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hlme(fixed, mixture, random, subject, classmb, ng = 1,
idiag = FALSE, nwg = FALSE, cor=NULL, data, B,
convB=0.0001,convL=0.0001,convG=0.0001,prior,
maxiter=500, subset=NULL, na.action=1)~ and the covariates are separated by + on the right of the ~.
By default, an intercept is infixed, the covariates with class-specific reg+.
By default, an intercept is included. If no intercept, -1 should be the first term included.+.
No intercept should be included in this formula.ng=1 no mixture nor classmb should be specified. If ng>1, mixture is required.FALSE, a non structured matrix of variance-covariance is considered (by default).
If TRUE a diagonal matrix of variance-covariance is considered.FALSE the variance-covariance matrix is common over latent classes (by default).
If TRUE a class-specific proportional parameter multiplies the varifixed, mixture, random, classmb and subject.details section.
If no vector is specified, a preliminary analysis involving the estimation of a standard lineB and detailed in section detailsBest with exception for variance-covariance parameters of the random-effects for which V contains the variance-covariance estimates of the Cholesky transformed parameters displayed in choleskyB or in the vector of maximum likelihood estimates best are included in the following order:
(1) ng-1 parameters are required for intercepts in the latent class membership model, and if covariates are included in classmb, ng-1 paramaters should be entered for each one;
(2) for all covariates in fixed, one parameter is required if the covariate is not in mixture, ng paramaters are required if the covariate is also in mixture;
(3) the variance of each random-effect specified in random (including the intercept)
if idiag=TRUE and the inferior triangular variance-covariance matrix of all the random-effects if idiag=FALSE;
(4) only if nwg=TRUE, ng-1 parameters for class-specific proportional coefficients
for the variance covariance matrix of the random-effects;
(5) the variance of the residual error.
We understand that it can be difficult to enter the correct number of parameters in B at the first place. So we recommend to run the program without specifying the initial vector B even if this model does not converge. As the final vector best has exactly the same structure as B (even when the program stops without convergence), it will help defining a satisfying vector of initial values B for next runs. Some caution should be made when using the program:
(1) As the log-likelihood of a latent class model can have multiple maxima, a careful choice of the initial values is crucial for ensuring convergence toward the global maximum.
The program can be run without entering the vector of initial values (see point 2).
However, we recommend to systematically enter initial values in B and try different sets of initial values.
(2) The automatic choice of initial values we provide requires the estimation of a preliminary linear mixed model. The user should be aware that first, this preliminary analysis can take time for large datatsets and second,
that the generated initial values can be very not likely and even may converge slowly to a local maximum.
This is a reason why specification of initial values in B should be preferred.
(4) Convergence criteria are very strict as they are based on derivatives of the log-likelihood in addition to the parameter and log-likelihood stability. In some cases, the program may not converge and reach the maximum number of iterations fixed at 100. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the parameter space. If the parameters are on the boundaries of the parameter space, the identifiability of the model should be assessed. If not, the program should be run again with other initial values, with a higher maximum number of iterations or less strict convergence tolerances.
Muthen B and Shedden K (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 55, 463-9
Proust C and Jacqmin-Gadda H (2005). Estimation of linear mixed models with a mixture of distribution for the random-effects. Computer Methods Programs Biomedicine 78, 165-73
postprob, plot.postprob, summary, plot.predict##### Example of a latent class model estimated for a varying number
# of latent classes:
# The model includes a subject- (ID) and class-specific linear
# trend (intercept and Time in fixed, random and mixture components)
# and a common effect of X1 and its interaction with time over classes
# (in fixed).
# The random-effects are assumed independent (idiag=TRUE). The variance
# of the random intercept and slope are assumed to be equal
# over classes (nwg=F).
# The covariate X3 predicts the class membership (in classmb).
# !CAUTION: for illustration, only default initial values where used but
# other sets of initial values should be tried to ensure convergence
# towards the global maximum.
data(data_hlme)
### homogeneous linear mixed model (standard linear mixed model)
### with independent random-effects
m1<-hlme(Y~Time*X1,random=~Time,subject='ID',ng=1,idiag=TRUE,
data=data_hlme)
summary(m1)
### latent class linear mixed model with 2 classes
m2<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,
subject='ID',ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71,
29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97))
m2
summary(m2)
postprob(m2)
### same model as m2 with the vector of initial values specified
m3<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,
subject='ID',ng=2,data=data_hlme,B=c(0,0,0,30,25,0,-1,0,0,5,0,1,1))
m3
summary(m3)
## plot of predicted trajectories using some newdata
newdata<-data.frame(Time=seq(0,5,length=100),
X1=rep(0,100),X2=rep(0,100),X3=rep(0,100))
plot.predict(m3,newdata,"Time","right",bty="l")Run the code above in your browser using DataLab