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))> ML79.60454 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-15Which 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:corey.sparks@utsa.edu web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm [[alternative HTML version deleted]]
Dimitris Rizopoulos
2008-Jul-16 18:22 UTC
[R] Likelihood ratio test between glm and glmer fits
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 <corey.sparks at UTSA.EDU>:
> 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:corey.sparks at utsa.edu
> web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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
2008/7/16 Dimitris Rizopoulos <Dimitris.Rizopoulos at med.kuleuven.be>:> 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)Yes, that seems quite natural, but then try to compare with the deviance: logLik(gm0) logLik(gm1) (d0 <- deviance(gm0)) (d1 <- deviance(gm1)) (LR <- d0 - d1) pchisq(LR, 1, lower = FALSE) Obviously the deviance in glm is *not* twice the negative log-likelihood as it is in glmer. The question remains which of these two quantities is appropriate for comparison. I am not sure exactly how the deviance and/or log-likelihood are calculated in glmer, but my feeling is that one should trust the deviance rather than the log-likelihoods for these purposes. This is supported by the following comparison: Ad an arbitrary random effect with a close-to-zero variance and note the deviance: tmp <- rep(1:4, each = nrow(cbpp)/4) gm2 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | tmp), family = binomial, data = cbpp) (d2 <- deviance(gm2)) This deviance is very close to that obtained from the glm model. I have included the mixed-models mailing list in the hope that someone could explain how the deviance is computed in glmer and why deviances, but not likelihoods are comparable to glm-fits. Best Rune> > > 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 <corey.sparks at UTSA.EDU>: > >> 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:corey.sparks at utsa.edu >> web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm >> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help at 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 at 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. >-- Rune Haubo Bojesen Christensen Master Student, M.Sc. Eng. Phone: (+45) 30 26 45 54 Mail: rhbc at imm.dtu.dk, rune.haubo at gmail.com DTU Informatics, Section for Statistics Technical University of Denmark, Build.321, DK-2800 Kgs. Lyngby, Denmark
On Thu, Jul 17, 2008 at 2:50 AM, Rune Haubo <rhbc at imm.dtu.dk> wrote:> 2008/7/16 Dimitris Rizopoulos <Dimitris.Rizopoulos at med.kuleuven.be>: >> 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) > > Yes, that seems quite natural, but then try to compare with the deviance: > > logLik(gm0) > logLik(gm1) > > (d0 <- deviance(gm0)) > (d1 <- deviance(gm1)) > (LR <- d0 - d1) > pchisq(LR, 1, lower = FALSE) > > Obviously the deviance in glm is *not* twice the negative > log-likelihood as it is in glmer. The question remains which of these > two quantities is appropriate for comparison. I am not sure exactly > how the deviance and/or log-likelihood are calculated in glmer, but my > feeling is that one should trust the deviance rather than the > log-likelihoods for these purposes. This is supported by the following > comparison: Ad an arbitrary random effect with a close-to-zero > variance and note the deviance: > > tmp <- rep(1:4, each = nrow(cbpp)/4) > gm2 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | tmp), > family = binomial, data = cbpp) > (d2 <- deviance(gm2)) > > This deviance is very close to that obtained from the glm model. > > I have included the mixed-models mailing list in the hope that someone > could explain how the deviance is computed in glmer and why deviances, > but not likelihoods are comparable to glm-fits.In that example I think the problem may be that I have not yet written the code to adjust the deviance of the glmer fit for the null deviance.>> 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 <corey.sparks at UTSA.EDU>: >> >>> 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:corey.sparks at utsa.edu >>> web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm >>> >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-help at 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 at 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. >> > > > > -- > Rune Haubo Bojesen Christensen > > Master Student, M.Sc. Eng. > Phone: (+45) 30 26 45 54 > Mail: rhbc at imm.dtu.dk, rune.haubo at gmail.com > > DTU Informatics, Section for Statistics > Technical University of Denmark, Build.321, DK-2800 Kgs. Lyngby, Denmark > > ______________________________________________ > R-help at 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. >
This particular case with a random intercept model can be handled by glmmML, by bootstrapping the p-value. Best, G?ran On Thu, Jul 17, 2008 at 1:29 PM, Douglas Bates <bates at stat.wisc.edu> wrote:> On Thu, Jul 17, 2008 at 2:50 AM, Rune Haubo <rhbc at imm.dtu.dk> wrote: >> 2008/7/16 Dimitris Rizopoulos <Dimitris.Rizopoulos at med.kuleuven.be>: >>> 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) >> >> Yes, that seems quite natural, but then try to compare with the deviance: >> >> logLik(gm0) >> logLik(gm1) >> >> (d0 <- deviance(gm0)) >> (d1 <- deviance(gm1)) >> (LR <- d0 - d1) >> pchisq(LR, 1, lower = FALSE) >> >> Obviously the deviance in glm is *not* twice the negative >> log-likelihood as it is in glmer. The question remains which of these >> two quantities is appropriate for comparison. I am not sure exactly >> how the deviance and/or log-likelihood are calculated in glmer, but my >> feeling is that one should trust the deviance rather than the >> log-likelihoods for these purposes. This is supported by the following >> comparison: Ad an arbitrary random effect with a close-to-zero >> variance and note the deviance: >> >> tmp <- rep(1:4, each = nrow(cbpp)/4) >> gm2 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | tmp), >> family = binomial, data = cbpp) >> (d2 <- deviance(gm2)) >> >> This deviance is very close to that obtained from the glm model. >> >> I have included the mixed-models mailing list in the hope that someone >> could explain how the deviance is computed in glmer and why deviances, >> but not likelihoods are comparable to glm-fits. > > In that example I think the problem may be that I have not yet written > the code to adjust the deviance of the glmer fit for the null > deviance. > >>> 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 <corey.sparks at UTSA.EDU>: >>> >>>> 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:corey.sparks at utsa.edu >>>> web: https://rowdyspace.utsa.edu/users/ozd504/www/index.htm >>>> >>>> >>>> [[alternative HTML version deleted]] >>>> >>>> ______________________________________________ >>>> R-help at 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 at 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. >>> >> >> >> >> -- >> Rune Haubo Bojesen Christensen >> >> Master Student, M.Sc. Eng. >> Phone: (+45) 30 26 45 54 >> Mail: rhbc at imm.dtu.dk, rune.haubo at gmail.com >> >> DTU Informatics, Section for Statistics >> Technical University of Denmark, Build.321, DK-2800 Kgs. Lyngby, Denmark >> >> ______________________________________________ >> R-help at 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. >> > > ______________________________________________ > R-help at 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. >-- G?ran Brostr?m