RE: st: Fitting a linear regression with interval (inequality) constraints using nl

[Cameron McIntosh <cnm100@hotmail.com>]

I think that you might be able to find an R or other custom solution:
van de Schoot, R., Hoijtink, H. & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443-463. http://www.statmodel.com/download/vandeschoot.pdf

Kelderman, H. (1987). LISREL models for inequality constraints in factor and regression analysis. In P. Cuttance & R. Ecob (Eds.), Structural modeling by example: applications in educational, behavioral, and social research (pp. 121-135). New York: Cambridge University Press.

Shapiro, A (1988). Towards a Unified Theory in Inequality-Constrained Testing in Multivariate Analysis. International Statistical Review, 56, 49-62.

Berger, R.L. (1989). Uniformly More Powerful Tests for Hypotheses Concerning Linear Inequalities and Normal Means. Journal of the American Statistical Association, 84, 192-199.

Liu, H., & Berger, R.L. (1995). Uniformly More Powerful One-Sided Tests for Hypotheses About Linear Inequalities. The Annals of Statistics, 23, 55-72.http://www.west.asu.edu/rlberge1/papers/aos95.pdf

Gromping, U. (2010). Inference with Linear Equality and Inequality Constraints Using R: The Package ic.infer. Journal of Statistical Software, 33(10).http://www.jstatsoft.org/v33/i10/paper

Gromping, U. (February 14, 2012). Inequality constrained inference in linear normal situations: Package ‘ic.infer’, Version 1.1-3.http://cran.r-project.org/web/packages/ic.infer/index.html
Geweke, J. (1986). Exact inference in the inequality constrained normal linear regression model. Journal of Applied Econometrics, 1(2), 127–141.

Ohtani, K. (2005). Sampling properties of the inequality constrained least squares estimator when the use of a proxy variable is inevitable. Kobe University Economic Review, 51, 11-19.http://www.econ.kobe-u.ac.jp/doc/seminar/ER/51/files/ohtani.pdf

Koenker, R., & Ng, P. (2005). Inequality Constrained Quantile Regression. Sankhya: The Indian Journal of Statistics, 67(2), 418-440.http://sankhya.isical.ac.in/search/67_2/2005019.pdf

Paula, G.A. (1999). Leverage in Inequality-constrained Regression Models. Journal of the Royal Statistical Society, Series D (The Statistician), 48(4), 529–538.

Wang, L. (2004). Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations. Annals of the Institute of Statistical Mathematics, 56(2), 251-264. http://www.ism.ac.jp/editsec/aism/pdf/056_2_0251.pdf

Wolak, F.A. (1989). Testing inequality constraints in linear econometric models. Journal of Econometrics, 41, 205-235.  http://www.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Testing%20Inequality%20Constraints%20in%20Linear%20Econometric%20Models_Wolak.pdf

Wang, J. (2000). Approximate Representation of Estimators in Constrained Regression Problems. Scandinavian Journal of Statistics,27(1), 21–33.

Zhu, J., Santerre, R., & Chang, X.-W. (2005). A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning. Journal of Geodesy, 78, 528–553.http://www.cs.mcgill.ca/~chang/pub/bayesian.pdf

de A. Lima Neto, E., & de A.T. de Carvalho, F. (2010).  Constrained linear regression models for symbolic interval-valued variables. Computational Statistics & Data Analysis, 54(2), 333-347.

Wan, A.T.K., & Ohtani, K. (2000). Minimum mean-squared error estimation in linear regression with an inequality constraint. Journal of Statistical Planning and Inference, 86(1), 157-173.
Xu, J. and Wang, J. (2008) Two-stage estimation of inequality-constrained marginal linear models with longitudinal data. Journal of Statistical Planning and Inference 138 (6), pp. 1905-1918.

Mead, J., & Renaut, R.A. (2010). Least Squares Problems with Inequality Constraints as Quadratic Constraints. Linear Algebra and its Applications, 432(8), 1936-1949.

Abdel-Aziz, M.R. (2006) On the Solution of Constrained and Weighted Linear Least Squares Problems. International Mathematical Forum, 1(22), 1067-1076.http://www.m-hikari.com/imf-password/21-24-2006/abdel-azizIMF21-24-2006.pdf ;

Cam

----------------------------------------
> Date: Tue, 14 Feb 2012 22:19:57 +0000
> Subject: Re: st: Fitting a linear regression with interval (inequality) constraints using nl
> From: njcoxstata@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> -nl- often benefits from careful initialisation of parameters.
>
> Apart from that, the only easy thing I can say is that you have a
> difficult problem.
>
> Nick
>
> On Tue, Feb 14, 2012 at 5:56 PM, Lieke Boonen (SiRM)
> <Lieke.Boonen@sirm.nl> wrote:
>
> > The problem we face is that we have to estimate a restricted OLS model for = which all betas have to be positive. We use the nl command (non lineair) in= áwhich we estimate the exp(beta) to make sure the beta is positive. However= áit takes a long time to converge and we want to know if there is an easier= ásolution.
> >
> > In SAS you use the proc nlin command in which you state bounds for the beta= áto be larger than 0. You thus specify a normal lineair regression and add = the bound that the beta is larger than 0. In Stata we tried the constraint = regression (cnsreg) but we cannot create a constraint wich beta>0.
> >
> > Is there something we are missing or is the code we have written below the = only code that Works in such a situation?
> >
> > Thanks for your help.
> >
> > We have written the following code: (76 betas)
> >
> > nl (gemiddelde_kosten_gewogen =3D exp({lnb1})*lgnw1 + exp({lnb2})*lgnw2 + e=
> > xp({lnb3})*lgnw3 + exp({lnb4})*lgnw4 + exp({lnb5})*lgnw5 ///
> > á á á á á á+ exp({lnb6})*lgnw6 + exp({lnb7})*lgnw7 + exp({lnb8})*lgnw8 + e=
> > xp({lnb9})*lgnw9 + exp({lnb10})*lgnw10 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb11})*lgnw11 + exp(=
> > {lnb12})*lgnw12 + exp({lnb13})*lgnw13 + exp({lnb14})*lgnw14 + exp({lnb15})*=
> > lgnw15 ///
> > á á á á á á+ exp({lnb16})*lgnw16 + exp({lnb17})*lgnw17 + exp({lnb18})*lgnw=
> > 18 + exp({lnb19})*lgnw19 + exp({lnb20})*lgnw20 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb21})*lgnw21 + exp(=
> > {lnb22})*lgnw22 + exp({lnb23})*lgnw23 + exp({lnb24})*lgnw24 + exp({lnb25})*=
> > lgnw25 ///
> > á á á á á á+ exp({lnb26})*lgnw26 + exp({lnb27})*lgnw27 + exp({lnb28})*lgnw=
> > 28 + exp({lnb29})*lgnw29 + exp({lnb30})*lgnw30 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb31})*ape1 + exp({l=
> > nb32})*ape2 + exp({lnb33})*ape3 + exp({lnb34})*ape4 + exp({lnb35})*ape5 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb36})*ape6 + exp({l=
> > nb37})*ape7 + exp({lnb38})*ape8 + exp({lnb39})*ape9 + exp({lnb40})*ape10 //= /
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb41})*drempel_laag_= niet + exp({lnb42})*drempel_laag + exp({lnb43})*drempel_hoog_niet + exp({ln=
> > b44})* drempel_hoog ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb45})*mph + exp({ln= b46})*eph + exp({lnb47}) * avi11 + exp({lnb48})*avi21 + exp({lnb49})*avi31 =
> > +exp({lnb50})* avi41 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb51}) * avi12 +exp(=
> > {lnb52})*avi22 + exp({lnb53})*avi32 +exp({lnb54})* avi42 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb55}) * avi13 +exp(=
> > {lnb56})*avi23 + exp({lnb57})*avi33 +exp({lnb58})* avi43 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb59}) * avi14 + exp=
> > ({lnb60})*avi24 + exp({lnb61})*avi34 +exp({lnb62})* avi44 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb63}) * ses1a + exp= ({lnb64})*ses2a + exp({lnb65}) *ses3a + exp({lnb66})*ses4a + exp({lnb67}) *= áses1b + exp({lnb68})*ses2b ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb69}) *ses3b + exp(= {lnb70})*ses4b + exp({lnb71}) * fkg0 + exp({lnb72}) * fkg1 + exp({lnb73}) *=
> > áfkg2 + exp({lnb74}) * fkg3 ///
> > á á á á á á á á á á á á á á á á á á á á á á á + exp({lnb75}) * fkg4 + exp(=
> > {lnb76}) * fkg5), noconst
>
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