lmestSearch {LMest}

Search for the global maximum of the log-likelihood

Description

Function that searches for the global maximum of the log-likelihood of different models and selects the optimal number of states.

Usage

lmestSearch(responsesFormula = NULL, latentFormula = NULL,
            data, index, k,
            version = c("categorical", "continuous"),
            weights = NULL, nrep = 2, tol1 = 10^-5,
            tol2 = 10^-10, out_se = FALSE, miss.imp = FALSE, seed = NULL, ...)

Arguments

responsesFormula

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

latentFormula

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

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

k

a vector of integer values for the number of latent states

weights

an optional vector of weights for the available responses

version

type of responses for the LM model: "categorical" and "continuous"

nrep

number of repetitions of each random initialization

tol1

tolerance level for checking convergence of the algorithm in the random initializations

tol2

tolerance level for checking convergence of the algorithm in the last deterministic initialization

out_se

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

miss.imp

Only for continuous responses: how to deal with missing values (TRUE for imputation through the imp.mix function, FALSE for missing at random assumption)

seed

an integer value with the random number generator

...

additional arguments to be passed to functions lmest or lmestCont

Details

The function combines deterministic and random initializations strategy to reach the global maximum of the model log-likelihood. It uses one deterministic initialization (start=0) and a number of random initializations (start=1) proportional to the number of latent states. The tolerance level is set equal to 10^-5. Starting from the best solution obtained in this way, a final run is performed (start=2) with a default tolerance level equal to 10^-10.

Missing responses are allowed according to the model to be estimated.

Value

Returns an object of class 'LMsearch' with the following components:

out.single

Output of every LM model estimated for each number of latent states given in input

Aic

Values the Akaike Information Criterion for each number of latent states given in input

Bic

Values of the Bayesian Information Criterion for each number of latent states given in input

lkv

Values of log-likelihood for each number of latent states given in input.

Author(s)

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

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

### Example with data on drug use in wide format

data("data_drug")
long <- data_drug[,-6]

# add labels referred to the identifier

long <- data.frame(id = 1:nrow(long),long)

# reshape data from the wide to the long format

long <- reshape(long,direction = "long",
                idvar = "id",
                varying = list(2:ncol(long)))

out <- lmestSearch(data = long,
                   index = c("id","time"),
                   version = "categorical",
                   k = 1:3,
                   weights = data_drug[,6],
                   modBasic = 1,
                   seed = 123)

out
summary(out$out.single[[3]])

## Not run: 

### Example with data on self rated health

# LM model with covariates in the measurement model

data("data_SRHS_long")
SRHS <- data_SRHS_long[1:1000,]

# Categories rescaled to vary from 1 (“poor”) to 5 (“excellent”)

SRHS$srhs <- 5 - SRHS$srhs

out1 <- lmestSearch(data = SRHS,
                    index = c("id","t"),
              version = "categorical",
             responsesFormula = srhs ~ -1 +
             I(gender - 1) +
             I( 0 + (race == 2) + (race == 3)) +
             I(0 + (education == 4)) +
             I(0 + (education == 5)) + I(age - 50) +
             I((age-50)^2/100),
                   k = 1:2,
                   out_se = TRUE,
                   seed = 123)
summary(out1)
summary(out1$out.single[[2]])
                   
## End(Not run)