Re: [Gretl-users] Nonlinear switching regression vs Loop constructs

On Fri, 28 Jan 2011, GREg Ory wrote: OK, so now you have two attempted solutions, Jack Lucchetti's (via nls) and mine (via grid-search over mu, sigma). Each has problems: Jack's does not constrain mu and sigma in the range that you say is acceptable, and mine has a couple of errors: missing the factor of pi/sqrt(3) in building the "logist" series, and failing to notice (as per the PDF you attached) that the coefficient on the "logist" term is constrained to equal 1 (without which constraint, I suppose, the thing is not identified). Our candidate solutions also differ in whether they build in fixed effects (mine does, by using the "panel" command) or not (Jack's). I'm not sure which is appropriate. Anyway, in case it's of interest, I'm appending below a re-write of the grid-search variant that fixes the mistakes noted above. If you want to remove the fixed effects, just put "ols" instead of "panel" for the estimation commands. In this version I've also rescaled the data to make the results comparable with Jack's NLS variant. And I've added a check: I noticed that when I ran the script the "optimal" mu and sig were at the lower limits of their ranges. But, given the way the script is written, this doesn't necessarily mean these values are "superior" -- all it means is that were not improved upon by any other values. So I also try running the panel model with mu and sig at the upper limits of their ranges -- and I find this makes no difference to the fit. That is, it appears that variation in mu and sig, within the limits you specified, is completely irrelevant to the fit of the equation. <script> open gretl_plant.gdt scalar R2max = 0 scalar optmu scalar optsig scalar nvals = 0 # apply Jack's scaling Price /=100 HHI *= 100 Domestic_Sales /= 10000 Export_Sales /= 10000 Total_import /= 10000 loop for (mu=0.28; mu<0.501; mu+=.01) --quiet loop for (sig=0.01; sig<0.201; sig+=.01) --quiet series logist = 1/(1+exp(1.8138*(mu-HHI)/sig)) series y = Price - logist panel y const Cost Domestic_Sales Export_Sales \ Soda PCFT Total_import --quiet r2 = $rsq if r2 > R2max optmu = mu optsig = sig R2max = r2 endif nvals++ endloop endloop printf "Number of points checked = %d\n", nvals printf "R^2 is maximized at %.4f for mu = %g, sig = %g\n", R2max, optmu, optsig series logist = 1/(1+exp(1.8138*(optmu-HHI)/optsig)) series y = Price - logist panel y const Cost Domestic_Sales Export_Sales \ Soda PCFT Total_import # but also try setting (mu, sig) to max acceptable values optmu = 0.5 optsig = 0.2 series logist = 1/(1+exp(1.8138*(optmu-HHI)/optsig)) series y = Price - logist panel y const Cost Domestic_Sales Export_Sales \ Soda PCFT Total_import </script> Allin Cottrell