MaxLikCode - Revision history

Admin: /* Gradient and Hessian code */

2013-08-05T10:35:06Z

‎Gradient and Hessian code

Admin: /* Gradient and Hessian code */

2013-08-05T10:34:57Z

‎Gradient and Hessian code

Admin: /* nll_lin.m */

2012-10-26T12:59:54Z

‎nll_lin.m

Admin: /* MLse.m */

2012-10-26T12:58:33Z

‎MLse.m

Admin: /* MLse.m */

2012-10-26T09:44:15Z

‎MLse.m

Admin: /* MLse.m */

2012-10-26T09:14:10Z

‎MLse.m

Admin: /* MLse.m */

2012-10-26T09:08:26Z

‎MLse.m

Admin: /* MLse.m */

2012-10-19T08:41:25Z

‎MLse.m

Admin: /* gradp.m */

2012-10-18T09:52:06Z

‎gradp.m

Admin: /* Gradient and Hessian code */

2012-10-18T09:51:39Z

‎Gradient and Hessian code

@@ Line 124: / Line 124: @@
 == Gradient and Hessian code ==
-These two functions are needed in order to calculate the Hessian and Gradient (Source: Michael [http://www.hec.unil.ch/mrockinger/WebsiteMR/Bienvenue.html Rockinger].
+These two functions are needed in order to calculate the Hessian and Gradient (Source: Michael [http://www.hec.unil.ch/mrockinger/WebsiteMR/Bienvenue.html Rockinger]).
 === HessMp.m ===

@@ Line 124: / Line 124: @@
 == Gradient and Hessian code ==
-These two functions are needed in order to calculate the Hessian and Gradient.
+These two functions are needed in order to calculate the Hessian and Gradient (Source: Michael [http://www.hec.unil.ch/mrockinger/WebsiteMR/Bienvenue.html Rockinger].
 === HessMp.m ===

@@ Line 100: / Line 100: @@
 == nll_lin.m ==
-This is the negative log likelihood function for a linear model. Save this as nll_lin.m.
+This is the negative log likelihood function for a linear model assuming conditional normality. Save this as nll_lin.m.
 <source>

@@ Line 82: / Line 82: @@
 W_p = 1-chi2cdf(W,2);
-fprintf('Wald test = %6.2f; p-value = %6.4f \n', W, W_p);</source>
+fprintf('Wald test = %6.2f; p-value = %6.4f \n', W, W_p);
 == nll_lin.m ==

@@ Line 79: / Line 79: @@
 rest = (R*thetaopt - b);
-W = (R*thetaopt - b)'*inv(R*V*R')*(R*thetaopt - b);
+W = rest'*inv(R*V*R')*rest;
 W_p = 1-chi2cdf(W,2);

@@ Line 7: / Line 7: @@
 <source>
 % Code to
-% a) simulate linear model, y_i = 0.2 + 0.6 x_1i -1.5 x_2i + err_i
+% a) simulate linear model, y_i = 0.2 + 0.2 x_1i -0.1 x_2i + 0.9 x_3i + err_i
 %       x_1i and x_s1 come from N(0,1)
 %       err_i ~ N(0,sd^2)
@@ Line 13: / Line 13: @@
 % c) estimate ot by ML
 % d) estimate different ML standard errors
+%
 % This code requires the following Functions:
@@ Line 19: / Line 20: @@
 clear all
-T   = 1000;                     % set sample size
+%% a) simulate linear model
-b0  = [0.2; 0.6; -1.5];         % set parameter values
-sd  = 0.5;                      % set error standard deviation
+T   = 100;                     % set sample size
-x   = [ones(T,1) randn(T,2)];   % simulate X matrix
+b0  = [0.2; 0.2; -0.1; 0.8; 0];      % set parameter values
 err = randn(T,1)*sd;            % simulate error terms
 y = x*b0 + err;                 % calculate y_i s
 [b,bse,res,n,rss,r2] = OLSest(y,x,1);   % OLS estimation
 datamat = [y x];                        % define data matrix for use in nll_lin
-theta0 = [mean(y); 0; 0; std(y)];       % this sets the initial parameter vector
+theta0 = [mean(y); zeros(size(b0,1)-1,1); std(y)];       % this sets the initial parameter vector
 options = optimset; % sets optimisation options to default
 [thetaopt] = fminunc(@nll_lin,theta0,options,datamat,1);
-−
 H = HessMp(@nll_lin,thetaopt,datamat,1); % this returns the negative of the Hessian
-g = gradp(@nll_lin,thetaopt,datamat,0);  % this returns a (T x size(theta0,1)) matrix of gradients
+g = gradp(@nll_lin,thetaopt,datamat,0);  % this returns a (T x size(thetaopt,1)) matrix of gradients
 J = (g'*g);                             % calculates the OPG
@@ Line 43: / Line 51: @@
 disp('   Est     se(OLS)     se(H)     se(J)     se(SW)');
 disp([thetaopt [bse;0] se_H se_J se_SW]);
 </source>
 == nll_lin.m ==

@@ Line 3: / Line 3: @@
 == MLse.m ==
-This code simulates a linear model, estimates it by PLS and ML and calculates standard errors. For this code to run you need to have the following function accessible to MATLAB (i.e. in the same folder or on a pre-specified search path: OLSest, nll_lin, HessMp, gradp. You will also need the optimization toolbox. If you do not have access to the optimisation toolbox you can replace fminunc with fminsearch as the later is part of the main MATLAB software package.
+This code simulates a linear model, estimates it by OLS and ML and calculates standard errors. For this code to run you need to have the following function accessible to MATLAB (i.e. in the same folder or on a pre-specified search path: OLSest, nll_lin, HessMp, gradp. You will also need the optimization toolbox. If you do not have access to the optimisation toolbox you can replace fminunc with fminsearch as the later is part of the main MATLAB software package.
 <source>

@@ Line 84: / Line 84: @@
 <source>
-g = gradp(@nll_lin,betaopt,datamat,0);  % this returns a (T x size(theta0,1)) matrix of gradients
+g = gradp(@nll_lin,betaopt,datamat,0);  % this returns a (T x size(thetaopt,1)) matrix of gradients
 </source>

@@ Line 74: / Line 74: @@
 === HessMp.m ===
-Download the file from [[media:HessMp.m|here]]. An example call to this function can be seen in the above MLse.m code. The first input is a handle to the Function that is used to calculate the Hessian (here nll_lin). All other inputs follow the inputs required for that function (here <source enclose=none>(theta, data , vec)</source>). When used for calculating the variance-covariance matrix of parameter estimates we want to feed in the estimated parameters (<source enclose=none>thetaopt</source>)
+Download the file from [[media:HessMp.m|here]]. An example call to this function can be seen in the above MLse.m code. The first input is a handle to the Function that is used to calculate the Hessian (here nll_lin). All other inputs follow the inputs required for that function (here <source enclose=none>(theta, data , vec)</source>). When used for calculating the variance-covariance matrix of parameter estimates we want to feed in the estimated parameters (<source enclose=none>thetaopt</source>). The Hessian routine expects the function to return a scalar likelihood function and hence the input for <source enclose=none>vec</source> is <source enclose=none>1</source> (see definition of <source enclose=none>nll_lin.m</source>).
 <source>
@@ Line 81: / Line 81: @@
 === gradp.m ===
-Download the file from [[media:gradp.m|here]]
+Download the file from [[media:gradp.m|here]]. An example call to this function can be seen in the above MLse.m code. The first input is a handle to the Function that is used to calculate the Gradient (here nll_lin). All other inputs follow the inputs required for that function (here <source enclose=none>(theta, data , vec)</source>). When used for calculating the variance-covariance matrix of parameter estimates we want to feed in the estimated parameters (<source enclose=none>thetaopt</source>). The Gradient will calculate the gradient for either the scalar log-likelihood (if the <source enclose=none>vec</source> input is set to 1) or the gradient at every observation (if the <source enclose=none>vec</source> input is set to 0 - see definition of <source enclose=none>nll_lin.m</source>). To calculate the OPG we need the latter.
 <source>
 g = gradp(@nll_lin,betaopt,datamat,0);  % this returns a (T x size(theta0,1)) matrix of gradients
 </source>