{smcl} {* *! version 1.0 03aug2015}{...} {viewerjumpto "Syntax" "examplehelpfile##syntax"}{...} {viewerjumpto "Description" "examplehelpfile##description"}{...} {viewerjumpto "Options" "examplehelpfile##options"}{...} {viewerjumpto "Remarks" "examplehelpfile##remarks"}{...} {viewerjumpto "Examples" "examplehelpfile##examples"}{...} {viewerjumpto "References" "references##references"}{...} {title:Title} {phang} {bf:regmain} {hline 2} Regression Specifying a Specific Error Term Distribution {marker syntax}{...} {title:Syntax} {p 8 17 2} {cmdab:regmain} {depvar} {indepvars} [{cmd:,} {it:options}] {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab:Main} {synopt:{opt dist:ribution}}which distribution to use{p_end} {synopt:{opt init:ial}}initial values for the coefficients{p_end} {synopt:{opt nog:raph}}supresses the output of graphs{p_end} {synopt:{opt fam:ily}}allows you to compare all of the members in a distributio family. Either sgt or gb2.{p_end} {synopt:{it:{help ml##noninteractive_maxopts:maximize_options}}}control the maximization process{p_end} {synoptline} {p2colreset}{...} {marker description}{...} {title:Description} {pstd} {cmd:regmain} fits a model of {depvar} on {indepvars} using maximum likelihood with an error term distribution specified {marker options}{...} {title:Options} {dlgtab:Main} {phang} {opt distribution} SGT FAMILY: sgt, gt, st, sged, ged, t, normal, snormal, cauchy, scauchy, laplace, slaplace GB2 FAMILY: gb2, gg, ln, lt, lcauchy, gamma, exp Other: ols, lad, egb2, segb2 {phang} {opt initial} list of numbers that specifies the initial values of the coefficients. {phang} {opt nograph} supresses the output of post estimation graphs. {phang} {opt family} Select gb2 or sgt, cannot be used with distribution. This option will run MLE regression with each distribution in the family and return a table of log-likelihood values {phang}{marker noninteractive_maxopts} {it:maximize_options}: {opt dif:ficult}, {opt tech:nique(algorithm_spec)}, {opt iter:ate(#)}, [{cmdab:no:}]{opt lo:g}, {opt tr:ace}, {opt grad:ient}, {opt showstep}, {opt hess:ian}, {opt showtol:erance}, {opt tol:erance(#)}, {opt ltol:erance(#)}, {opt nrtol:erance(#)}; see {manhelp maximize R}. {marker distributions}{...} {title:Distributions} {pstd} The following distributions or regression specifications can be used in the distribution option: {p2colreset}{...} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: SGT Family}{p_end} {synopt:{cmd:sgt}}Skewed Generalized T distribution (parameters: sigma lambda p q){p_end} {synopt:{cmd:gt}}Generalized T distribution (parameters: sigma p q){p_end} {synopt:{cmd:st}}Skewed T distribution (parameters: sigma lambda q){p_end} {synopt:{cmd:sged}}Skewed Generalized Error Distribution (parameters: sigma lambda p){p_end} {synopt:{cmd:ged}}Generalized Error Distribution (parameters: sigma p){p_end} {synopt:{cmd:t}}T distribution (parameters: sigma q){p_end} {synopt:{cmd:snormal}}Skewed Normal Distribution (parameters: sigma lambda ){p_end} {synopt:{cmd:normal}}Normal Distribution (parameters: sigma ){p_end} {synopt:{cmd:scauchy}}Skewed Cauchy Distribution (parameters: sigma lambda ){p_end} {synopt:{cmd:cauchy}}Cauchy Distribution (parameters: sigma ){p_end} {synopt:{cmd:slaplace}}Skewed Laplace Distribution (parameters: sigma lambda ){p_end} {synopt:{cmd:laplace}}LaplaceDistribution (parameters: sigma){p_end} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: GB2 Family}{p_end} {synopt:{cmd:gb2}}Generalized Beta Distribution of the 2nd Kind (parameters: sigma p q){p_end} {synopt:{cmd:gg}}Generalized Gamma Distribution(parameters: sigma p ){p_end} {synopt:{cmd:ln}}Log-Normal Distribution(parameters: sigma){p_end} {synopt:{cmd:lt}}Log-T Distribution(parameters: sigma q){p_end} {synopt:{cmd:lcauchy}}Log-Cauchy Distribution(parameters: sigma ){p_end} {synopt:{cmd:gamma}}Gamma Distribution(parameters: p ){p_end} {synopt:{cmd:exp}}Exponential Distribution(parameters: none ){p_end} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Other options}{p_end} {synopt:{cmd:ols}}Default, same as reg command {p_end} {synopt:{cmd:lad}}least absolute deviations, same as qreg command{p_end} {synopt:{cmd:egb2}}exponential GB2 distribution(parameters: sigma delta p q){p_end} {synopt:{cmd:segb2}}Symmetric EGB2 distribution(parameters: sigma delta q){p_end} {p2colreset}{...} {marker remarks}{...} {title:Remarks} {pstd} In cases where the convergence is difficult, try to use the option {cmd: technique(bfgs)}, or the other {cmd: technique} options. {cmd: technique(bfgs)} is often more robust than the default {cmd: technique(nr)}. {pstd} The default maximum number of iterations is 1000. {pstd} When specifying initial values, include values for estimation parameters as well as distributional parameters. The number of distributional parameters varies depending on which distribution is selected. {marker examples}{...} {title:Examples} {phang}{cmd:. clear}{p_end} {phang}{cmd:. set obs 1000}{p_end} {phang}{cmd:. set seed 1234}{p_end} {phang}{cmd:. gen x1 = rnormal(2,3)}{p_end} {phang}{cmd:. gen x2 = runiform(1,2)}{p_end} {phang}{cmd:. gen y = 1 + x1 + x2 + rt(5)}{p_end} {phang}{cmd:. regmain y x1 x2, dist(st) initial(1 1 1 3) nograph}{p_end} {marker author}{...} {title:Author}{...} {phang} Authored by James McDonald and Jonathan Jensen at Brigham Young University. For support contact Jonathan at jonathanjens@gmail.com. {marker references}{...} {title:References} {phang} Hansen, C., J. McDonald, and P. Theodossiou (2007) "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models" Economics: The Open-Access, Open-Assessment E-Journal {p_end} {phang} McDonald J., R. Michelfelder, and P. Theodossiou (2010) "Robust Estimation with Flexible Parametric Distributions: Estimation of Utility Stock Betas" Quantitative Finance 375-387 {p_end} {phang} McDonald, J.; Newey, W. (1998). "Partially Adaptive Estimation of Regression Models via the Generalized t Distribution". Econometric Theory. 4 (3): 428–457 {p_end} {phang} McDonald, J.B. (1984) "Some generalized functions for the size distributions of income", Econometrica 52, 647–663. {p_end} {title:Also see} {phang} https://en.wikipedia.org/wiki/Generalized_beta_distribution {p_end} {phang} https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution {p_end}