Re: [R] Likelihood ratio test between glm and glmer fits

Wed, 16 Jul 2008 11:17:29 -0700

well, for computing the p-value you need to use pchisq() and dchisq() (check ?dchisq for more info). For model fits with a logLik method you can directly use the following simple function: 

lrt <- function (obj1, obj2) {
    L0 <- logLik(obj1)
    L1 <- logLik(obj2)
    L01 <- as.vector(- 2 * (L0 - L1))
    df <- attr(L1, "df") - attr(L0, "df")
    list(L01 = L01, df = df,
        "p-value" = pchisq(L01, df, lower.tail = FALSE))
}

library(lme4)
gm0 <- glm(cbind(incidence, size - incidence) ~ period,
              family = binomial, data = cbpp)
gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
              family = binomial, data = cbpp)

lrt(gm0, gm1)


However, there are some issues regarding this likelihood ratio test.
1) The null hypothesis is on the boundary of the parameter space, i.e., you test whether the variance for the random effect is zero. For this case the assumed chi-squared distribution for the LRT may *not* be totally appropriate and may produce conservative p-values. There is some theory regarding this issue, which has shown that the reference distribution for the LRT in this case is a mixture of a chi-squared(df = 0) and chi-squared(df = 1). Another option is to use simulation-based approach where you can approximate the reference distribution of the LRT under the null using simulation. You may check below for an illustration of this procedure (not-tested): 

X <- model.matrix(gm0)
coefs <- coef(gm0)
pr <- plogis(c(X %*% coefs))
n <- length(pr)
new.dat <- cbpp
Tobs <- lrt(gm0, gm1)$L01
B <- 200
out.T <- numeric(B)
for (b in 1:B) {
    y <- rbinom(n, cbpp$size, pr)
    new.dat$incidence <- y
    fit0 <- glm(formula(gm0), family = binomial, data = new.dat)
    fit1 <- glmer(formula(gm1), family = binomial, data = new.dat)
    out.T[b] <- lrt(fit0, fit1)$L01
}
# estimate p-value
(sum(out.T >= Tobs) + 1) / (B + 1)
2) For the glmer fit you have to note that you work with an approximation to the log-likelihood (obtained using numerical integration) and not the actual log-likelihood. 

I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


Quoting COREY SPARKS <[EMAIL PROTECTED]>:


Dear list,
I am fitting a logistic multi-level regression model and need to test the difference between the ordinary logistic regression from a glm() fit and the mixed effects fit from glmer(), basically I want to do a likelihood ratio test between the two fits. 


The data are like this:
My outcome is a (1,0) for health status, I have several (1,0) dummy variables RURAL, SMOKE, DRINK, EMPLOYED, highereduc, INDIG, male, divorced, SINGLE, chronic, vigor_d and moderat_d and AGE is continuous (20 to 100). 
My higher level is called munid and has 581 levels.
The data have 45243 observations.

Here are my program statements:

#GLM fit
ph.fit.2<-glm(poorhealth~RURAL+SMOKE+DRINK+EMPLOYED+highereduc+INDIG+AGE+male+divorced+SINGLE+chronic+vigor_d+moderat_d,family=binomial(), data=mx.merge) 
#GLMER fit
ph.fit.3<-glmer(poorhealth~RURAL+SMOKE+DRINK+EMPLOYED+INSURANCE+highereduc+INDIG+AGE+male+divorced+SINGLE+chronic+vigor_d+moderat_d+(1|munid),family=binomial(), data=mx.merge)
I cannot find a method in R that will do the LR test between a glm and a glmer fit, so I try to do it using the liklihoods from both models 

#form the likelihood ratio test between the glm and glmer fits
x2<--2*(logLik(ph.fit.2)-logLik(ph.fit.3))


    ML

79.60454
attr(,"nobs")
    n
45243
attr(,"nall")
    n
45243
attr(,"df")
[1] 14
attr(,"REML")
[1] FALSE
attr(,"class")
[1] "logLik"

#Get the associated p-value
dchisq(x2,14)
         ML

5.94849e-15
Which looks like an improvement in model fit to me. Am I seeing this correctly or are the two models even able to be compared? they are both estimated via maximum likelihood, so they should be, I think. 
Any help would be appreciated.

Corey

Corey S. Sparks, Ph.D.

Assistant Professor
Department of Demography and Organization Studies
University of Texas San Antonio
One UTSA Circle
San Antonio, TX 78249
email:[EMAIL PROTECTED]
web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm


        [[alternative HTML version deleted]]

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.






Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Reply via email to