I am running mixed effect Cox models using the coxme function {coxme} in R, and I would like to check the assumption of proportional hazard.
I know that the PH assumption can be verified with the cox.zph function {survival} on cox.ph model.
However, I cannot find the equivalent for coxme models.
In 2015 a similar question has been posted here, but had no answer.
my questions are:
1) how to test PH assumption on mixed effect cox model coxme?
2) if there is no equivalent of the cox.zph for coxme models, is it valid for publication in scientific article to run mixed effect coxme model but test the PH assumption on a cox.ph model identical to the coxme model but without random effect?
Thanks in advance for your answers.
Regards
You can use frailty option in coxph function. Let's say, your random effect variable is B, your fixed effect variable is A. Then you fit your model as below
myfit <- coxph( Surv(Time, Censor) ~ A + frailty(B) , data = mydata )
Now, you can use cox.zph(myfit) to test the proportional hazard assumption.
I don't have enough reputation to comment, but I don't think using the frailty option in the coxph function will work. In the cox.zph documentation, it says:
Random effects terms such a frailty or random effects in a coxme model are not checked for proportional hazards, rather they are treated as a fixed offset in model.
Thus, it's not taking the random effects into account when testing the proportional hazards assumption.
Related
I would like to estimate a random effects (RE) multinomial logit model.
I have been applying mblogit from the mclogit package. However, once I introduce RE into my model, it fails to converge.
Is there a workaround this?
For instance, I tried to adjust the fitting process of mblogit and increase the maximal number of iterations (maxit), but did not succeed to correctly write the syntax for the control function. Would this be the right approach? And if so, could you advise me how to implement it into my model which so far looks as follows:
meta.mblogit <- mblogit(Migration ~ ClimateHazard4 , weights = logNsquare,
data = meta.df, subset= Panel==1, random = ~1|StudyID,
)
Here, both variables (Migration and ClimateHazard4) are factor variables.
Or is there an alternative approach you could recommend me for an estimation of RE multinomial logit?
Thank you very much!
The documentation for the multinom() function from the nnet package in R says that it "[f]its multinomial log-linear models via neural networks" and that "[t]he response should be a factor or a matrix with K columns, which will be interpreted as counts for each of K classes." Even when I go to add a tag for nnet on this question, the description says that it is software for fitting "multinomial log-linear models."
Granting that statistics has wildly inconsistent jargon that is rarely operationally defined by whoever is using it, the documentation for the function even mentions having a count response and so seems to indicate that this function is designed to model count data. Yet virtually every resource I've seen treats it exclusively as if it were fitting a multinomial logistic regression. In short, everyone interprets the results in terms of logged odds relative to the reference (as in logistic regression), not in terms of logged expected count (as in what is typically referred to as a log-linear model).
Can someone clarify what this function is actually doing and what the fitted coefficients actually mean?
nnet::multinom is fitting a multinomial logistic regression as I understand...
If you check the source code of the package, https://github.com/cran/nnet/blob/master/R/multinom.R and https://github.com/cran/nnet/blob/master/R/nnet.R, you will see that the multinom function is indeed using counts (which is a common thing to use as input for a multinomial regression model, see also the MGLM or mclogit package e.g.), and that it is fitting the multinomial regression model using a softmax transform to go from predictions on the additive log-ratio scale to predicted probabilities. The softmax transform is indeed the inverse link scale of a multinomial regression model. The way the multinom model predictions are obtained, cf.predictions from nnet::multinom, is also exactly as you would expect for a multinomial regression model (using an additive log-ratio scale parameterization, i.e. using one outcome category as a baseline).
That is, the coefficients predict the logged odds relative to the reference baseline category (i.e. it is doing a logistic regression), not the logged expected counts (like a log-linear model).
This is shown by the fact that model predictions are calculated as
fit <- nnet::multinom(...)
X <- model.matrix(fit) # covariate matrix / design matrix
betahat <- t(rbind(0, coef(fit))) # model coefficients, with expicit zero row added for reference category & transposed
preds <- mclustAddons::softmax(X %*% betahat)
Furthermore, I verified that the vcov matrix returned by nnet::multinom matches that when I use the formula for the vcov matrix of a multinomial regression model, Faster way to calculate the Hessian / Fisher Information Matrix of a nnet::multinom multinomial regression in R using Rcpp & Kronecker products.
Is it not the case that a multinomial regression model can always be reformulated as a Poisson loglinear model (i.e. as a Poisson GLM) using the Poisson trick (glmnet e.g. uses the Poisson trick to fit multinomial regression models as a Poisson GLM)?
I have developed a binomial logistic regression using glm function in R. I need three outputs which are
Log likelihood (no coefficients)
Log likelihood (constants only)
Log likelihood (at optimal)
What functions or packages do I need to obtain these outputs?
Say we have a fitted model m.
log-likelihood of full model (i.e., at MLE): logLik(m)
log-likelihood of intercept-only model: logLik(update(m, . ~ 1))
although the latter can probably be retrieved without refitting the model if we think carefully enough about the deviance() and $null.deviance components (these are defined with respect to the saturated model)
Suppose we have the following linear mixed effects model:
How do we fit this nested model in R?
For now, I tried two things:
Rewrite the model as:
Then using lmer function in lme4 package to fit the mixed effect model and put Xi as both random and fixed effect covariate as:
lmer(y ~ X-1+(0+X|subject))
But when I pass the result to BIC and do the model selection, it always picks the simplest model, which is not correct.
I tried to regress y_i on X_i first and treat X_i as the fixed effect, then I will get the estimate of the slope, i.e. phi_i vector. Then see phi_i as the new observations and regress on C_i again to get the beta. But it seems not correct since we do not know C_i in the real problem and it looks like C_i and beta jointly decide the coefficients.
So, are there other ways to fit this kind of model in R and where are my mistakes?
Thanks for any help!
I've fit two models, one with gam and another with gamm.
gam(y ~ x, family= betar)
gamm(y ~ x)
So the only difference is the distributional assumption. I use betar with gam and normal with gamm.
I would like to compare these two models, but I am guessing AIC will not work since the two models are based on different methods? Is there then some other suitable estimate I can use for comparison? I know I could just fit the second with gam, but let's ignore that for the sake of this question.
AIC is independent of the type of model used as soon as y is exactly the same observation to be predicted. This is only a computation of deviance explained penalised by the number of parameters fitted.
However, depending on the goal of your model, if you want to be able to use the model for prediction for instance, you should use validation to compare model performance. 10-fold cross-validation would be a good idea for instance.