The PROBIT Procedure - support.sas.com

1 SAS/STAT User s GuideThe PROBIT ProcedureThis document is an individual chapter fromSAS/STAT User s correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. User s , NC: SAS Institute 2013, SAS Institute Inc., Cary, NC, USAAll rights reserved. Produced in the United States of a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or byany means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS a web download or e-book.

2 Your use of this publication shall be governed by the terms established by the vendor at the timeyou acquire this scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher isillegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronicpiracy of copyrighted materials. Your support of others rights is Government License Rights; Restricted Rights:The Software and its documentation is commercial computer softwaredeveloped at private expense and is provided with RESTRICTED RIGHTS to the United States Government.

3 Use, duplication ordisclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, asapplicable, FAR , DFAR (a), DFAR (a) and DFAR and, to the extent required under law, the minimum restricted rights as set out in FAR (DEC 2007). If FAR is applicable, this provisionserves as notice under clause (c) thereof and no other notice is required to be affixed to the Software or documentation. TheGovernment s rights in Software and documentation shall be only those set forth in this Institute Inc.

4 , SAS Campus Drive, Cary, North Carolina 2013 SAS provides a complete selection of books and electronic products to help customers use SAS software to its fullest potential. Formore information about our offerings, call and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in theUSA and other countries. indicates USA brand and product names are trademarks of their respective and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc.

5 In the USA and other countries. indicates USA registration. Other brand and product names are trademarks of their respective companies. 2013 SAS Institute Inc. All rights reserved. all that you need on your journey to knowledge and additional books and Greater Insight into Your SAS Software with SAS 79 The PROBIT ProcedureContentsOverview: PROBIT Procedure ..6728 Getting Started: PROBIT Procedure ..6729 Estimating the Natural Response Threshold Parameter ..6729 Syntax: PROBIT Procedure ..6733 PROC PROBIT Statement.

6 6733BY Statement ..6739 CDFPLOT Statement ..6739 CLASS Statement ..6748 EFFECTPLOT Statement ..6751 ESTIMATE Statement ..6752 INSET Statement ..6753 IPPPLOT Statement ..6755 LPREDPLOT Statement ..6763 LSMEANS Statement ..6771 LSMESTIMATE Statement ..6772 MODEL Statement ..6773 OUTPUT Statement ..6779 PREDPPLOT Statement ..6780 SLICE Statement ..6789 STORE Statement ..6789 TEST Statement ..6790 WEIGHT Statement ..6790 Details: PROBIT Procedure ..6790 Missing Values ..6790 Response Level Ordering ..6790 Computational Method.

7 6792 Distributions ..6793 INEST=SAS-data-set..6793 Model Specification ..6794 Lack-of-Fit Tests ..6794 Rescaling the Covariance Matrix ..6795 Tolerance Distribution ..6796 Inverse Confidence Limits ..6796 OUTEST=SAS-data-set..6797 XDATA=SAS-data-set..6798 Traditional High-Resolution Graphics ..67986728 FChapter 79: The PROBIT ProcedureDisplayed Output ..6800 ODS Table Names ..6801 ODS Graphics ..6802 Examples: PROBIT Procedure ..6805 Example : Dosage Levels ..6805 Example : Multilevel Response ..6814 Example : Logistic Regression.

8 6820 Example : An Epidemiology Study ..6822 Example : Model Postfitting analysis ..6833 References ..6836 Overview: PROBIT ProcedureThe PROBIT Procedure calculates maximum likelihood estimates of regression parameters and the natural(or threshold) response rate for quantal response data from biological assays or other discrete event data. Thisincludes PROBIT , logit, ordinal logistic, and extreme value (or gompit) regression analysis developed from the need to analyze qualitative (dichotomous or polytomous) dependentvariables within the regression framework.

9 Many response variables are binary by nature (yes/no), whileothers are measured ordinally rather than continuously (degree of severity). Researchers have shown ordinaryleast squares (OLS) regression to be inadequate when the dependent variable is discrete (Collett 2003; Agresti2002). PROBIT or logit analyses are more appropriate in this PROBIT Procedure computes maximum likelihood estimates of the parameters andCof the probitequation by using a modified Newton-Raphson algorithm. When the responseYis binary, with values 0 and1, the PROBIT equation /where is a vector of parameter estimatesFis a cumulative distribution function (normal, logistic, or extreme value)xis a vector of explanatory variablespis the probability of a responseCis the natural (threshold) response rateNotice that PROC PROBIT , by default, models the probability of thelowerresponse levels.

10 The choice ofthe distribution functionF(normal for the PROBIT model, logistic for the logit model, and extreme value orGompertz for the gompit model) determines the type of analysis . For most problems, there is relatively littledifference between the normal and logistic specifications of the model. Both distributions are symmetricabout the value zero. The extreme value (or Gompertz) distribution, however, is not symmetric, approaching0 on the left more slowly than it approaches 1 on the right. You can use the extreme value distribution wheresuch asymmetry is Started: PROBIT ProcedureF6729 For ordinal response models, the response,Y, of an individual or an experimental unit can be restricted to oneof a (usually small) number, 1/, of ordinal values, denoted for convenience by1;:::;k; example, the severity of coronary disease can be classified into three response categories as 1=no disease,2=angina pectoris, and 3=myocardial infraction.