GMM_seropositivity Files

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\f0\fs24 \cf0 The file seropositivity.R contains 3 functions:\
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The function Gaussian_mixture_EM(Data, N) simply calls the package mclust and estimates parameters for the best fitting Gaussian Mixture Model (GMM) using expectation maximization.\
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Example 1:\
# Randomly generate GMM data\
Data = c(rnorm(100,3,1),rnorm(10,6,2))\
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# Call the function for N=2 Gaussian components\
EM = Gaussian_mixture_EM(Data, 2)\
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# Output includes:\
EM$Data\
EM$McLust\
EM$Summary\
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The function Gaussian_mixture_MLE(EM_fit) takes the output of Gaussian_mixture_EM(Data, N) as its input and computes a maximum likelihood estimation for the best fitting parameters. \
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NOTE: because this is a \'93brute force\'94 technique the process may take a very long time. Parameters that change are printed out until the MLE ends.\
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Example 2:\
# Using the EM output from Example 1 as the input\
MLE = Gaussian_mixture_MLE(EM)\
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# Output includes:\
MLE$Data\
MLE$Initial_params\
MLE$MLE_params\
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The function bootstrap_ks_GMM(GMM, trials) takes the output of Gaussian_mixture_MLE(EM_fit) as its input and implements a parametric bootstrapping procedure to compute the KS statistics for each component of the GMM for each trial as well as a p-value for each component.\
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Example 3:\
# Using the MLE output from Example 2 as the input with 1000 trials\
BTS = bootstrap_ks_GMM(MLE, 1000)\
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# Output includes:\
BTS$KS_stat_seronegative\
BTS$KS_stat_seropositive\
BTS$KS_seroN_pvalue\
BTS$KS_seroP_pvalue}