file where the functions to create Z with 4 nearest corners are
• Functions_CreateQ.R: Source file where the functions to create Q are
• Functions_Estimation.R: Source file where the functions to estimate the parameters are
• Functions_Estimation_Binomial.R Source file where the functions to estimate the parameters are for binomial response
• Functions_LogL.R: Source file where the log likelihood function for normal response is
• Functions_LogL_Binomial.R: Source file where the log likelihood function for binomial response is
• Check_Q_and_Matern_functions_V4.R: Source file where the functions to create regular lattice is
• HL_Correction.R: HL Correction file

Scripts to run simulations:

• Simulations_Scenarios_1-3.R: Scenarios 1-3
• Simulations_Scenarios_4.R: Scenario 4
• Simulations_Scenarios_4_Binom.R: Scenario 4 for binomial response
• Simulations_Scenarios_5.R: Scenario 5

Directions:

• Copy the source function scripts in the working directory and set working directory in the simulations scripts.

Simulations 1-3:

• Set number_of_iterations = desired number of iterations (200 to follow the paper).
• For scenario 1 set: xshift = 0, yshift = 0, removepoints_number = 0
• For scenario 2 set: xshift = 0.2, yshift = 0, removepoints_number = 20
• For scenario 3 set: xshift = 0.5, yshift = 0.5, removepoints_number = 20
• Lattice parameters for the observation locations may be changed in line 35 to 39
• Matern parameters range and alpha may be changed in lines 82 and 83
• Means and standard deviation of the parameters beta, tau, and phi from all the simulations will be the output
• For Scenario 3 using the Z construction with 4 parameters, uncomment line 20 and comment out line 19.

Simulations 4 (normal response):

• Set number_of_iterations = desired number of iterations (200 to follow the paper).
• Means and standard deviation of the parameters beta, tau, and phi from all the simulations will be the output

Simulations 4 (binomial response):

• Set number_of_iterations = desired number of iterations (200 to follow the paper).
• Lattice spacing may be changed in line 43
• Matern parameters range and alpha may be changed in lines 54 and 55
• Means and standard deviation of the parameters beta and tau from all the simulations will be the output for both HL method and spaMM method

Simulations 5:

• Set number_of_iterations = desired number of iterations (200 to follow the paper).
• For 5(a) keep line 40, N.obs = 1000 fixed. Run different simulations by changing reps in line 29 (number of observations in each location)
• For 5(b) change line 40, N.obs = 500, 1000, 1500, and 2000 in the different simulations. Keep reps = 3 fixed in line 29
• Means and standard deviation of the parameters beta, tau, phi and time taken from all the simulations will be the output for both HL method and spaMM method

Contact:

• Murshid Saqlain ([email protected]) for any questions related to the code.

References:

• Lindgren, F., Rue, H. and Lindström, J., 2011. An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(4), pp.423-498.