R: fit mixed effect model - r
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!
Related
Multinomial logit with random effects does not converge using mblogit
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!
How do you compare a gam model with a gamm model? (mgcv)
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.
coxme proportional hazard assumption
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.
lmmlasso - how to specify a random intercept, and make a prediction?
I'm new to R and statistical modelling, and am looking to use the lmmlasso library in r to fit a mixed effects model, selecting only the best fixed effects out of ~300 possible variables. For this model I'd like to include both a fixed intercept, a random effect, and a random intercept. Looking at the manual on CRAN, I've come across the following: x: matrix of dimension ntot x p including the fixed-effects covariables. An intercept has to be included in the first column as (1,...,1). z: random effects matrix of dimension ntot x q. It has to be a matrix, even if q=1. While it's obvious what I need to do for the fixed intercept I'm not quite sure how to include both a random intercept and effect. Is it exactly the same as the fixed matrix, where I include (1...1) in my first column? In addition to this, I'm looking to validate the resulting model I get with another dataset. For lmmlasso is there a function similar to predict in lme4 that can be used to compute new predictions based on the output I get? Alternatively, is it viable/correct to construct a new model using lmer using the variables with non-zero coefficients returned by lmmlasso, and then use predict on the new model? Thanks in advance.
R: Linear regression model does not work very well
I'm using R to fit a linear regression model and then I use this model to predict values but it does not predict very well boundary values. Do you know how to fix it?
ZLFPS is:
ZLFPS<-c(27.06,25.31,24.1,23.34,22.35,21.66,21.23,21.02,20.77,20.11,20.07,19.7,19.64,19.08,18.77,18.44,18.24,18.02,17.61,17.58,16.98,19.43,18.29,17.35,16.57,15.98,15.5,15.33,14.87,14.84,14.46,14.25,14.17,14.09,13.82,13.77,13.76,13.71,13.35,13.34,13.14,13.05,25.11,23.49,22.51,21.53,20.53,19.61,19.17,18.72,18.08,17.95,17.77,17.74,17.7,17.62,17.45,17.17,17.06,16.9,16.68,16.65,16.25,19.49,18.17,17.17,16.35,15.68,15.07,14.53,14.01,13.6,13.18,13.11,12.97,12.96,12.95,12.94,12.9,12.84,12.83,12.79,12.7,12.68,27.41,25.39,23.98,22.71,21.39,20.76,19.74,19.49,19.12,18.67,18.35,18.15,17.84,17.67,17.65,17.48,17.44,17.05,16.72,16.46,16.13,23.07,21.33,20.09,18.96,17.74,17.16,16.43,15.78,15.27,15.06,14.75,14.69,14.69,14.6,14.55,14.53,14.5,14.25,14.23,14.07,14.05,29.89,27.18,25.75,24.23,23.23,21.94,21.32,20.69,20.35,19.62,19.49,19.45,19,18.86,18.82,18.19,18.06,17.93,17.56,17.48,17.11,23.66,21.65,19.99,18.52,17.22,16.29,15.53,14.95,14.32,14.04,13.85,13.82,13.72,13.64,13.5,13.5,13.43,13.39,13.28,13.25,13.21,26.32,24.97,23.27,22.86,21.12,20.74,20.4,19.93,19.71,19.35,19.25,18.99,18.99,18.88,18.84,18.53,18.29,18.27,17.93,17.79,17.34,20.83,19.76,18.62,17.38,16.66,15.79,15.51,15.11,14.84,14.69,14.64,14.55,14.44,14.29,14.23,14.19,14.17,14.03,13.91,13.8,13.58,32.91,30.21,28.17,25.99,24.38,23.23,22.55,20.74,20.35,19.75,19.28,19.15,18.25,18.2,18.12,17.89,17.68,17.33,17.23,17.07,16.78,25.9,23.56,21.39,20.11,18.66,17.3,16.76,16.07,15.52,15.07,14.6,14.29,14.12,13.95,13.89,13.66,13.63,13.42,13.28,13.27,13.13,24.21,22.89,21.17,20.06,19.1,18.44,17.68,17.18,16.74,16.07,15.93,15.5,15.41,15.11,14.84,14.74,14.68,14.37,14.29,14.29,14.27,18.97,17.59,16.05,15.49,14.51,13.91,13.45,12.81,12.6,12,11.98,11.6,11.42,11.33,11.27,11.13,11.12,11.11,10.92,10.87,10.87,28.61,26.4,24.22,23.04,21.8,20.71,20.47,19.76,19.38,19.18,18.55,17.99,17.95,17.74,17.62,17.47,17.25,16.63,16.54,16.39,16.12,21.98,20.32,19.49,18.2,17.1,16.47,15.87,15.37,14.89,14.52,14.37,13.96,13.95,13.72,13.54,13.41,13.39,13.24,13.07,12.96,12.95,27.6,25.68,24.56,23.52,22.41,21.69,20.88,20.35,20.26,19.66,19.19,19.13,19.11,18.89,18.53,18.13,17.67,17.3,17.26,17.26,16.71,19.13,17.76,17.01,16.18,15.43,14.8,14.42,14,13.8,13.67,13.33,13.23,12.86,12.85,12.82,12.75,12.61,12.59,12.59,12.45,12.32)
QPZL<-c(36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16)
ZLDBFSAO<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2)
My model is:
fit32=lm(log(ZLFPS) ~ poly(QPZL,2,raw=T) + ZLDBFSAO)
results3 <- coef(summary(fit32))
first3<-as.numeric(results3[1])
second3<-as.numeric(results3[2])
third3<-as.numeric(results3[3])
fourth3<-as.numeric(results3[4])
fifth3<-as.numeric(results3[5])
#inverse model used for prediction of FPS
f1 <- function(x) {first3 +second3*x +third3*x^2 + fourth3*1}
You can see my dataset here. This dataset contains the values that I have to predict. The FPS variation per QP is heterogenous. See dataset. I added a new column.
The fitted dataset is a different one.
To test the model just write exp(f1(selected_QP)) where selected QP varies from 16 to 36. See the given dataset for QP values and the FPS value that the model should predict.
You can run the model online here.
When I'm using QP values in the middle, let's say between 23 and 32 the model predicts the FPS value pretty well. Otherwise, the prediction has big error value.
Regarding the linear regression model I should use Weighted Least Squares as a Solution to Heteroskedasticity of the fitted dataset. For references, see here, here and here. fit32=lm(log(ZLFPS) ~ poly(QPZL,2,raw=T) + ZLDBFSAO, weights=1/(1+0.5*QPZL^2)) The other code remains the same. This model gives me lower prediction error than the previous.