---
title: "Read me"
output: pdf_document
---

This is a list of the files provided to show the proposal in the paper: 
"*Variable selection for hidden Markov models with continuous variables and missing data*" written by

- F. Pennoni (University of Milano-Bicocca, IT)
- F. Bartolucci (University of Perugia, IT)
- S. Pandolfi (University of Perugia, IT)

The code was written/evaluated in R with the following software versions:
R version 4.2.2 (2022-10-31)
Platform: a2.7 GHz Intel Core i7 quad-core
Running under: macOS Monterey 12.6.6

This folder contains the following data and files that can be used to provide an example of data and results proposed in the paper.

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**Implemented functions**

The following functions have been implemented to estimate the hidden Markov model with missing data and perform model selection:

- lmbasic.cont.MISS.R 	--->	estimate the basic HM model for continuous outcomes with intermittent missingness  using the extended EM algorithm 


- lmestContMISS.R --->	Estimate the HM model for continuous outcomes with intermittent missingness 

- regress_miss.R ---> Fit  a multiple linear regression model under the MAR assumption on the responses
 
- item_selection.R --> Perform item selection with the steps described in the article (tol by default is 10^-10)
 	
- complk_cont_miss.R ---> Compute complete log-likelihood of the basic HM model for continuous outcomes (internal use)

- forward_regress_miss.R ---> Stepwise regression for Y with covariates X where ind is the index of the response variable on which it makes model selection

- drawHMBasicCont.R --->   Draw samples of size n from a basic latent Markov model for continuous data

- compute_BIC.R ---> Compute Bayesian information criterion (internal use)

- count_eq.R ---> Required internal function

- functions.R ---> Required internal function

- bootstrapMISS.R ---> Perform non-parametric bootstrap procedure in order to compute standard errors of model parameters 

- lmestDecoding.R ---> Perform local decoding

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**Application** 


- dt1.Rdata ---> Data for example_trial.R

- example_trial.R ---> Example file that loads the data "dt.RData" and applies the proposed procedure for model and variables selection; also apply the non-parametric bootstrap once the model is estimated. It produces the output file example_trial.Rdata

- ResultsApplication.R ---> Print the results of the estimated model and some descriptive plots of the data

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**SimulationStudy**

- SimulatedScenario1.R ---> Example file that reproduces one of the simulated scenarios presented in the paper with a proportion of missing values of 0.05 

- TakeResSim.R ---> Read the results of the simulations from file SimulatedScenario1.R