est_lm_cov_latent: Estimate LM model with covariates in the latent model

In LMest: Generalized Latent Markov Models

Estimate LM model with covariates in the latent model

Description

Main function for estimating the LM model with covariates in the latent model.

The function is no longer maintained. Please look at lmest function.

Usage

est_lm_cov_latent(S, X1=NULL, X2=NULL, yv = rep(1,nrow(S)), k, start = 0, tol = 10^-8,
                  maxit = 1000, param = "multilogit", Psi, Be, Ga, fort = TRUE,
                  output = FALSE, out_se = FALSE, fixPsi = FALSE)

Arguments

S	array of available configurations (n x TT x r) with categories starting from 0 (use NA for missing responses)
X1	matrix of covariates affecting the initial probabilities (n x nc1)
X2	array of covariates affecting the transition probabilities (n x TT-1 x nc2)
yv	vector of frequencies of the available configurations
k	number of latent states
start	type of starting values (0 = deterministic, 1 = random, 2 = initial values in input)
tol	tolerance level for checking convergence of the algorithm
maxit	maximum number of iterations of the algorithm
param	type of parametrization for the transition probabilities ("multilogit" = standard multinomial logit for every row of the transition matrix, "difflogit" = multinomial logit based on the difference between two sets of parameters)
Psi	intial value of the array of the conditional response probabilities (mb x k x r)
Be	intial value of the parameters affecting the logit for the initial probabilities (if start=2)
Ga	intial value of the parametes affecting the logit for the transition probabilities (if start=2)
fort	to use fortran routine when possible (FALSE for not use fortran)
output	to return additional output (V,PI,Piv,Ul)
out_se	to compute the information matrix and standard errors
fixPsi	TRUE if Psi is given in input and is not updated anymore

Value

lk	maximum log-likelihood
Be	estimated array of the parameters affecting the logit for the initial probabilities
Ga	estimated array of the parameters affecting the logit for the transition probabilities
Piv	estimate of initial probability matrix
PI	estimate of transition probability matrices
Psi	estimate of conditional response probabilities
np	number of free parameters
aic	value of AIC for model selection
bic	value of BIC for model selection
lkv	log-likelihood trace at every step
V	array containing the posterior distribution of the latent states for each response configuration and time occasion
Ul	matrix containing the predicted sequence of latent states by the local decoding method
sePsi	standard errors for the conditional response matrix
seBe	standard errors for Be
seGa	standard errors for Ga
call	command used to call the function

Author(s)

Francesco Bartolucci, Silvia Pandolfi, University of Perugia, http://www.stat.unipg.it/bartolucci

References

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

Examples

## Not run: 
# Example based on self-rated health status (SRHS) data
# load SRHS data
data(data_SRHS_long)
dataSRHS = data_SRHS_long

TT <- 8
head(dataSRHS)
res <- long2matrices(dataSRHS$id, X = cbind(dataSRHS$gender-1,
dataSRHS$race == 2 | dataSRHS$race == 3, dataSRHS$education == 4,
dataSRHS$education == 5, dataSRHS$age-50, (dataSRHS$age-50)^2/100),
Y = dataSRHS$srhs)

# matrix of responses (with ordered categories from 0 to 4)
S <- 5-res$YY
n <- dim(S)[1]

# matrix of covariates (for the first and the following occasions)
# colums are: gender,race,educational level (2 columns),age,age^2)
X1 <- res$XX[,1,]
X2 <- res$XX[,2:TT,]

# estimate the model
est2f <- est_lm_cov_latent(S, X1, X2, k = 2, output = TRUE, out_se = TRUE)
summary(est2f)

# average transition probability matrix
PI <- round(apply(est2f$PI[,,,2:TT], c(1,2), mean), 4)

# Transition probability matrix for white females with high educational level
ind1 <- X1[,1] == 1 & X1[,2] == 0 & X1[,4] == 1)
PI1 <- round(apply(est2f$PI[,,ind1,2:TT], c(1,2), mean), 4)

# Transition probability matrix for non-white male, low educational level
ind2 <- (X1[,1] == 0 & X1[,2] == 1 & X1[,3] == 0 & X1[,4] == 0)
PI2 <- round(apply(est2f$PI[,,ind2,2:TT], c(1,2), mean), 4)

## End(Not run)

LMest documentation built on Aug. 27, 2023, 5:06 p.m.