maxlikmtProfileLimits#

Purpose#

Computes confidence limits by inversion of the likelihood ratio statistic.

Format#

out1 = maxlikmtProfileLimits(&logl, out0[, ...., c1])#
Parameters:

  • &logl (pointer) – Pointer to log-likelihood function used to generate results of an estimation by a call to maxlikmt().

  • out0 (struct) – Instance of maxlikmtResults structure containing results of an estimation generated by a call to maxlikmt().

  • ... (Various) – Optional input arguments. They can be any set of structures, matrices, arrays, strings, required to compute the log-likelihood function.

  • c1 – The set of optional input arguments must contain the instance of the maxlikmtResults structure used in the call to

maxlikmt() that produced the results in out0.

c1.bayesAlpha

Exponent of the Dirichlet random variates used in the weighted bootstrap. Default = 1.4.

c1.priorProc

Pointer to a procedure for computing the prior. Assumes a uniform prior if not provided.

c1.numSamples

Number of re-samples in the weighted likelihood bootstrap.

c1.BayesFname

Filename for the simulated posterior parameters dataset. Defaults to a unique “BAYESxxxx” pattern.

c1.maxBootTime

Maximum time allowed for resampling.

c1.Bounds

Bounds on parameters, either 1x2 for all parameters or Kx2 for individual parameter bounds. Default = {-1e256, 1e256}.

c1.algorithm

Descent algorithm for optimization, includes BFGS, DFP, Newton, and BHHH.

c1.switch

Controls algorithm switching based on various performance metrics.

c1.lineSearch

Method for line search in optimization, includes augmented trust region method and others. Default varies based on constraints.

c1.active

Kx1 vector to control which parameters are active or fixed at start value.

c1.numObs

Number of observations, required if the log-likelihood function returns a scalar.

c1.maxIters

Maximum number of iterations for the optimization process. Default = 10000.

c1.tol

Convergence tolerance, optimization stops when all elements of the direction vector are below this value. Default = 1e-5.

c1.weights

Vector of weights for the objective function returning a vector. Default = 1.

c1.covParType

Determines the type of covariance matrix computed, QML or ML. Default = 1.

c1.alpha

Probability level for statistical tests. Default = .05.

c1.feasibleTest

If nonzero, parameters are tested for feasibility before computing the function in line search. Default = 1.

c1.maxTries

Maximum number of attempts in random search. Default = 100.

c1.randRadius

Radius of the random search, if attempted. Default = .001.

c1.gradMethod

Method for computing numerical gradient, includes central, forward, and backward difference.

c1.hessMethod

Method for computing numerical Hessian, similar options as gradient computation.

c1.gradStep

Increment size for computing numerical gradient, can be scalar or Kx1 vector.

c1.hessStep

Increment size for computing numerical Hessian, options similar to gradStep.

c1.gradCheck

If nonzero and analytical gradients/Hessian provided, numerical versions are computed for comparison.

c1.state

Seed for random number generator, ensuring reproducibility.

c1.title

Title of the run, for identification in output.

c1.printIters

If nonzero, iteration information is printed. Default = 0.

c1.disableKey

If nonzero, keyboard input is disabled during execution.
Returns:

out1 (struct) – Instance of maxlikmtResults structure that is a duplicate of out0 except that the member, out1.profileLimits, has been set to the confidence limits by inversion of the likelihood ratio statistic.

Example#

library maxlikmt;

// Define the log-likelihood function
proc lpr(struct PV p, y, x, ind);
    local s2, b0, b, yh, u, res, g1, g2;

    struct modelResults mm;

    b0 = pvUnpack(p,"b0");
    b = pvUnpack(p,"b");
    s2 = pvUnpack(p,"variance");

    yh = b0 + x * b;
    res = y - yh;
    u = y[.,1] ./= 0;

    if ind[1];
        mm.function = u.*lnpdfmvn(res,s2) + (1-u).*(ln(cdfnc(yh/sqrt(s2))));
    endif;

    if ind[2];
        yh = yh/sqrt(s2);
        g1 = ((res~x.*res)/s2)~((res.*res/s2)-1)/(2*s2);
        g2 = (-(ones(rows(x),1)~x)/sqrt(s2))~(yh/(2*s2));
        g2 = (pdfn(yh)./cdfnc(yh)).*g2;
        mm.gradient = u.*g1 + (1-u).*g2;
    endif;

    retp(mm);
endp;

struct PV p0;
p0 = pvPack(pvCreate, 1, "b0");
p0 = pvPack(p0, 1|1|1, "b");
p0 = pvPack(p0, 1, "variance");

struct maxlikmtControl c0;
c0 = maxlikmtcontrolcreate;
c0.title = "Tobit Example";
c0.Bounds = {-10 10, -10 10, -10 10, -10 10, .1 10};

z = loadd(getGAUSSHome("pkgs/maxlikmt/examples/maxlikmttobit.dat"));
y = z[., 1];
x = z[., 2:4];

struct maxlikmtResults out1;
out1 = maxlikmt(&lpr, p0, y, x, c0);

// Compute limits by inversion of likelihood ratio statistic
out1 = maxlikmtProfileLimits(&lpr, out1, y, x, c0);

// Print the results
call maxlikmtPrt(out1);
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