CODEWITHSUNDEEP
rpackageglmmle
Jasmine Helen
Jasmine Helen

Reputation: 99

R: The estimate parameter is different between GLM model and optim() package

I want to find estimate parameter with optim() package in R. And I compare my result with GLM model in R. The code is

d <- read.delim("http://dnett.github.io/S510/Disease.txt")
d$disease=factor(d$disease)
d$ses=factor(d$ses)
d$sector=factor(d$sector)
str(d)

oreduced <- glm(disease~age+sector, family=binomial(link=logit), data=d)
summary(oreduced)

y<-as.numeric(as.character(d$disease))
x1<-as.numeric(as.character(d$age))
x2<-as.numeric(as.character(d$sector))

nlldbin=function(param){
  eta<-param[1]+param[2]*x1+param[3]*x2
  p<-1/(1+exp(-eta))
  -sum(y*log(p)+(1-y)*log(1-p),na.rm=TRUE)
}
MLE_estimates<-optim(c(Intercept=0.1,age=0.1,sector2=0.1),nlldbin,hessian=TRUE)

MLE_estimatesenter

The result with GLM model

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.15966    0.34388  -6.280 3.38e-10 ***
age          0.02681    0.00865   3.100 0.001936 ** 
sector2      1.18169    0.33696   3.507 0.000453 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

And with optim()

$par
  Intercept         age     sector2 
-3.34005918  0.02680405  1.18101449

Can someone please tell me why its different and how to fix this? Thank you

Upvotes: 1

Views: 182

Answers (1)

J. Mini
J. Mini

Reputation: 1610

You've given R two different problems. In your GLM, all of the parameters in the formula are factor variables. This mean that you've told R that they can only take particular values (e.g. d$disease can only take values 0 and 1). In your MLE approach, you've converted them to numeric variables, meaning that they can take any value and that your data just happens to use a small set of values.

The "fix" is to only give R one problem to solve. For example, if you instead fit glm(y~x1+x2, family=binomial(link=logit)), which uses no factor variables, you get pretty much the same parameter estimates with both the MLE as with the fitted model. You've seen this before.

Upvotes: 1

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