# Write an R function that takes as input binomial responses and covariates and uses

the Newton-Raphson algorithm to compute the coefficients of a binomial GLM. You

could use the ‘Kidney stone surgery’ data or any other dataset that includes at least

2 explanatory variables.

Medical statistics.

1. Select, read and summarize a paper of your own interest. The paper has to be

related to the material we have covered in class. Submit the paper and a 2-3

page report that includes a short summary of the paper, the design of the study, its

findings, the statistical methods used, and anything else you think relevant. Further,

comment 011 anything you particularly liked or disliked about the paper. In class we

briefly discussed an article published 011 http: //authoritynutrit ion. com/. The

references that articles on that website provide could be used for this exercise. [20]

2. write an R function that takes as input binomial responses and covariates and uses

the Newton-Raphson algorithm to compute the coefficients of a binomial GLM. You

could use the ‘Kidney stone surgery’ data or any other dataset that includes at least

2 explanatory variables. For the ‘Kidney stone surgery” data, some of the steps could

(but don“t have to) be done as follows

First enter the data

intercept, small=0, keyhole=0, successes, failures

r1<-c(1,0,0,234,36)

r2<-c(1,0,1,81,6)

r3<-c(1,1,0,55,25)

r4<-c(1,1,1,192,71)

Put all data in a matrix

data<-rbind(r1,r2,r3,r4)

Write the function

bglm<-function(data){

beta<-matrix(c(x,x,x)) # X’s denote the initial values of your choice

Define the likelihood, its first and second derivatives

Newton-Raphson algorithm

Finish by returning the vector of coefficients

return(beta);

Double check your results by comparing them to results from a statistical software.

Note that, more general functions can be written by allowing more inputs, such as

initial values etc. (but this is not necessary for the current exercise).

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