# [R] GLM, log-binomial likelihood

From: francogrex <francogrex_at_mail.com>
Date: Tue, 26 Jun 2007 02:23:10 -0700 (PDT)

Dear R-help users, I have a question concerning re-writing a function in R:

Suppose I have the data, y is number of successes and N is total number of trials and x is the variable
(example:)

```x	y	N
1	10	150
0	1	100

```

I want to estimate the risk ratio by determining the coefficients of a log-binomial regression so I use:

> glm(cbind(y, N - y) ~ x, family = binomial(link = "log"))
Coefficients:

```(Intercept)            x
-4.605        1.897
```

I know that the equivalent negative log-likelihood function is:

logregfun = function(a, b) {
p.pred = exp(a + b * x)
-sum(dbinom(y, size = N, prob = p.pred, log = TRUE)) }

But I am interesting in doing the calculation not using the glm function but by optimizing the log-likelihood myself (so that I can play around with it later, add priors etc...): using the above negative-log likelihood and optim I can calculate the coefficients.
But how can I re-write the log-likelihood function if my data are in a list (and not provided as number of successes and total number of trials): such as

```x	y
0	0
0	1
1	1
0	1
...	...
```

etc until 250 rows (or sometimes more)?
where 0 indicates absence and 1 indicates presence/success

Thanks

```--
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