# Difference between with and without “weight” option of the same data on logistic regression in R

I still keep checking from my previous question here. The next, I tried the case of proportion(=yes/yes+no), using previous best answer. Yes, I got it. But, I couldn’t understand the case without “weight=n”. When estimating as the proportion without “weight=n”, I can’t understand how to estimate deviance(or log-likelihood). please give me some advice.

x   <- c(2, 3, 5, 6)
yes <- c(2, 1, 3, 4)
no  <- c(3, 4, 2, 1)
n   <- yes + no
yp  <- yes / n


with “weight = n”

modelcp <- glm(yp ~ x,family = binomial, weight = n)
(result <- summary(modelcp))
#            Estimate Std. Error z value Pr(>|z|)
#(Intercept)  -2.0608     1.3486  -1.528    0.126
#x             0.5152     0.3147   1.637    0.102
#    Null deviance: 4.2576  on 3  degrees of freedom
#Residual deviance: 1.2762  on 2  degrees of freedom

deviance(modelcp)
# 1.276154
-2*logLik(modelcp)
#'log Lik.' 9.096343 (df=2)

#-----Using modified method of best answer on my previous question-----#
beta <- c(-2.0608, 0.5152)
logistic <- function(x) 1/(1+exp(-x)) # Common helper function
Lambda.0 <- function(beta, x, success, failure,y, with.binomial=TRUE) {
p <- logistic(beta+beta*x)
cnst <- ifelse(isTRUE(with.binomial), sum((lchoose((success+failure), success*n/(success + failure)))),0)
cnst+sum(n*(y*log(p)+(1-y)*log(1-p)))
}

-2 * Lambda.0(beta, x, yes, no, yp) # 9.096343: includes log binomial coefficients
-2 * Lambda.0(beta, x, yes, no, yp,with.binomial=FALSE) # 24.74444
sum(lchoose(n, yp*n)) * -2 # -15.64809 = 24.74444 - 9.096343


without “weight=n”

modelcpout <- glm(yp~x,family=binomial)
(result <- summary(modelcpout))
#            Estimate Std. Error z value Pr(>|z|)
#(Intercept)  -2.0608     3.0155  -0.683    0.494
#x             0.5152     0.7038   0.732    0.464
#    Null deviance: 0.85152  on 3  degrees of freedom
#Residual deviance: 0.25523  on 2  degrees of freedom

deviance(modelcpout)
# 0.2552307
-2*logLik(modelcpout)
#'log Lik.' 3.094208 (df=2)


my previous question : Difference between binary and count data of same data on logistic regression in R

• Isn't this answered here? stats.stackexchange.com/questions/141412/… – Paul Hewson Jan 28 '20 at 17:10
• Thank you for your information. I think it's related. But, I can't understand how to calculate "3.0942"... It means, where does "logLik(modelcout)=-1.547104" come from? humm... I confuse. – 51sep Jan 29 '20 at 16:34
• I uploaded my answer of this question, but I don't have confidence about it yet. If someone makes it, please give me some advice, thank you. stats.stackexchange.com/questions/446966/… – 51sep Feb 1 '20 at 16:54
• @51sep Does this answer your question: stats.stackexchange.com/questions/259502 ? if it is not, can you explain why. If it is, can you confirm. – Sextus Empiricus Dec 5 '20 at 10:23