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A-quick-tour-of-RHLP

Introduction

RHLP: Flexible and user-friendly probabilistic segmentation of time series (or structured longitudinal data) with smooth and/or abrupt regime changes by a mixture model-based 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 data

data("univtoydataset")

Set up RHLP 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

rhlp <- emRHLP(univtoydataset$x, univtoydataset$y, K, p, q, 
               variance_type, n_tries, max_iter, threshold, verbose, verbose_IRLS)
## EM: Iteration : 1 || log-likelihood : -2119.27308534609
## EM: Iteration : 2 || log-likelihood : -1149.01040321999
## EM: Iteration : 3 || log-likelihood : -1118.20384281234
## EM: Iteration : 4 || log-likelihood : -1096.88260636121
## EM: Iteration : 5 || log-likelihood : -1067.55719357295
## EM: Iteration : 6 || log-likelihood : -1037.26620122646
## EM: Iteration : 7 || log-likelihood : -1022.71743069484
## EM: Iteration : 8 || log-likelihood : -1006.11825447077
## EM: Iteration : 9 || log-likelihood : -1001.18491883952
## EM: Iteration : 10 || log-likelihood : -1000.91250763556
## EM: Iteration : 11 || log-likelihood : -1000.62280600209
## EM: Iteration : 12 || log-likelihood : -1000.3030988811
## EM: Iteration : 13 || log-likelihood : -999.932334880131
## EM: Iteration : 14 || log-likelihood : -999.484219706691
## EM: Iteration : 15 || log-likelihood : -998.928118038989
## EM: Iteration : 16 || log-likelihood : -998.234244664472
## EM: Iteration : 17 || log-likelihood : -997.359536276056
## EM: Iteration : 18 || log-likelihood : -996.152654857298
## EM: Iteration : 19 || log-likelihood : -994.697863447307
## EM: Iteration : 20 || log-likelihood : -993.186583974542
## EM: Iteration : 21 || log-likelihood : -991.81352379631
## EM: Iteration : 22 || log-likelihood : -990.611295217008
## EM: Iteration : 23 || log-likelihood : -989.539226273251
## EM: Iteration : 24 || log-likelihood : -988.55311887915
## EM: Iteration : 25 || log-likelihood : -987.539963690533
## EM: Iteration : 26 || log-likelihood : -986.073920116541
## EM: Iteration : 27 || log-likelihood : -983.263549878169
## EM: Iteration : 28 || log-likelihood : -979.340492188909
## EM: Iteration : 29 || log-likelihood : -977.468559852711
## EM: Iteration : 30 || log-likelihood : -976.653534236095
## EM: Iteration : 31 || log-likelihood : -976.5893387433
## EM: Iteration : 32 || log-likelihood : -976.589338067237

Summary

rhlp$summary()
## ---------------------
## Fitted RHLP model
## ---------------------
## 
## RHLP model with K = 5 components:
## 
##  log-likelihood nu       AIC       BIC       ICL
##       -976.5893 33 -1009.589 -1083.959 -1083.176
## 
## Clustering table (Number of observations in each regimes):
## 
##   1   2   3   4   5 
## 100 120 200 100 150 
## 
## Regression coefficients:
## 
##       Beta(K = 1) Beta(K = 2) Beta(K = 3) Beta(K = 4) Beta(K = 5)
## 1    6.031875e-02   -5.434903   -2.770416    120.7699    4.027542
## X^1 -7.424718e+00  158.705091   43.879453   -474.5888   13.194261
## X^2  2.931652e+02 -650.592347  -94.194780    597.7948  -33.760603
## X^3 -1.823560e+03  865.329795   67.197059   -244.2386   20.402153
## 
## Variances:
## 
##  Sigma2(K = 1) Sigma2(K = 2) Sigma2(K = 3) Sigma2(K = 4) Sigma2(K = 5)
##       1.220624      1.110243      1.079394     0.9779734      1.028332

Plots

Fitted regressors

rhlp$plot(what = "regressors")

Estimated signal

rhlp$plot(what = "estimatedsignal")

Log-likelihood

rhlp$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.