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A-quick-tour-of-MRHLP

Introduction

MRHLP: Flexible and user-friendly probabilistic joint segmentation of multivariate time series (or multivariate structured longitudinal data) with smooth and/or abrupt regime changes by a mixture model-based multiple regression approach with a hidden logistic process, fitted by the EM algorithm.

It was written in R Markdown, using the knitr package for production.

See help(package="samurais") for further details and references provided by citation("samurais").

Load simulated data

data("multivtoydataset")

Set up MRHLP model parameters

K <- 5 # Number of regimes (mixture components)
p <- 3 # Dimension of beta (order of the polynomial regressors)
q <- 1 # Dimension of w (order of the logistic regression: to be set to 1 for segmentation)
variance_type <- "heteroskedastic" # "heteroskedastic" or "homoskedastic" model

Set up EM parameters

n_tries <- 1
max_iter <- 1500
threshold <- 1e-6
verbose <- TRUE
verbose_IRLS <- FALSE

Estimation

mrhlp <- emMRHLP(multivtoydataset$x, multivtoydataset[,c("y1", "y2", "y3")], 
                 K, p, q, variance_type, n_tries, max_iter, threshold, verbose,
                 verbose_IRLS)
## EM: Iteration : 1 || log-likelihood : -4975.54177550763
## EM: Iteration : 2 || log-likelihood : -3108.34368262058
## EM: Iteration : 3 || log-likelihood : -3083.17524290617
## EM: Iteration : 4 || log-likelihood : -3052.50226046505
## EM: Iteration : 5 || log-likelihood : -3020.60866761548
## EM: Iteration : 6 || log-likelihood : -2967.37662637476
## EM: Iteration : 7 || log-likelihood : -2948.61300516787
## EM: Iteration : 8 || log-likelihood : -2945.45995948196
## EM: Iteration : 9 || log-likelihood : -2937.99296980136
## EM: Iteration : 10 || log-likelihood : -2924.28973590932
## EM: Iteration : 11 || log-likelihood : -2901.25080505023
## EM: Iteration : 12 || log-likelihood : -2859.88249265728
## EM: Iteration : 13 || log-likelihood : -2858.05147227319
## EM: Iteration : 14 || log-likelihood : -2856.38015373797
## EM: Iteration : 15 || log-likelihood : -2854.68196733762
## EM: Iteration : 16 || log-likelihood : -2852.69581368828
## EM: Iteration : 17 || log-likelihood : -2849.93140687413
## EM: Iteration : 18 || log-likelihood : -2846.34467342533
## EM: Iteration : 19 || log-likelihood : -2843.82658697638
## EM: Iteration : 20 || log-likelihood : -2842.75921489778
## EM: Iteration : 21 || log-likelihood : -2842.2361309076
## EM: Iteration : 22 || log-likelihood : -2841.91343876731
## EM: Iteration : 23 || log-likelihood : -2841.66202744546
## EM: Iteration : 24 || log-likelihood : -2841.41784741157
## EM: Iteration : 25 || log-likelihood : -2841.14668922972
## EM: Iteration : 26 || log-likelihood : -2840.82033081985
## EM: Iteration : 27 || log-likelihood : -2840.39141033072
## EM: Iteration : 28 || log-likelihood : -2839.74532802897
## EM: Iteration : 29 || log-likelihood : -2838.62532237046
## EM: Iteration : 30 || log-likelihood : -2836.64319641069
## EM: Iteration : 31 || log-likelihood : -2833.87378876047
## EM: Iteration : 32 || log-likelihood : -2831.75584262499
## EM: Iteration : 33 || log-likelihood : -2831.16293539695
## EM: Iteration : 34 || log-likelihood : -2831.0646784204
## EM: Iteration : 35 || log-likelihood : -2831.06467491195

Summary

mrhlp$summary()
## ----------------------
## Fitted MRHLP model
## ----------------------
## 
## MRHLP model with K = 5 regimes
## 
##  log-likelihood nu       AIC       BIC       ICL
##       -2831.065 98 -2929.065 -3149.921 -3149.146
## 
## Clustering table:
##   1   2   3   4   5 
## 100 120 200 100 150 
## 
## 
## ------------------
## Regime 1 (K = 1):
## 
## Regression coefficients:
## 
##       Beta(d = 1)   Beta(d = 2) Beta(d = 3)
## 1       0.4466558     0.8104534    -2.36719
## X^1   -25.5100013   -20.5995360    32.75195
## X^2   413.8717640   498.0085618  -541.38904
## X^3 -1811.4612012 -2477.5546420  2523.64723
## 
## Covariance matrix:
##                                   
##  1.17712613  0.1114059  0.07303969
##  0.11140591  0.8394152 -0.02442220
##  0.07303969 -0.0244222  0.85240361
## ------------------
## Regime 2 (K = 2):
## 
## Regression coefficients:
## 
##     Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1      21.30187   -4.108239    1.838238
## X^1  -199.86512  112.953325  112.257782
## X^2   905.60445 -449.623857 -493.914613
## X^3 -1316.42937  581.197948  694.872075
## 
## Covariance matrix:
##                                     
##   1.0409982 -0.180821350 0.137568024
##  -0.1808214  1.042169409 0.009699162
##   0.1375680  0.009699162 0.754147599
## ------------------
## Regime 3 (K = 3):
## 
## Regression coefficients:
## 
##     Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1     4.4721830    9.349642    6.349724
## X^1   0.7467282  -33.315977   17.837763
## X^2 -11.9302818   96.730621  -51.086769
## X^3  16.1571109  -85.951201   42.760070
## 
## Covariance matrix:
##                                     
##   1.02026230 -0.04094457 -0.02544812
##  -0.04094457  1.15656511  0.02852275
##  -0.02544812  0.02852275  0.99750511
## ------------------
## Regime 4 (K = 4):
## 
## Regression coefficients:
## 
##     Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1      1267.288   -840.5119   -10.37768
## X^1   -5458.816   3613.7273    19.40201
## X^2    7813.122  -5184.1100    14.37103
## X^3   -3718.619   2475.7168   -29.55020
## 
## Covariance matrix:
##                                       
##   0.822157811  0.006792726 -0.03667011
##   0.006792726  1.093351047 -0.07477892
##  -0.036670114 -0.074778924  0.85425249
## ------------------
## Regime 5 (K = 5):
## 
## Regression coefficients:
## 
##     Beta(d = 1) Beta(d = 2) Beta(d = 3)
## 1      194.7894    12.88268    483.8383
## X^1   -658.4685   -45.73544  -1634.9482
## X^2    753.1086    61.92925   1858.1529
## X^3   -286.1078   -27.37495   -702.9064
## 
## Covariance matrix:
##                                 
##  1.1282728 0.25684915 0.02034990
##  0.2568491 1.21055927 0.04414336
##  0.0203499 0.04414336 0.77644297

Plots

Fitted regressors

mrhlp$plot(what = "regressors")

Estimated signal

mrhlp$plot(what = "estimatedsignal")

Log-likelihood

mrhlp$plot(what = "loglikelihood")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.