Re: [Gretl-users] Maximum Likelihood estimation of Linear Probability specification (Binary Choice model)

Message: 5 Date: Mon, 7 Sep 2015 11:15:23 +0200 (CEST) From: "Riccardo (Jack) Lucchetti&quot;&lt;r.lucchetti(a)univpm.it&gt; To: Gretl list&lt;gretl-users(a)lists.wfu.edu&gt; Subject: Re: [Gretl-users] Maximum Likelihood estimation of Linear Probability specification (Binary Choice model) Message-ID:<alpine.DEB.2.20.1509071045130.8887@ec-4.econ.univpm.it> Content-Type: text/plain; charset="iso-8859-15"; Format="flowed" On Mon, 7 Sep 2015, Alecos Papadopoulos wrote: > >I need to estimate a "Linear Probability" Specification in a Binary Choice > >model, using specifically maximum likelihood estimation. > >The log-likelihood of such a specification is > > > >loglik = y*log(x.*b) + (1-y)*(1-x.*b) > > > >where y is the scalar DepVar, "x" is the vector of regressors and "b" is the > >vector of unknown parameters. I guess you mean loglik = y*log(x.*b) + (1-y)*log(1-x.*b) and besides, since y is binary, you might want to use <hansl> series ndx = lincomb(X, b) series loglik = y ? ln(ndx) : ln(1-ln(ndx)) </hansl> instead, which saves a few floating-point operations. > >The argument of the natural logarithm is not inherently constrained to range > >in (0,1), so in the iterative maximization process, negative values of x.*b > >or (1-x.*b) may be encountered at some of the observations, which is not > >admissible for the logarithm. The syntax I suggested above circumvents the problem somehow, since it ensures that you take the log only once per observation, instead of twice. > >Left as is, with a "catch" preceding the mle command, Gretl ignores the lot > >and moves to the next round of randomly generated regressors (this is a Monte > >Carlo study) etc. But there are cases where this happens with/all/ generated > >samples. Note that the true specification here is indeed the Linear > >Probability model (underlying error is Uniform). > > > >Is there a way to tell Gretl to continue "insisting" on the sample where at > >some step it encountered inadmissible values for the logarithm? I guess you can introduce a few checks via an ad-hoc function (sample code follows): <hansl> function scalar badobs(series m) scalar up = sum(m>1) scalar dn = sum(m<0) if xmax(up, dn) > 0 printf "UP = %d, DOWN = %d\n", up, dn endif return up + dn end function nulldata 1000 series x = uniform() series p = -0.5 + 2 * x series y = uniform() < p list X = const x ols y X matrix b = $coeff series loglik = NA mle loglik = y ? ln(ndx) : ln(1-ndx) series ndx = lincomb(X, b) scalar bad = badobs(ndx) params b end mle -v series B = missing(loglik) xtab y B </hansl> Note that with the solution above, having "bad" values for the index function is not really a problem if the happen to occur for the "appropriate" value of y (for example: ndx < 0 is not a problem if y=1). ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES)