180 心理科学 编码的优化，因此MCMC算法耗时较多。对于1000个被试 Responses.Journal of Educational and Behaviorial Statistics.1999 60个项目的测验，若链长为5000，链数为1，MCMC算法的参 24(4):342-366 数估计则需化费1一2个小时。若链长更长，链数更多，则耗 6 Bradlow E T,Wainer H,Wang X.A Bayesian random effects 时更多，这是MCMC算法中一个值得注意的问题，也是 model for testlets.Psychometrika.1999,64:153-168 MCMC算法有待进一步研究的问题（如算法的优化等）。 7 Wainer H.Bradlow E T.,Du Z.Testlet response theory:An analog for the 3PL model useful in adaptive testing.In:Van der 前已述及，RT中有些模型的参数估计非常复杂，如多 维IRT,题组(testlet)相依IRT及高维的认知诊断模型（如 Linden WJ.Glas CA W.(Eds.).Computerized adaptive testing: Theory and practice.Boston,MA:Kluwer-Nijhoff,2001:245- Fusion model,High-order DINA model).,对于这些模型的参 270 数估计，E一M算祛难于实现，但可用MCMC算法来实现，能 8 Hatz S M.Rousson L.Stout W.Skills diagnosis:Theory and 更好地解决实际问题。这也是本研究正在研究的间题。 practice(Technical Report).Princeton.N:Educational Testing Service 5参考文献 9 Jimmy D T,Douglas J A.Higher-order latent trait models for 1王权编译.“马尔可夫链蒙特卡洛”(MCMC)方法在估计RT陕 cognitive diagnosis.Psychometrika,2004,69(3):333-353 型参数中的应用.考试研究，2006.(4)：45-63 10 Jiang Yanlin.Estimating parameters for multidimensional item 2漆书青，现代测量理论在考试中的应用。华中师范大学出版社， response theory models by MCMC methods (unpublished doctoral 2003:233-268 dissertation).Michigan State University,2005 3 Albert J H.Bayesian estimation of normal ogive item response 11 Gentle J E.Elements of Computational Statistics.Science Press. curves using Gibbs sampling.Journal of Educational Statistics, 2006:39-66 1992,(17):251-269 12龚光鲁、钱敏平.应用随机过程教程.清华大学出版社，2003：191 4 Richard Patz J,Brian Junker W.A straightforward approech to Markov -202 Chain Monte Carlo Methods for Item Response Models,Joumal of 13茆诗松、王静龙、禳骁龙.高等数理统计.高等教育出版社，1998： Educational and Behaviorial Statistics,1999,24(2):146-178 444-459 5 Richard Patz J,Brian Junker W.Application and Extensions of 14 Mislevy R J.Bock R D.Bilog3 Item analysis and test scoring with MCMC in IRT:Multipe Item Types,Missing Data,and Rated binary Logistic Models 2nded.Scientific Sotfware Ine..1990 New Method of Parameter Estimation under the IRT Model-MCMC Algorithm Tu Dongbol,Qi Shuqing,Cai Yan2,Dai Haiqi,Ding Shuliang3 College of Education,Jiangxi Normal University,Nanchang,330027) (2 College of Mathemetic and Information Science,Jiangxi Normal University,Nanchang,330027) (College of Comprter Information Engineering,Jiangxi Normal University,Nanchang,330027) Abstract This paper demonstrates the MCMC method,which is now widely used in parameter estimation in the IRT model abroad and discusses its application in the parameter estimation of IRT models.M-H algorithm within Gibbs samplings to estimate the parameters of 2PLM and 3PLM under some conditions such as small,medium or large samples was wsed.To test the feasibility and veracity of the MCMC method,the Monte Carlo simulation method was used.The simulation researches show (1)the MCMC method can be used in the parameter estimation of 2PLM and 3PLM;(2)the MCMC method is better than E-M in the veracity of parameter estimation;(3)the MCMC method will take more time to estimate parameters;(4)the MCMC method can be used to estimate parameters of other IRT. Key words:MCMC,Logistic model,E-M algorithm (上接第165页) A Review of Developmental Research on Children of Parental Divorce Lin Xunyi,Sang Biao (Department of Psychology,East China Normal University,Shanghai,200062) Abstract This review presented literature on divorce.It involved the changes of theorical perspectives and methodology in the research on divorce.It also probed into the mechanism that produced developmental trajectories into factors that influenced the development of children with divorced parents as well as a transactional model examining the multiple trajectories of interacting risks and protective factors.Finally,suggestions on public policies in China which will promote the well-being of children of parental divorce were made. Key words:children with divoreed parents,developmental research,public policy 万方数据180 心理科学 编码的优化，因此MCMC算法耗时较多。对于1000个被试 60个项目的测验，若链长为5000、链数为1，MCMC算法的参 数估计则需化费1—2个小时。若链长更长、链数更多．则耗 时更多，这是MCMC算法中一个值得注意的问题，也是 MCMC算法有待进一步研究的问题(如算法的优化等)。 前已述及，IRT中有些模型的参数估计非常复杂，如多 维IRT、题组(testlet)相依IRT及高维的认知诊断模型(如 Fusion model，High—order DINA model)，对于这些模型的参 数估计，E—M算法难予实现，但可用MCMC算法来实现，能 更好地解决实际问题。这也是本研究正在研究的问题。 5 参考文献 4 5 王权编译．“马尔可夫链蒙特卡洛”(MCMC)方法在估计IRT模 型参数中的应用．考试研究，2006，(4)：45—63 漆书青．现代测量理论在考试中的应用．华中师范大学出版社， 2003：233—268 Albert J H．Bayesian estimation of normal ogive item response curves using Gibbs sampling．Journal of Educational Statistics， 1992，(17)：25l一269 Richard Patz J，Brian Junker W．A straightforward approach to Markov Chain Monte Carlo Methods for Item Response Models，Jourml of Educational and Behaviorial Statistics，1999，24(2)：146—178 Riehard Patz J，Brian Junker W．Application and Extensions of MCMC in IRT：Multipe Item Types，Missing Data，and Rated Responses．Journal of Educational and Behavioria[Statistics，1999， 24(4)：342 366 6 Bradlow E T．Wainer H．Wang X．A Bayesian random effects model for testlets．Psychometrika．1999．64：153—168 7 Wainer H．Bradlow E T．，Du Z．Testlet response theory：An analog for the 3PL model useful in adaptive testing In：Van der Linden W J，Glas C A W．(Eds．)．Computerized adaptive testing： Theory and practice．Boston，MA：Kluwer—Nijhoff，2001：245— 270 8 Hatz S M，Rousson L，Stout W．Skills diagnosis：Theory and practice(Technical Report)．Princeton，NJ：Educational Testing Serviee 9 Jimmy D T。Douglas J A．Higher—order latent trait models for cognitive diagnosis．Psyehometrika，2004，69(3)：333—353 10 Jiang Yanlin．Estimating parameters for multidimensional item response theory models by MCMC methods(unpublished doctoral dissertation)．Michigan State University，2005 11 Gentle J E．Elements of Computational Statistics．Science Press， 2006：39—66 12龚光鲁、钱敏乎．应用随机过程教程．清华大学出版社，2003：191 ～202 13茆诗松、王静龙、濮晓龙．高等数理统计．高等教育出版社，1998： 444—459 14 Mislevy R J，Boek R D．Bil093 Item analysis and test scoring with binary Logistic Models 2nded．Scientific Software Inc．，1990 New Method of Parameter Estimation under the IRT Model～MCMC Algorithm 乳Dongb01，Qi Shuqin91，Cai Yan2，Dai Haiqil，Ding Shulian93 (1 College of Education，Jiangxi Normal University，Nanchang，330027) (2 College of Mathemetie and Information Science，Jiangxi Normal University，Nanchang，330027) (3 CoUege of Comprter Information Engineering，Jiangxi Normal University，Nanehang，330027) Abstraet This paper demonstrates the MCMC method．which is now widely used in parameter estimation in the IRT model abroad and discusses its application in the parameter estimation of IRT models．M·H algorithm within Gibbs samplings to estimate the parameters of 2PLM and 3PLM under some conditions such as small．medium or large samples was wsed．To test the feasibility and veracity of the MCMC method，the Monte Carlo simulation method was used．The simulation researches show(1)the MCMC method can be used in the parameter estimation of 2PLM and 3PLM；(2)the MCMC method ia better than E—M in the veracity of parameter estimation；(3)the MCMC method will take more time to estimate parameters；(4)the MCMC method can be used to estimate parameters of other IRT． Key words：MCMC，Logistic model，E—M algorithm (上接第165页) A Review of Developmental Researeh oil Children of Parental Divoree Lin Xunyi，Sang Biao (Department of Psychology，East China Normal University，Shanghai，200062) Abstract This review presented literature on divorce．It involved the changes of theorical perspectives and methodology in the research on divorce．It also probed into the mechanism that produced developmental trajectories，into factors that influenced the development。of children with divorced parentS as well as a transactional modeI examining the multiple trajectories of interacting risks and protecti‘ve factors．Finally，suggestions on public policies in China which will promote the well-being of children of parental divorce were made． Key words：children with divorced parents，developmental research，public policy 万方数据