{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T08:03:42Z","timestamp":1784361822331,"version":"3.55.0"},"reference-count":49,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T00:00:00Z","timestamp":1770076800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"Philosophy and Social Sciences Planning Project of Guangdong Province in China","award":["GD24XXL03"],"award-info":[{"award-number":["GD24XXL03"]}]},{"name":"Striving for the First-Class, Improving Weak Links and Highlighting Features (SIH) Key Discipline for Psychology in South China Normal University"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Applied Psychological Measurement"],"published-print":{"date-parts":[[2026,9]]},"abstract":"\n The Markov chain Monte Carlo (MCMC) method is more and more widely used to estimate variance components in generalizability theory (GT). However, as an essential part of MCMC method, uninformative priors haven\u2019t been explored and different GT researches vary in the use of uninformative priors. This study focused on effect of the different uninformative priors on estimating variance components. Based on\n p \u00d7 i \u00d7 r<\/jats:italic>\n design, eight uninformative prior distributions were chosen for simulation study and empirical study, including\n \n \n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \u223c<\/mml:mo>\n i<\/mml:mi>\n n<\/mml:mi>\n v<\/mml:mi>\n \u2212<\/mml:mo>\n g<\/mml:mi>\n a<\/mml:mi>\n m<\/mml:mi>\n m<\/mml:mi>\n a<\/mml:mi>\n \n (<\/mml:mo>\n \n 0.001<\/mml:mn>\n ,<\/mml:mo>\n 0.001<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 1],\n \n \n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \u223c<\/mml:mo>\n i<\/mml:mi>\n n<\/mml:mi>\n v<\/mml:mi>\n \u2212<\/mml:mo>\n g<\/mml:mi>\n a<\/mml:mi>\n m<\/mml:mi>\n m<\/mml:mi>\n a<\/mml:mi>\n \n (<\/mml:mo>\n \n 1<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 2],\n \n \n \n \n \n \u2009<\/mml:mo>\n \u03c3<\/mml:mi>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n \u223c<\/mml:mo>\n u<\/mml:mi>\n n<\/mml:mi>\n i<\/mml:mi>\n f<\/mml:mi>\n o<\/mml:mi>\n r<\/mml:mi>\n m<\/mml:mi>\n \n (<\/mml:mo>\n \n 0.001<\/mml:mn>\n ,<\/mml:mo>\n 1000<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [<\/jats:bold>\n prior 3\n ]<\/jats:bold>\n ,\n \n \n \n \u03c3<\/mml:mi>\n \u223c<\/mml:mo>\n u<\/mml:mi>\n n<\/mml:mi>\n i<\/mml:mi>\n f<\/mml:mi>\n o<\/mml:mi>\n r<\/mml:mi>\n m<\/mml:mi>\n \n (<\/mml:mo>\n \n 0<\/mml:mn>\n ,<\/mml:mo>\n 100<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 4],\n \n \n \n log<\/mml:mi>\n \u2061<\/mml:mo>\n \n (<\/mml:mo>\n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n \u223c<\/mml:mo>\n u<\/mml:mi>\n n<\/mml:mi>\n i<\/mml:mi>\n f<\/mml:mi>\n o<\/mml:mi>\n r<\/mml:mi>\n m<\/mml:mi>\n \n (<\/mml:mo>\n \n \u2212<\/mml:mo>\n 10<\/mml:mn>\n ,<\/mml:mo>\n 10<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 5],\n \n \n \n \n 1<\/mml:mn>\n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mfrac>\n \u223c<\/mml:mo>\n p<\/mml:mi>\n a<\/mml:mi>\n r<\/mml:mi>\n e<\/mml:mi>\n t<\/mml:mi>\n o<\/mml:mi>\n \n (<\/mml:mo>\n \n 1<\/mml:mn>\n ,<\/mml:mo>\n 0.001<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2009<\/mml:mo>\n \n [<\/mml:mo>\n \n prior<\/mml:mtext>\n \u2009<\/mml:mo>\n 6<\/mml:mn>\n <\/mml:mrow>\n ]<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ,\n \n \n \n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \n \n (<\/mml:mo>\n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n +<\/mml:mo>\n \n \u03c4<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mfrac>\n \u223c<\/mml:mo>\n u<\/mml:mi>\n n<\/mml:mi>\n i<\/mml:mi>\n f<\/mml:mi>\n o<\/mml:mi>\n r<\/mml:mi>\n m<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 7], and\n \n \n \n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \n \n 2<\/mml:mn>\n \u03c4<\/mml:mi>\n \n (<\/mml:mo>\n \n \u03c3<\/mml:mi>\n +<\/mml:mo>\n \u03c4<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mfrac>\n \u223c<\/mml:mo>\n u<\/mml:mi>\n n<\/mml:mi>\n i<\/mml:mi>\n f<\/mml:mi>\n o<\/mml:mi>\n r<\/mml:mi>\n m<\/mml:mi>\n \n (<\/mml:mo>\n \n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 8]. The three posterior point estimations (i.e., mean, median and mode) with full data and 10% missing\/sparse data were as calculated as well. After conducting simulation study and empirical study, the result shows that: (1)\n \n \n \n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \u223c<\/mml:mo>\n i<\/mml:mi>\n n<\/mml:mi>\n v<\/mml:mi>\n \u2212<\/mml:mo>\n g<\/mml:mi>\n a<\/mml:mi>\n m<\/mml:mi>\n m<\/mml:mi>\n a<\/mml:mi>\n \n (<\/mml:mo>\n \n 0.001<\/mml:mn>\n ,<\/mml:mo>\n 0.001<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 1] performs best and more stably in posterior point estimations in most scenarios, while\n \n \n \n \n 1<\/mml:mn>\n \n \u03c3<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:mfrac>\n \u223c<\/mml:mo>\n p<\/mml:mi>\n a<\/mml:mi>\n r<\/mml:mi>\n e<\/mml:mi>\n t<\/mml:mi>\n o<\/mml:mi>\n \n (<\/mml:mo>\n \n 1<\/mml:mn>\n ,<\/mml:mo>\n 0.001<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n [prior 6] is always the worst one; (2) The differences among methods are mainly reflected in variance component\n \n \n \n \n \u03c3<\/mml:mi>\n i<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n \n \n \u03c3<\/mml:mi>\n r<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and prior 6 has obvious extreme bias values with the maximum value even reaching 281.09 and 167.59; (3) Posterior mean estimations always produce the biggest biases, but posterior median estimations are the best; (4) The differences in estimating variance components between uninformative priors become greater when the number of levels of the variance components is small; (5) The results between full data and 10% missing\/sparse data are about the same. The small amount of missing\/sparse data has a minimal impact on the results. The running time of eight distributions ranges from 489.78 to 692.58 seconds and does not differ from each other too much.\n <\/jats:p>","DOI":"10.1177\/01466216261415631","type":"journal-article","created":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T11:42:47Z","timestamp":1770118967000},"page":"325-355","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Influence of Uninformative Prior Distributions for MCMC Method on Estimating Variance Components in Generalizability Theory"],"prefix":"10.1177","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2526-8682","authenticated-orcid":false,"given":"Guangming","family":"Li","sequence":"first","affiliation":[{"name":"South China Normal University"},{"name":"South China Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,2,3]]},"reference":[{"key":"e_1_3_9_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3456-0"},{"key":"e_1_3_9_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/08957347.2011.532417"},{"key":"e_1_3_9_4_1","doi-asserted-by":"publisher","DOI":"10.1177\/00131644211049746"},{"key":"e_1_3_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsp.2013.11.008"},{"key":"e_1_3_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2272(1999)17:2<118::AID-GEPI3>3.0.CO;2-V"},{"key":"e_1_3_9_7_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v076.i01"},{"key":"e_1_3_9_8_1","doi-asserted-by":"publisher","DOI":"10.3102\/00028312221106773"},{"key":"e_1_3_9_9_1","volume-title":"Scoring performance assessments based on judgements: Utilizing meta-analysis to estimate variance components in generalizability theory for unbalancedsituations","author":"Chiu C. W. T.","year":"1999","unstructured":"Chiu C. W. T. (1999). Scoring performance assessments based on judgements: Utilizing meta-analysis to estimate variance components in generalizability theory for unbalancedsituations [Unpublished doctoral dissertation]. Michigan State University."},{"key":"e_1_3_9_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0650-7"},{"key":"e_1_3_9_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpsycho.2021.01.006"},{"key":"e_1_3_9_12_1","volume-title":"The dependability of behavioral measurements: Theory of generalizability for scores and profiles","author":"Cronbach L. J.","year":"1972","unstructured":"Cronbach L. J., Gleser G. C., Nanda H., Rajaratnam N. (1972). The dependability of behavioral measurements: Theory of generalizability for scores and profiles. Wiley."},{"key":"e_1_3_9_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/3316112"},{"key":"e_1_3_9_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00180-017-0719-1"},{"key":"e_1_3_9_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/08957347.2014.973562"},{"key":"e_1_3_9_16_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428-016-0823-0"},{"key":"e_1_3_9_17_1","volume-title":"Hierarchical Bayeslinear models for meta-analysis","author":"DuMouchel W. E.","year":"1994","unstructured":"DuMouchel W. E. (1994). Hierarchical Bayeslinear models for meta-analysis. Technical Report no. 27. National Institute of Statistical Sciences."},{"key":"e_1_3_9_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12080"},{"key":"e_1_3_9_19_1","volume-title":"Applied missing data analysis","author":"Enders C. K.","year":"2010","unstructured":"Enders C. K. (2010). Applied missing data analysis. Guilford Press."},{"key":"e_1_3_9_20_1","doi-asserted-by":"publisher","DOI":"10.1177\/0272989X12453504"},{"key":"e_1_3_9_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA117A"},{"key":"e_1_3_9_22_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780429258411"},{"key":"e_1_3_9_23_1","volume-title":"Bayesian data analysis","author":"Gelman A.","year":"2014","unstructured":"Gelman A., Carlin J. B., Stern H. S., Dunson D. B., Vehtari A., Rubin D. B. (2014). Bayesian data analysis. CRC Press."},{"key":"e_1_3_9_24_1","doi-asserted-by":"publisher","DOI":"10.1037\/0021-9010.83.6.960"},{"key":"e_1_3_9_25_1","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.pan.a029818"},{"key":"e_1_3_9_26_1","doi-asserted-by":"publisher","DOI":"10.1037\/apl0000102"},{"key":"e_1_3_9_27_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428-017-0986-3"},{"key":"e_1_3_9_28_1","doi-asserted-by":"publisher","DOI":"10.3102\/00346543064003425"},{"key":"e_1_3_9_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2112"},{"key":"e_1_3_9_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/j.2333-8504.2005.tb01991.x"},{"key":"e_1_3_9_31_1","doi-asserted-by":"publisher","DOI":"10.1080\/15305050701632247"},{"key":"e_1_3_9_32_1","doi-asserted-by":"publisher","DOI":"10.3390\/su15010002"},{"key":"e_1_3_9_33_1","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2018.01065"},{"key":"e_1_3_9_34_1","doi-asserted-by":"publisher","DOI":"10.1177\/02655322211070840"},{"key":"e_1_3_9_35_1","volume-title":"Informative variance priors for Bayesian multilevel models","author":"Liu L.","year":"2024","unstructured":"Liu L. (2024). Informative variance priors for Bayesian multilevel models [Doctoral thesis]. University of Washington."},{"key":"e_1_3_9_36_1","doi-asserted-by":"publisher","DOI":"10.1177\/0149206314554215"},{"key":"e_1_3_9_37_1","unstructured":"Mao X. Shin D. Brennan R. L. (2005). Estimating the variability of estimated variance components and related statistics using the MCMC procedure: An exploratory study. In Paper presented at the Annual Meeting of the National Council on Measurement in Education Montreal 2005."},{"key":"e_1_3_9_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12144-022-02886-6"},{"key":"e_1_3_9_39_1","doi-asserted-by":"publisher","DOI":"10.1177\/0013164419846936"},{"key":"e_1_3_9_40_1","volume-title":"Informative prior distributions in multilevel\/hierarchical linear growth models: Demonstrating the use of Bayesian updating for fixed effects","author":"Schaper A. D.","year":"2014","unstructured":"Schaper A. D. (2014). Informative prior distributions in multilevel\/hierarchical linear growth models: Demonstrating the use of Bayesian updating for fixed effects [Doctoral thesis]. University of Oregon."},{"key":"e_1_3_9_41_1","doi-asserted-by":"publisher","DOI":"10.1002\/1098-2272(200009)19:2<127::AID-GEPI2>3.0.CO;2-S"},{"key":"e_1_3_9_42_1","volume-title":"Generalizability theory: A primer","author":"Shavelson R. J.","year":"1991","unstructured":"Shavelson R. J., Webb N. M. (1991). Generalizability theory: A primer. Sage."},{"key":"e_1_3_9_43_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0258(20010215)20:3<435::AID-SIM804>3.0.CO;2-E"},{"issue":"1998","key":"e_1_3_9_44_1","first-page":"1","article-title":"Noninformative Bayesian priors interpretation and problems with construction and application","volume":"3","author":"Syversveen A. R.","year":"1998","unstructured":"Syversveen A. R. (1998). Noninformative Bayesian priors interpretation and problems with construction and application. Preprint Statistics, 3(1998), 1\u201311. https:\/\/www.researchgate.net\/publication\/2288953_Noninformative_Bayesian_Priors_Interpretation_And_Problems_With_Construction_And_Applications.","journal-title":"Preprint Statistics"},{"key":"e_1_3_9_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tsc.2021.100994"},{"key":"e_1_3_9_46_1","doi-asserted-by":"publisher","DOI":"10.1080\/00223891.2023.2268193"},{"key":"e_1_3_9_47_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000107"},{"key":"e_1_3_9_48_1","doi-asserted-by":"publisher","DOI":"10.1177\/0265532207076365"},{"key":"e_1_3_9_49_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-025-08550-w"},{"key":"e_1_3_9_50_1","doi-asserted-by":"publisher","DOI":"10.3724\/SP.J.1041.2014.01897"}],"container-title":["Applied Psychological Measurement"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01466216261415631","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/01466216261415631","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01466216261415631","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T07:46:28Z","timestamp":1784360788000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/01466216261415631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,3]]},"references-count":49,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["10.1177\/01466216261415631"],"URL":"https:\/\/doi.org\/10.1177\/01466216261415631","relation":{},"ISSN":["0146-6216","1552-3497"],"issn-type":[{"value":"0146-6216","type":"print"},{"value":"1552-3497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,3]]}}}