NSCS 344, Week 8

Assignment: Least-squares model fitting

*** Due date: Start of class in Week 9 ***

Part 1: Make a function to compute the mean squared error (3 points)

Follow along with the notes to create a function that computes the mean squared error between the data and the model for a given value of σ

Part 2: Plot the mean squared error as a function of sigma (3 points)

Use your function to compute the error for a range of sigma values
Plot the error as a function of sigma

Part 3: Use fmincon to automatically find the minimum of the error function (4 points)

Follow along with the notes to use fmincon to automatically find the minimum of the error function
Add a star to your error plot at this minimum value

Part 4: Use fmincon to fit a softmax function with two parameters (2 Extra Credit points)

Extend your model to include two parameters

Use fmincon to fit both σ (which determines β) and θ. To fit more than one parameter you will need to define your likelihood function to have two free parameters

function error = twoParameterSoftmax(rsk, EV_risky, EV_safe, sigma, theta)

and your function handle slightly differently too ...

fHandle = @(x) twoParameterSoftmax(rsk, EV_risky, EV_safe, x(1), x(2));

Then you'll need a vector of starting points, lower bounds and upper bounds, to give a starting point, lower bound and upper bound for each of the parameters (σ and θ)

LB = [0 -inf]; % lower bound 0 for sigma, -inf for theta
UB = [inf inf]; % upper bound inf for sigma, inf for theta
X0 = [1 0]; % initial condition 1 for sigma, 0 for theta

After all of this, you call fmincon in exactly the same way, but instead of giving you a single best fitting parameter, the output is a vector of best fitting parameters.