Hi,
Does anyone have any idea about performing Hansen's threshold regression in SAS?
Or how can I find the document about it on the SAS platform?
Thanks,
Lynn
Hello @LynnChen
At this time, there is no procedure that provides canned routine for Hansen(2000)'s threshold regression model directly. We may consider this functionality in the future, but at this time, you may consider following options:
For two regimes threshold regression like the following:
you may perform the estimation by looping over all possible gammas(or a grid of gammas) as discussed below:
If T is big, take a grid of w_i; e.g., i might be in the range of 10%*T and 90%*T.
For multiple regimes, the combination of gammas should be looped over---but in that case, maybe the new procedure PROC BART is a better choice,
https://go.documentation.sas.com/doc/en/pgmsascdc/v_027/casstat/casstat_bart_details02.htm
Another alternative is similar to the following PROC MODEL switching regression example:
SAS Help Center: Switching Regression Example
which may provide an easier way to estimate this model, if you can accept that the solution is achieved by approximating the step function as the continuous function ProbNorm(.) --Note that this is a nonlinear optimization problem and the initial values or optimization method might matter.
Following is an example that estimates the threshold model using the PROC MODEL approach:
title1 'Threshold Regression Example'; data switch; call streaminit('pcg', 12345); do t = 1 to 1000; e = rand('normal'); x = rand('normal'); z = rand('normal'); w = rand('uniform'); if(w<0.345) then y = 1 + 1.5*x + 2 * z + 0.5*e; else y = 1 + 1.5*x - 2 * z + 0.5*e; mylogL = (1/2)*( (log(2*3.1415)) + log( 0.5**2 ) + ((0.5*e)*( 1/0.5**2 )*(0.5*e)) ) ; output; end; run; proc means data=switch; var mylogL; run; proc model data=switch; parms sig1=1 int1 b1 b21 b22 gamma=0.5; bounds 0.0001 < sig1; a = (w - gamma)*100; /* Upper bound of integral */ d = probnorm(a); /* Normal CDF as an approx of switch */ /* Regime 1 */ y1 = int1 + x * b1 + z * b21 ; /* Regime 2 */ y2 = int1 + x * b1 + z * b22 ; /* Composite regression equation */ y = (1 - d)*y1 + d*y2; /* Resulting log-likelihood function */ logL = (1/2)*( (log(2*3.1415)) + log( sig1**2 ) + (resid.y*( 1/sig1**2 )*resid.y) ) ; errormodel y ~ general(logL); fit y / method=marquardt converge=1.0e-6; run; quit;
I hope this helps!
Hello @LynnChen
At this time, there is no procedure that provides canned routine for Hansen(2000)'s threshold regression model directly. We may consider this functionality in the future, but at this time, you may consider following options:
For two regimes threshold regression like the following:
you may perform the estimation by looping over all possible gammas(or a grid of gammas) as discussed below:
If T is big, take a grid of w_i; e.g., i might be in the range of 10%*T and 90%*T.
For multiple regimes, the combination of gammas should be looped over---but in that case, maybe the new procedure PROC BART is a better choice,
https://go.documentation.sas.com/doc/en/pgmsascdc/v_027/casstat/casstat_bart_details02.htm
Another alternative is similar to the following PROC MODEL switching regression example:
SAS Help Center: Switching Regression Example
which may provide an easier way to estimate this model, if you can accept that the solution is achieved by approximating the step function as the continuous function ProbNorm(.) --Note that this is a nonlinear optimization problem and the initial values or optimization method might matter.
Following is an example that estimates the threshold model using the PROC MODEL approach:
title1 'Threshold Regression Example'; data switch; call streaminit('pcg', 12345); do t = 1 to 1000; e = rand('normal'); x = rand('normal'); z = rand('normal'); w = rand('uniform'); if(w<0.345) then y = 1 + 1.5*x + 2 * z + 0.5*e; else y = 1 + 1.5*x - 2 * z + 0.5*e; mylogL = (1/2)*( (log(2*3.1415)) + log( 0.5**2 ) + ((0.5*e)*( 1/0.5**2 )*(0.5*e)) ) ; output; end; run; proc means data=switch; var mylogL; run; proc model data=switch; parms sig1=1 int1 b1 b21 b22 gamma=0.5; bounds 0.0001 < sig1; a = (w - gamma)*100; /* Upper bound of integral */ d = probnorm(a); /* Normal CDF as an approx of switch */ /* Regime 1 */ y1 = int1 + x * b1 + z * b21 ; /* Regime 2 */ y2 = int1 + x * b1 + z * b22 ; /* Composite regression equation */ y = (1 - d)*y1 + d*y2; /* Resulting log-likelihood function */ logL = (1/2)*( (log(2*3.1415)) + log( sig1**2 ) + (resid.y*( 1/sig1**2 )*resid.y) ) ; errormodel y ~ general(logL); fit y / method=marquardt converge=1.0e-6; run; quit;
I hope this helps!
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