Goodness of Fit of Logistic Regression Models for Random Graphs
Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness of fit of the regression to check if the covariates are sufficient to explain the whole topol...
Saved in:
| Published in | Journal of computational and graphical statistics Vol. 27; no. 1; pp. 98 - 109 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
02.01.2018
Taylor & Francis |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness of fit of the regression to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W-graph. Using a variational Bayes framework, we infer the residual graphon by averaging over a series of blockwise constant functions. This approach allows us to define a generic goodness-of-fit criterion, which corresponds to the posterior probability for the residual graphon to be constant. Experiments on toy data are carried out to assess the accuracy of the procedure. Several networks from social sciences and ecology are studied to illustrate the proposed methodology. |
|---|---|
| AbstractList | The logistic regression model constitutes a natural and simple tool to understand how covariates (when available) contribute to explain the topology of a binary network. After estimating the logistic parameters, one of the main questions which arises in practice is to assess the goodness of fit of the corresponding model. To address this problem, we add a general term, related to the graphon function of W-graph models, to the logistic function. Such an extra term aims at characterizing the residual structure of the network, that is not explained by the covariates. We approximate this new generic logistic model using a class of models with blockwise constant residual structure. This framework allows to derive a Bayesian procedure from a model based selection context using goodness-of-fit criteria. All these criteria depend on marginal likelihood terms for which we do provide estimates relying on two series of variational approximations. Experiments on toy data are carried out to assess the inference procedure. Finally, six networks from social sciences and ecology are studied to illustrate the proposed methodology. Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness-of-fit of the regression in order to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W-graph. Using a variational Bayes framework, we infer the residual graphon by averaging over a series of blockwise constant functions. This approach allows us to define a generic goodness-of-fit criterion, which corresponds to the posterior probability for the residual graphon to be constant. Experiments on toy data are carried out to assess the accuracy of the procedure. Several networks from social sciences and ecology are studied to illustrate the proposed methodology. Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness of fit of the regression to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W-graph. Using a variational Bayes framework, we infer the residual graphon by averaging over a series of blockwise constant functions. This approach allows us to define a generic goodness-of-fit criterion, which corresponds to the posterior probability for the residual graphon to be constant. Experiments on toy data are carried out to assess the accuracy of the procedure. Several networks from social sciences and ecology are studied to illustrate the proposed methodology. |
| Author | Robin, Stéphane Latouche, Pierre Ouadah, Sarah |
| Author_xml | – sequence: 1 givenname: Pierre surname: Latouche fullname: Latouche, Pierre – sequence: 2 givenname: Stéphane surname: Robin fullname: Robin, Stéphane – sequence: 3 givenname: Sarah surname: Ouadah fullname: Ouadah, Sarah |
| BackLink | https://hal.science/hal-01583801$$DView record in HAL |
| BookMark | eNo9kNFqwjAUhsNwMHV7BCG3u6g7J2mT9GqITB10DGS7DmmTakUbScpgb78WnVf_4ZzvPxffhIxa3zpCZghzBAUvCAKVAJgzQDlHnuZC8DsyxozLhEnMRv3cM8kAPZBJjAcAQJHLMXlde29bFyP1NV013RCF3zWxayq6dbvQnxrf0g9v3THS2ge6Na31J7oO5ryPj-S-Nsfonq45Jd-rt6_lJik-1-_LRZFUHPIuYbVhVhlRidIpi6KWFkxVSpEClznPmACVW1mXJThrec4qZFwYJpVzwNOUT8nz5e_eHPU5NCcTfrU3jd4sCj3sADPFFeAP9mx2YavgYwyuvhUQ9GBM_xvTgzF9Ndb3ZpfeIXY-3EppqgQDnvE_NylnuQ |
| CitedBy_id | crossref_primary_10_1007_s10462_021_10088_y crossref_primary_10_1109_ACCESS_2023_3314336 crossref_primary_10_1109_TSIPN_2022_3188458 crossref_primary_10_1111_rssc_12489 crossref_primary_10_1080_03610918_2022_2032158 crossref_primary_10_1080_10618600_2018_1554486 crossref_primary_10_1093_biomet_asab057 crossref_primary_10_1111_sjos_12410 |
| Cites_doi | 10.1007/978-0-387-75969-2 10.1109/TCBB.2006.55 10.1038/nrg1272 10.1214/13-AOAS691 10.18637/jss.v040.i08 10.1198/016214502388618906 10.1023/A:1008932416310 10.1016/j.csda.2012.01.027 10.18637/jss.v024.i01 10.1023/A:1021692202530 10.1073/pnas.252631999 10.1137/S003614450342480 10.1086/jar.33.4.3629752 10.1007/s11222-007-9046-7 10.1111/j.2517-6161.1977.tb01600.x 10.1214/10-AOAS382 10.18637/jss.v070.i01 10.1007/s003579900004 10.1198/016214507000000446 10.1001/jama.1997.03550100049038 10.1016/0378-8733(83)90021-7 10.1073/pnas.0912983107 10.1016/j.patcog.2008.06.019 10.1103/RevModPhys.74.47 10.1086/228667 10.1561/2200000005 10.1016/j.jctb.2006.05.002 10.1016/j.csda.2013.02.005 10.1371/journal.pone.0001740 10.1214/14-EJS903 10.1007/978-1-4614-6868-4 10.1038/30918 10.1016/j.jtrangeo.2013.03.004 10.1111/j.1467-985X.2007.00471.x 10.1177/1471082X1001200105 10.1214/10-AOAS361 10.1051/proc/201447004 10.1198/016214501753208735 10.1214/14-AOS1272 10.1098/rspa.1946.0056 10.1080/01621459.1995.10476572 10.1080/01621459.1987.10478385 10.1016/j.patrec.2010.01.026 |
| ContentType | Journal Article |
| Copyright | 2018 American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2018 American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION 1XC |
| DOI | 10.1080/10618600.2017.1349663 |
| DatabaseName | CrossRef Hyper Article en Ligne (HAL) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Mathematics |
| EISSN | 1537-2715 |
| EndPage | 109 |
| ExternalDocumentID | oai_HAL_hal_01583801v1 10_1080_10618600_2017_1349663 44862035 |
| GroupedDBID | -~X .4S .7F .DC .QJ 0BK 0R~ 2AX 30N 4.4 5GY AAAVI AAENE AAJMT AAKYL AALDU AAMIU AAPUL AAQRR ABBHK ABCCY ABFAN ABFIM ABJNI ABJVF ABLIJ ABLJU ABPEM ABQHQ ABTAI ABXSQ ABXUL ABXYU ABYWD ACGFO ACGFS ACIWK ACMTB ACTIO ACTMH ADACV ADCVX ADGTB ADODI AEGXH AEGYZ AEISY AELLO AENEX AEOZL AEPSL AEUPB AEYOC AFOLD AFVYC AFWLO AFXKK AGDLA AGMYJ AHDLD AIAGR AIJEM AIRXU AKBRZ AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AQRUH ARCSS AVBZW BDTQF BHOJU BLEHA CCCUG CS3 D0L DGEBU DKSSO DQDLB DSRWC DU5 EBS ECEWR EFSUC EJD E~A E~B F5P FUNRP FVPDL GTTXZ HF~ HQ6 HZ~ H~P IAO IEA IGG IGS IOF IPNFZ J.P JAA JAAYA JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JST KYCEM M4Z MS~ NA5 NY~ O9- P2P PQQKQ RIG RNANH ROSJB RTWRZ RWL RXW S-T SA0 SNACF TAE TEJ TFL TFT TFW TN5 TTHFI TUS UT5 UU3 V1K WZA XWC ZGOLN ~S~ AAYXX ABPAQ ABQDR AHDZW AWYRJ CITATION H13 IPSME TBQAZ TDBHL TUROJ 07G 1XC 29K AAIKQ AAKBW ACAGQ ACGEE ADULT AELPN AEUMN AGCQS AGLEN AGROQ AHMOU ALCKM AMATQ AMXXU BCCOT BPLKW C06 CRFIH D-I DMQIW DWIFK FEDTE GIFXF HGD HVGLF IVXBP JSODD LJTGL NUSFT QCRFL RNS TAQ TFMCV TOXWX UB9 |
| ID | FETCH-LOGICAL-c309t-2fa2d8a6c6be8d16f7d0acb76403793526089d7fbb0edd392c1236a278ee03443 |
| ISSN | 1061-8600 |
| IngestDate | Fri Sep 06 12:48:28 EDT 2024 Thu Aug 22 11:18:51 EDT 2024 Wed Mar 06 03:17:53 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | variational approximations W-graph model logistic regression Random graphs |
| Language | English |
| License | Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c309t-2fa2d8a6c6be8d16f7d0acb76403793526089d7fbb0edd392c1236a278ee03443 |
| ORCID | 0000-0003-1045-069X 0000-0002-6206-6895 |
| PageCount | 12 |
| ParticipantIDs | hal_primary_oai_HAL_hal_01583801v1 crossref_primary_10_1080_10618600_2017_1349663 jstor_primary_44862035 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-01-02 |
| PublicationDateYYYYMMDD | 2018-01-02 |
| PublicationDate_xml | – month: 01 year: 2018 text: 2018-01-02 day: 02 |
| PublicationDecade | 2010 |
| PublicationTitle | Journal of computational and graphical statistics |
| PublicationYear | 2018 |
| Publisher | American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America Taylor & Francis |
| Publisher_xml | – name: American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America – name: Taylor & Francis |
| References | cit0033 cit0034 cit0031 cit0032 cit0030 Caron F. (cit0011) 2008 Hoff P. (cit0026) 2008 cit0039 cit0037 cit0038 Airoldi E. M. (cit0001) 2013 cit0035 cit0036 Yang J. J. (cit0055) 2014 cit0022 cit0023 cit0020 cit0021 Coleman J. (cit0015) 1966; 12 Bishop C. (cit0008) 2003 Beal M. (cit0006) 2002 cit0028 cit0029 Chan S. (cit0012) 2014 cit0027 cit0024 cit0046a cit0025 Analytics R. (cit0003) 2015 cit0056 cit0053 cit0010 cit0054 cit0051 Latouche P. (cit0040) 2015 cit0052 cit0050 Dempster A. (cit0017) 1977; 39 Bishop C. (cit0007) 2006 cit0019 Diaconis P. (cit0018) 2008; 7 cit0016 Breiger R. (cit0009) 1981; 12 cit0013 cit0057 cit0014 cit0058 cit0044 cit0045 cit0042 cit0043 cit0041 cit0004 cit0048 cit0005 cit0049 cit0002 cit0046 cit0047 |
| References_xml | – ident: cit0047 doi: 10.1007/978-0-387-75969-2 – ident: cit0036 doi: 10.1109/TCBB.2006.55 – ident: cit0005 doi: 10.1038/nrg1272 – ident: cit0032 doi: 10.1214/13-AOAS691 – volume-title: Pattern Recognition and Machine Learning year: 2006 ident: cit0007 contributor: fullname: Bishop C. – volume: 7 start-page: 33 year: 2008 ident: cit0018 publication-title: Rend. Mat. Appl. contributor: fullname: Diaconis P. – ident: cit0021 doi: 10.18637/jss.v040.i08 – ident: cit0027 doi: 10.1198/016214502388618906 – ident: cit0030 doi: 10.1023/A:1008932416310 – ident: cit0051 doi: 10.1016/j.csda.2012.01.027 – ident: cit0024 doi: 10.18637/jss.v024.i01 – ident: cit0034 doi: 10.1023/A:1021692202530 – ident: cit0054 – ident: cit0050 – ident: cit0014 doi: 10.1073/pnas.252631999 – ident: cit0044 doi: 10.1137/S003614450342480 – ident: cit0056 doi: 10.1086/jar.33.4.3629752 – ident: cit0016 doi: 10.1007/s11222-007-9046-7 – volume: 39 start-page: 1 year: 1977 ident: cit0017 publication-title: Journal of the Royal Statistical Society doi: 10.1111/j.2517-6161.1977.tb01600.x contributor: fullname: Dempster A. – ident: cit0037 doi: 10.1214/10-AOAS382 – ident: cit0033 doi: 10.18637/jss.v070.i01 – ident: cit0048 doi: 10.1007/s003579900004 – ident: cit0029 doi: 10.1198/016214507000000446 – ident: cit0046a doi: 10.1001/jama.1997.03550100049038 – ident: cit0028 doi: 10.1016/0378-8733(83)90021-7 – start-page: 1060 year: 2014 ident: cit0055 publication-title: Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics contributor: fullname: Yang J. J. – ident: cit0046 doi: 10.1073/pnas.0912983107 – ident: cit0057 doi: 10.1016/j.patcog.2008.06.019 – ident: cit0002 doi: 10.1103/RevModPhys.74.47 – ident: cit0010 doi: 10.1086/228667 – ident: cit0023 doi: 10.1561/2200000005 – start-page: 657 year: 2008 ident: cit0026 publication-title: Advances in Neural Information Processing Systems contributor: fullname: Hoff P. – volume: 12 start-page: 481 year: 1966 ident: cit0015 publication-title: Behavioral Science contributor: fullname: Coleman J. – ident: cit0041 doi: 10.1016/j.jctb.2006.05.002 – ident: cit0022 doi: 10.1016/j.csda.2013.02.005 – ident: cit0049 doi: 10.1371/journal.pone.0001740 – ident: cit0039 doi: 10.1214/14-EJS903 – year: 2015 ident: cit0003 publication-title: doMC: Foreach Parallel Adaptor for ‘Parallel’, R Package Version 1.3.4 contributor: fullname: Analytics R. – start-page: 208 year: 2014 ident: cit0012 publication-title: Proceedings of the 31st International Conference on Machine Learning (ICML-14) contributor: fullname: Chan S. – ident: cit0020 doi: 10.1007/978-1-4614-6868-4 – ident: cit0004 – ident: cit0053 doi: 10.1038/30918 – ident: cit0019 doi: 10.1016/j.jtrangeo.2013.03.004 – ident: cit0025 doi: 10.1111/j.1467-985X.2007.00471.x – ident: cit0038 doi: 10.1177/1471082X1001200105 – ident: cit0042 doi: 10.1214/10-AOAS361 – ident: cit0043 doi: 10.1051/proc/201447004 – start-page: 692 year: 2013 ident: cit0001 publication-title: Advances in Neural Information Processing Systems contributor: fullname: Airoldi E. M. – ident: cit0045 doi: 10.1198/016214501753208735 – start-page: 1 year: 2015 ident: cit0040 publication-title: Statistics and Computing contributor: fullname: Latouche P. – ident: cit0013 doi: 10.1214/14-AOS1272 – start-page: 453 volume-title: Bayesian Statistics 7: Proceedings of the 7th Valencia International Meeting year: 2002 ident: cit0006 contributor: fullname: Beal M. – year: 2008 ident: cit0011 publication-title: Proceedings of the 25th International Conference on Machine Learning contributor: fullname: Caron F. – ident: cit0031 doi: 10.1098/rspa.1946.0056 – ident: cit0035 doi: 10.1080/01621459.1995.10476572 – ident: cit0052 doi: 10.1080/01621459.1987.10478385 – volume: 12 start-page: 156 year: 1981 ident: cit0009 publication-title: Social Networks contributor: fullname: Breiger R. – start-page: 57 year: 2003 ident: cit0008 publication-title: Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence contributor: fullname: Bishop C. – ident: cit0058 doi: 10.1016/j.patrec.2010.01.026 |
| SSID | ssj0001697 |
| Score | 2.271826 |
| Snippet | Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted,... The logistic regression model constitutes a natural and simple tool to understand how covariates (when available) contribute to explain the topology of a... |
| SourceID | hal crossref jstor |
| SourceType | Open Access Repository Aggregation Database Publisher |
| StartPage | 98 |
| SubjectTerms | Mathematics Modeling Statistics |
| Title | Goodness of Fit of Logistic Regression Models for Random Graphs |
| URI | https://www.jstor.org/stable/44862035 https://hal.science/hal-01583801 |
| Volume | 27 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1BT9swFLY6dmEHBGxoZYCsaTeUzkmc2Dmhig3KBt0kisQtcmyH7rBmGu0O_BH-Ls92nDSiSLBLWrlu0vp9fu_Zfu97CH2isQxZoaMgLZkOqNnDzzKhgoyKRFIiC22TxC7G6eiKfrtOrnu9-6WopcW8GMi7lXkl_yNVaAO5mizZF0i2uSk0wHuQL1xBwnB9loxPq0pZVQUeX_nLnum7jB7Ly3zjQlxnrtqN5V04BMukqt-Hlqb69gnHVNpCD36T0Gys2-4uf9K0W2rnJpLHFFUHyVt3FGxsG0xrU8uaSDLRnt__WAglpt396HrjIeR246Fdpk4e1QBZUqPgJQQ8Je7ERXvVyoKIueRNr3sdL0AHY06RutLUtUkOLYPCY23vwiPNw8yzTJweGxi6xbTWmR127dHwMv_55SQ_Pxt_737a0GyPhuf5FFAALhKPwXT_g2X164hliVnVx2TcmPiwrtrj_6ZPDePk88pf03F6Xk1NyO1y9Kv1ZSabaKOWNR46RG2hnp5tozcXDYPv7TZav2wk_RYdeaDhqsQANPPigYZboGEHNAxAww5o2AHtHbo6-To5HgV15Y1AwmydB1EpIsVFKlOYqyqEeayIkAVLKYlBoSewCOaZYmVREK0UuNjSkPiIiHGtDYdkvIPWZtVMv0c4LOOIMCE5WAtaypTHmkiuQ8a0KiRXfTTwQ5P_cQQreVjz1vqxzM1Y5vVY9tFHIyPfd7Xc-mjHjm_TjVJYupM42X3Otz-g9Rbwe2ht_neh98H3nBcHFgcP-HaAEw |
| link.rule.ids | 230,315,786,790,891,27957,27958 |
| linkProvider | Taylor & Francis |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Goodness+of+fit+of+logistic+regression+models+for+random+graphs&rft.jtitle=Journal+of+computational+and+graphical+statistics&rft.au=Latouche%2C+Pierre&rft.au=Robin%2C+Stephane&rft.au=Ouadah%2C+Sarah&rft.date=2018-01-02&rft.pub=Taylor+%26+Francis&rft.issn=1061-8600&rft.eissn=1537-2715&rft.volume=27&rft.issue=1&rft.spage=98&rft.epage=109&rft_id=info:doi/10.1080%2F10618600.2017.1349663&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai_HAL_hal_01583801v1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1061-8600&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1061-8600&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1061-8600&client=summon |