Fitting Poisson with Numeric Methods

Overview


The method presented here for fitting a Poisson distribution to a dataset utilizes Newton's method

Implementation


The implementation uses the Poisson glm library to compute the log Likelihood of the given dataset. The logLikelihood function in the library takes 3 parameters

  • the dataset - an array of objects
  • y function - a function that takes an item from the inputted dataset and returns the y value (count) registerd in that item
  • mu function - function that returns the value of mu for the given set of {% \beta %} values.
{% \mu_i = exp[\vec{x}_i^T \vec{\beta}] %}
In addition, it uses the Newton Library to perform the Newton-Raphson optimization routine. 

/*
Define the function to optimized.  Here, the function takes four paremeters, the values for 
the beta vector, and then runs the logLikelihood function in the poisson glm library. 
*/
let f = function(b0, b1, b2, b3){
    let logL = pl.logLikelihood(data, item=>item.num_awards, item=>{
        let eta = b0+b1*item.progAcademic + b2*item.progVocational + b3*item.math;
        let mu = Math.exp(eta);
        return mu;
    });
    return logL;
}

//create an iterator from the newtons method library
let test = op.iterator(f, [0,0,0,0]);
    
//run several interations
for(let i=0;i<100;i++){
    test.iterate();
}
Try it!

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