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Random Effects Generalized Ordered Probit Estimation with Autofit Option

regoprob2depvar[indepvars] [ifexp] [inrange] [,i(varname)quadrat(#)plpl(varlist)nplnpl(varlist)autofitautofit2(alpha)constraints(clist)level(#)maximize_options]

regoprob2shares all the features of the estimation commands; for help see est.regoprob2typed without arguments redisplays previous results.

The syntax of predict following

regoprob2is

predict[type]newvarname(s) [ifexp] [inrange] [,statisticoutcome(outcome)]where

statisticis

pprobability marginal on the individual effect (specify one new variable andoutcome()option, or specify k new variables, k = # of outcomes); the defaultxblinear prediction xb (outcome()option required)stdpS.E. of linear prediction (outcome()option required)stddpS.E. of difference in linear predictions (outcome()option isoutcome(outcome1,outcome2))

Note that you specify one new variable with

xb,stdp, andstddpand specify either one or k new variables withp.These statistics are available both in and out of sample; type "

predict...if e(sample)..." if wanted only for the estimation sample.

Description

regoprob2is a user-rewritten program that estimates panel data generalized ordered probit models with random effects. The actual values taken on by the dependent variable are irrelevant except that larger values are assumed to correspond to "higher" outcomes. The generalized model relaxes theparallel regressionassumption of standard ordered probit models; see help oprobit and its random effects counterpart reoprob.regoprob2modifies Stefan Boes´ regoprob (regoprob) program and is backward compatible with it but offersoneadditional powerful option, namely theautofitoption.

regoprob2supports linear constraints and allows the user to partially relax the parallel regression assumption by specifying variables innpl()orpl(). The likelihood contribution for each unit is approximated using Gauss-Hermite quadrature.

regoprob2requires installation of theregoprob,goprobitand theghquadmcommands. Theautofitoption greatly simplifies the process of identifying partial proportional odds models that fit the data.

Options

i()specifies the variable corresponding to an independent unit (e.g., a subject id).i(varname)is not optional.

quadrat()specifies the number of points to use for the Gauss-Hermite quadrature. It is optional, and the default is 12. Increasing this value improves accuracy, but also increases computation time.

pl,npl,npl(),pl(),autofitandautofit2()provide alternative means for imposing or relaxing the proportional odds/ parallel lines assumption. Only one may be specified at a time.If

autofitis selected, the standard significance level is 0.05 and an iterative process is used to identify the partial proportional odds model that best fits the data.With

autofit2(alpha)one can choose another significance level than the standard one.alphais the desired significance level for the tests;alphamust be greater than 0 and less than 1. Ifautofitis specified without parameters, the default alpha-value is .05. Note that, the higheralphais, the easier it is to reject the parallel lines assumption, and the less parsimonious the model will tend to be. This option can take a little while because several models may need to be estimated. The use ofautofitis highly recommended but the other options provide more control over the final model if the user wants it.

plspecified without parameters constrains all independent variables to meet the parallel regression assumption. It will produce results that are equivalent tooprobit.nplspecified without parameters relaxes the parallel regression assumption for all explanatory variables. This is the default option.

pl(varlist)constrains the specified explanatory variables to meet the parallel regression assumption. All other variables do not need to meet the assumption. The variables specified must be a subset of the explanatory variables.

npl(varlist)frees the specified explanatory variables from meeting the parallel regression assumption. All other explanatory variables are constrained to meet the assumption. The variables specified must be a subset of the explanatory variables.

constraints(clist)specifies the linear constraints to be applied during estimation. The default is to perform unconstrained estimation. Constraints are defined with the constraint command.constraints(1)specifies that the model is to be constrained according to constraint 1;constraints(1-4)specifies constraints 1 through 4;constraints(1-4,8)specifies 1 through 4 and 8. Keep in mind that thepl, andnploptions work by generating across-equation constraints, which may affect how any additional constraints should be specified. When using theconstraintcommand, refer to equations by their equation #, e.g. #1, #2, etc.

level(#)specifies the confidence level in percent for the confidence intervals of the coefficients; see help level.

maximize_optionscontrol the maximization process; see help maximize. You should never have to specify them.

Options forpredict

p, the default, calculates predicted probabilitiesmarginalon the individual effect.If you do not specify the

outcome()option, you must specify k new variables. For instance, say you fitted your model by typing "regoprob2 happy income health, i(persnr)" and thathappytakes on three values. Then you could type "predict p1 p2 p3, p" to obtain all three predicted probabilities.If you also specify the

outcome()option, then you specify one new variable. Say thathappytook on values 1, 2, and 3. Then typing "predict p1, p outcome(1)" would produce the samep1as above, "predict p2, p outcome(2)" the samep2as above, etc. Ifhappytook on values 7, 22, and 93, you would specifyoutcome(7),outcome(22), andoutcome(93). Alternatively, you could specify the outcomes by referring to the equation number (outcome(#1),outcome(#2), andoutcome(#3).

xbcalculates the linear prediction. You must also specify theoutcome()option.

stdpcalculates the standard error of the linear prediction. You must specify optionoutcome().

stddpcalculates the standard error of the difference in two linear predictions. You must specify optionoutcome(), in this case with two particular outcomes of interest inside the parentheses; for example, "predict sed, stdp outcome(1,3)".

outcome()specifies for which outcome the statistic is to be calculated.equation()is a synonym foroutcome(): it does not matter which one you use.outcome()andequation()can be specified using (1)#1,#2, ..., with#1meaning the first category of the dependent variable,#2the second category, etc.; or (2) values of the dependent variable.

Remarks and MethodsFor further details see

regoprob(regoprob).regoprob2uses, asregoprobthe d1 method (analytic first derviatives) of Stata'smlcommands.

Examples

. regoprob2 satisfaction age children unemployment blue_collar, i(id)

. regoprob2 satisfaction age children unemployment blue_collar, i(id)autofit

. regoprob2 satisfaction age children unemployment blue_collar, i(id)autofit2(0.1)

. predict xb1, xb outcome(#1)

-------------------------------------------------AuthorChristian Pfarr University of Bayreuth christian.pfarr@uni-bayreuth.de http://www.fiwi.uni-bayreuth.de

Andreas Schmid University of Bayreuth andreas.schmid@uni-bayreuth.de

and

Udo Schneider University of Bayreuth udo.schneider@uni-bayreuth.de --------------------------------------------

AcknowledgementsStefan Boes of the University of Zurich wrote

regoproband kindly gave us the permission to use parts of his code forregoprob2. See regoprob for a description of the formerregoprobcommand.Richard Williams of the Notre Dame Department of Sociology wrote

gologit2and kindly gave me permission to use parts of his code for programminggoprobit. For a more detailed description ofgologit2and its features, see the reference below or gologit2.

reoprob2is a user-rewritten program ofregoproband combines the features ofgologit2andregoprob, i.e., estimates panel data generalized ordered probit models with the additional option of autofitting the model.

ReferencesPfarr, C., Schmid, A. and Schneider, U. (2010). "regoprob2: An extension of estimating random effects generalized ordered probit models." Working Paper No. xx, University Bayreuth.

Boes, S. and R. Winkelmann (2006) "The Effect of Income on Positive and Negative Subjective Well-Being." unpublished manuscript.

Butler, J.S. and R. Moffitt (1982) "A computationally efficient quadrature procedure for the one-factor multinomial probit model." Econometrica 50: 761-764.

Williams, Richard (2006) "Generalized Ordered Logit/ Partial Proportional Odds Models for Ordinal Dependent Variables." The Stata Journal 6(1): 58-82. A pre-publication version is available at http://www.nd.edu/~rwilliam/gologit2/gologit2.pdf.

Also seeManual:

[U] 23 Estimation and post-estimation commands,[U] 29 Overview of Stata estimation commandsOnline: help for regoprob, estcom, postest, constraint, oprobit, goprobit, ologit, gologit, gologit2, reoprob