LMest (version 3.1.2)

lmestMc: Estimate Markov Chain models

Description

Main function for estimating Markov Chain (MC) models for categorical responses with or without covariates.

Usage

lmestMc(responsesFormula = NULL,
        data, index, start = 0,
        modBasic = 0, weights = NULL,
        tol = 10^-8, maxit = 1000,
        out_se = FALSE, output = FALSE, fort = TRUE, seed = NULL)

Value

Returns an object of class 'MCbasic' for the basic model without covariates (see MCbasic-class), or an object of class 'MCcov' for the model with covariates (see MCcov-class).

Arguments

responsesFormula

a symbolic description of the model to fit. A detailed description is given in the ‘Details’ section

data

a data.frame in long format

index

a character vector with two elements, the first indicating the name of the unit identifier, and the second the time occasions

start

type of starting values (0 = deterministic, 1 = random, 2 = initial values in input)

modBasic

model on the transition probabilities (0 for time-heter., 1 for time-homog., from 2 to (TT-1) partial homog. of that order)

weights

an optional vector of weights for the available responses

tol

tolerance level for convergence

maxit

maximum number of iterations of the algorithm

out_se

to compute the information matrix and standard errors (FALSE is the default option)

output

to return additional output (PI,Piv) (MCcov-class)

fort

to use fortran routines when possible (By default is set to TRUE)

seed

An integer value with the random number generator state.

Author

Francesco Bartolucci, Silvia Pandolfi, Fulvia Pennoni, Alessio Farcomeni, Alessio Serafini

Details

The function lmestMc estimates the basic MC model and the MC model with covariates for categorical responses. The function requires data in long format and two additional column indicating the unit identifier and the time occasions.

responsesFormula is used to specify the basic MC models and the model with covariates:

• responsesFormula = y1 + y2 ~ NULL
  the MC model without covariates and two responses (y1 and y2) is specified;

• responsesFormula = NULL
  all the columns in the data except the "id" and "time" columns are used to estimate MC without covariates;

• responsesFormula = y1 ~ x1 + x2 | x3 + x4
  the MC model with one response (y1), two covariates affecting the initial probabilities (x1 and x2) and other two different covariates affecting the transition probabilities (x3 and x4) is specified;

• responsesFormula = y1 ~ x1 + x2
  the MC model with one response (y1) and two covariates (x1 and x2) affecting both the initial and transition probabilities is specified.

Missing responses are not allowed.

References

Bartolucci F., Pandolfi S., Pennoni F. (2017) LMest: An R Package for Latent Markov Models for Longitudinal Categorical Data, Journal of Statistical Software, 81(4), 1-38.

Bartolucci, F., Farcomeni, A. and Pennoni, F. (2013) Latent Markov Models for Longitudinal Data, Chapman and Hall/CRC press.

Examples

if (FALSE) {
# Basic Markov Chain  model

data("RLMSlong")

# Categories  rescaled from 1 “absolutely unsatisfied” to  5 “absolutely satisfied”

RLMSlong$value <- 5 - RLMSlong$value

out <- lmestMc(responsesFormula = value ~ NULL,
               index = c("id","time"),
               modBasic = 1,
               data = RLMSlong)

out
summary(out)



# Example of drug consumption data

data("data_drug")
long <- data_drug[,-6]
long <- data.frame(id = 1:nrow(long),long)
long <- reshape(long,direction = "long",
                idvar = "id",
                varying = list(2:ncol(long)))

out1 <- lmestMc(index = c("id","time"), data = long,
                weights = data_drug[,6], modBasic = 1, out_se = TRUE)

out1

### MC model with covariates
### Covariates: gender, race, educational level (2 columns), age and age^2

data("data_SRHS_long")
SRHS <- data_SRHS_long[1:2400,]

# Categories of the responses rescaled from 1 “poor” to 5 “excellent”

SRHS$srhs <- 5 - SRHS$srhs


out2 <- lmestMc(responsesFormula = srhs ~
                I( 0 + (race==2) + (race == 3)) +
                I(0 + (education == 4)) +
                I(0 + (education == 5)) +
                I(age - 50) +
                I((age-50)^2/100),
                index = c("id","t"),
                data = SRHS)
out2
summary(out2)

# Criminal data

data(data_criminal_sim)
data_criminal_sim = data.frame(data_criminal_sim)

out3 <- lmestMc(responsesFormula = y5~sex,
                index = c("id","time"),
                data = data_criminal_sim,
                output = TRUE)

out3

}