Usual problems encountered when using lcmm package
Source:vignettes/usual_problems.Rmd
usual_problems.Rmd
We list here some recurrent problems reported by users. Other issues, questions, concerns may have been reported in github: https://github.com/CecileProust-Lima/lcmm/issues/ .
Please refer to github, both closed and opened issues, before sending any question. And please ask the questions via github only.
Why my model did not converge?
It sometimes happens that a model does not converge correctly. This is due most of the time to the very stringent criterion based on the “derivatives”. This criterion uses both the first derivatives and the inverse of the matrix of the second derivatives (Hessian). It ensures that the program converges at a maximum. When it can’t be computed correctly (most of the time because the Hessian is not definite positive), the program reports “second derivatives = 1”.
There are several reasons that may induce a non convergence, e.g.:
When the time variable (or more generally a variable with random effects) is in a unit which induces too small associated parameters (for very small changes per day). In that case, changing the scale (for instance with months or years) may solve the problem.
In models with splines in the link function (lcmm, multlcmm, Jointlcmm, mpjlcmm) or with splines in the baseline risk function (Jointlcmm, mpjlcmm), a parameter associated with splines very close to zero may prevent for correct convergence as it is at the border of the parameter space. In that case, this parameter can be fixed to 0 and convergence should be reached immediately.
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When the data are not rich enough and/or the model is too complicated. In that case, this is a problem of numerical non identifiability. There are not many solutions (other than simplifying the model) but some directions may be :
- Be patient, it happens that after some iterations the derivatives might be invertible and the model converges (you can change maxiter or rerun the program from the estimates at the non convergence point). But this is usually no necessary to specify more than 100 or 200 iterations. The iterative algorithm is used to converge in a few dozen of iterations.
- You can try to assume a less stringent threshold (e.g., 0.01) but be
careful, convergence might be of lower quality.
- Run the model from different initial values.
How to choose the number of latent classes?
Selection of the number of latent classes is a complex question. In some cases, the number is known. When not, different tools can be used to guide the decision:
- Several statistical criteria such as BIC, SABIC, ICL or Entropy
- Statistical tests when available: score test for conditional independence in joint models
- Discrimination power as described by the classification table using the command postprob
- Size of the classes (we can consider that classes should be larger than 1% or 5% depending on the context)
- Clinical aspects and interpretation should also be taken into account
Finally, it can be useful to present and contrast models with different numbers of latent classes.
The complexity of the selection of the optimal number of latent classes is illustrated in the hlme vignette. Indeed, all the criteria may not be concordant in practice.
How to evaluate the quality of a classification?
Good discrimination of classes is usually sought when fitting latent class mixed models. Discriminatory power can be assessed using the entropy criterion (provided in summarytable) but also using the classification table (with command postprob). The description of the classes may also help comprehend the latent class structure.
(see hlme vignette for further details)
How to evaluate the fit of a model?
Different techniques can be used in this package to evaluate the goodness of fit. As in mixed models, one can compare the subject-specific predictions with the observations or plot the subject-specific residuals.
The comparison with more flexible models can also be useful (more flexible link functions, more flexible baseline risk functions, more flexible functions of time, etc.)
Each vignette includes a section on the evaluation of the model.
How to change the latent class in reference?
The order of the latent classes can be changed in any function (hlme, lcmm, Jointlcmm, mpjlcmm) using the permut function. Here is an example with the estimation of a two class linear mixed model:
mhlme <- hlme(IST ~ I(age-age_init),random=~ I(age-age_init),subject="ID",data=paquid)
set.seed(1234)
mhlme2 <- hlme(IST ~ I(age-age_init),random=~ I(age-age_init),subject="ID",data=paquid,ng=2,
mixture=~ I(age-age_init),classmb =~ CEP , B=random(mhlme))summary(mhlme2)
Heterogenous linear mixed model
fitted by maximum likelihood method
hlme(fixed = IST ~ I(age - age_init), mixture = ~I(age - age_init),
random = ~I(age - age_init), subject = "ID", classmb = ~CEP,
ng = 2, data = paquid)
Statistical Model:
Dataset: paquid
Number of subjects: 494
Number of observations: 2052
Number of observations deleted: 198
Number of latent classes: 2
Number of parameters: 10
Iteration process:
Convergence criteria satisfied
Number of iterations: 14
Convergence criteria: parameters= 2.3e-07
: likelihood= 5.5e-08
: second derivatives= 5.4e-14
Goodness-of-fit statistics:
maximum log-likelihood: -6010.69
AIC: 12041.38
BIC: 12083.4
Maximum Likelihood Estimates:
Fixed effects in the class-membership model:
(the class of reference is the last class)
coef Se Wald p-value
intercept class1 2.82685 1.02234 2.765 0.00569
CEP class1 -3.37139 1.00111 -3.368 0.00076
Fixed effects in the longitudinal model:
coef Se Wald p-value
intercept class1 25.54344 0.49563 51.537 0.00000
intercept class2 32.93897 0.54896 60.003 0.00000
I(...) class1 -0.51254 0.05028 -10.193 0.00000
I(...) class2 -0.57198 0.04923 -11.618 0.00000
Variance-covariance matrix of the random-effects:
intercept I(age - age_init)
intercept 10.89147
I(age - age_init) 0.03929 0.09386
coef Se
Residual standard error: 3.36817 0.06757The order of the latent classes can be changed by running:
summary(mhlme2)
Heterogenous linear mixed model
fitted by maximum likelihood method
hlme(fixed = IST ~ I(age - age_init), mixture = ~I(age - age_init),
random = ~I(age - age_init), subject = "ID", classmb = ~CEP,
ng = 2, data = paquid)
Statistical Model:
Dataset: paquid
Number of subjects: 494
Number of observations: 2052
Number of observations deleted: 198
Number of latent classes: 2
Number of parameters: 10
Iteration process:
Convergence criteria satisfied
Number of iterations: 14
Convergence criteria: parameters= 2.3e-07
: likelihood= 5.5e-08
: second derivatives= 5.4e-14
Goodness-of-fit statistics:
maximum log-likelihood: -6010.69
AIC: 12041.38
BIC: 12083.4
Maximum Likelihood Estimates:
Fixed effects in the class-membership model:
(the class of reference is the last class)
coef Se Wald p-value
intercept class1 2.82685 1.02234 2.765 0.00569
CEP class1 -3.37139 1.00111 -3.368 0.00076
Fixed effects in the longitudinal model:
coef Se Wald p-value
intercept class1 25.54344 0.49563 51.537 0.00000
intercept class2 32.93897 0.54896 60.003 0.00000
I(...) class1 -0.51254 0.05028 -10.193 0.00000
I(...) class2 -0.57198 0.04923 -11.618 0.00000
Variance-covariance matrix of the random-effects:
intercept I(age - age_init)
intercept 10.89147
I(age - age_init) 0.03929 0.09386
coef Se
Residual standard error: 3.36817 0.06757The models in objects mhlme2 and mhlme2perm are the same except for the permutation of the classes as shown with the cross-table:
How to make predictions on external data?
An object stemmed from a estimation function of lcmm package (hlme, lcmm, Jointlcmm, mpjlcmm) provides predictions on the data on which the model was estimated.
Different functions allows the same type of computations but on external data:
Classification with PredictClass
predictClass function computes the posterior classification and the posterior class-membership probabilities from any latent class model estimated in package lcmm.
For instance, using the 2-class model estimated above, the posterior probabilities and classification can be computed for the newdata, here the data of the second subject of paquid dataset:
Random-effects with predictRE
predictRE function computes the predicted random-effects of any model estimated within lcmm package for a new subject whose data (i.e., covariates and outcomes) are provided in newdata:
By default, the random-effects are aggregated over the latent classes (by a weighted sum using the posterior probabilities). The argument classpredRE = TRUE can be used to get class-specific random-effects:
predictRE(mhlme2, newdata=paquid[2:6,], classpredRE = TRUE)
ID class intercept I(age - age_init)
1 2 1 1.263606 -0.0378250
2 2 2 -3.668510 -0.1181933
Subject-specific predictions using predictY or predictL
For hlme models and Jointlcmm models without link function, subject-specific predictions can be obtained using predictY. This requires a first call to predictRE with classpredRE = TRUE to get the individual random-effects, which can then be passed to the predictY function using option predRE.
predRE_ID2 <- predictRE(mhlme2, paquid[2:6,], classpredRE = TRUE)
predictY(mhlme2, newdata = data.frame(age = seq(70, 85, by = 0.25), age_init = 70, CEP = 0), predRE = predRE_ID2)For model defining a latent process (lcmm, multlcmm, Jointlcmm with a link function), subject-specific predictions can be obtained in latent process scale using predictL.
Predictions of outcomes in their natural scale using predictYcond and predictYback
Predictions of the outcomes can be directly computed for a latent process value. This is useful when nonlinear link functions are used in the models. This is obtained with function predictYcond.
When an outcome is transformed and the transformed values are then included in a hlme model, predictions in the natural scale of the outcome can be obtained using the predictYback function. Only marginal predictions can be obtained in this setting.