{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T01:21:39Z","timestamp":1777857699752,"version":"3.51.4"},"reference-count":64,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>It is important for demographic analyses and policy-making to obtain accurate models of spatial diffusion, so that policy experiments can reflect endogenous spatial spillovers appropriately. Likewise, it is important to obtain accurate estimates and forecasts of demographic variables such as age-specific fertility rates, by regions and over time, as well as the uncertainty associated with such estimation. Here, we consider Bayesian hierarchical models with separable spatio-temporal dependence structure that can be estimated by borrowing strength from neighbouring regions and all years. Further, we do not consider the adjacency structure as a given, but rather as an object of inference. For this purpose, we use the local similarity of temporal patterns by developing a spatial clustering model based on Bayesian nonparametric smoothing techniques. The Bayesian inference provides the uncertainty associated with the clustering configurations that is typically lacking in classical analyses of large data sets in which a unique clustering representation can be insufficient. The proposed model is applied to 16-year data on age-specific fertility rates observed over 28 regions in Portugal, and provides statistical inference on the number of clusters, and local scaling and shrinkage levels. The corresponding central clustering configuration is able to capture spatial diffusion that has key demographic interpretations. Importantly, the exercise aids identification of peripheral regions with poor demographic prospects and development of regional policy for such places.<\/jats:p>","DOI":"10.2478\/jos-2021-0028","type":"journal-article","created":{"date-parts":[[2021,9,14]],"date-time":"2021-09-14T17:00:24Z","timestamp":1631638824000},"page":"611-653","source":"Crossref","is-referenced-by-count":4,"title":["Spatio-Temporal Patterns in Portuguese Regional Fertility Rates: A Bayesian Approach for Spatial Clustering of Curves"],"prefix":"10.1177","volume":"37","author":[{"given":"Zhen","family":"Zhang","sequence":"first","affiliation":[{"name":"Eli Lilly and Company , Indianapolis Indiana, U.S.A."}]},{"given":"Arnab","family":"Bhattacharjee","sequence":"additional","affiliation":[{"name":"Heriot-Watt University and National Institute of Economic and Social Research, Spatial Economics and Econometrics Centre. (SEEC) , Mary Burton Building, Edinburgh EH14 4AS, Scotland, United Kingdom ."}]},{"given":"Jo\u00e3o","family":"Marques","sequence":"additional","affiliation":[{"name":"University of Aveiro , Department of Social, Political and Territorial Sciences , Averiro , Portugal ."}]},{"given":"Tapabrata","family":"Maiti","sequence":"additional","affiliation":[{"name":"Michigan State University , Department of Statistics and Probability , East Lansing Michigan, U.S.A."}]}],"member":"179","published-online":{"date-parts":[[2021,9,13]]},"reference":[{"key":"2023121311155536244_j_jos-2021-0028_ref_001","doi-asserted-by":"crossref","unstructured":"Alkema, L., A.E. Raftery, P. Gerland, S.J. Clark, and F. Pelletier. 2012. \u201cEstimating the total fertility rate from multiple imperfect data sources and assessing its uncertainty\u201d. Demographic Research 26: 331\u2013362. DOI: https:\/\/doi.org\/10.4054\/DemRes.2012.26.15.10.4054\/DemRes.2012.26.15383753924273449","DOI":"10.4054\/DemRes.2012.26.15"},{"key":"2023121311155536244_j_jos-2021-0028_ref_002","doi-asserted-by":"crossref","unstructured":"Alkema, L., A.E. Raftery, P. Gerland, S.J. Clark, F. Pelletier, T. Buettner, and G.K. Heilig. 2011. \u201cProbabilistic projections of the total fertility rate for all countries\u201d. Demography 48(3): 815\u2013839. DOI: https:\/\/doi.org\/10.1007\/s13524-011-0040-5.10.1007\/s13524-011-0040-5336799921748544","DOI":"10.1007\/s13524-011-0040-5"},{"key":"2023121311155536244_j_jos-2021-0028_ref_003","doi-asserted-by":"crossref","unstructured":"Assun\u00e7\u00e3o, R.M., C.P. Schmertmann, J.E. Potter, and S.M. Cavenaghi. 2005. \u201cEmpirical bayes estimation of demographic schedules for small areas\u201d. Demography 42(3): 537\u2013558. DOI: https:\/\/doi.org\/10.1353\/dem.2005.0022.10.1353\/dem.2005.002216235612","DOI":"10.1353\/dem.2005.0022"},{"key":"2023121311155536244_j_jos-2021-0028_ref_004","doi-asserted-by":"crossref","unstructured":"Bailey, N., S. Holly, and M.H. Pesaran. 2016. \u201cA two-stage approach to spatio-temporal analysis with strong and weak cross-sectional dependence\u201d. Journal of Applied Econometrics 31(1): 249\u2013280. DOI: https:\/\/doi.org\/10.1002\/jae.2468.10.1002\/jae.2468","DOI":"10.1002\/jae.2468"},{"key":"2023121311155536244_j_jos-2021-0028_ref_005","doi-asserted-by":"crossref","unstructured":"Besag, J. 1974. \u201cSpatial interaction and the statistical analysis of lattice systems\u201d. Journal of the Royal Statistical Society: Series B (Methodological) 36(2): 192\u2013225. DOI: https:\/\/doi.org\/10.1111\/j.2517-6161.1974.tb00999.x.10.1111\/j.2517-6161.1974.tb00999.x","DOI":"10.1111\/j.2517-6161.1974.tb00999.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_006","doi-asserted-by":"crossref","unstructured":"Bhattacharjee, A., E. Castro, T. Maiti, and J. Marques. 2016. \u201cEndogenous spatial regression and delineation of submarkets: A new framework with application to housing markets\u201d. Journal of Applied Econometrics 31(1): 32\u201357. DOI: https:\/\/doi.org\/10.1002\/jae.2478.10.1002\/jae.2478","DOI":"10.1002\/jae.2478"},{"key":"2023121311155536244_j_jos-2021-0028_ref_007","doi-asserted-by":"crossref","unstructured":"Bhattacharjee, A., and S. Holly. 2013. \u201cUnderstanding interactions in social networks and committees\u201d. Spatial Economic Analysis 8(1): 23\u201353. DOI: https:\/\/doi.org\/10.1080\/17421772.2012.722669.10.1080\/17421772.2012.722669","DOI":"10.1080\/17421772.2012.722669"},{"key":"2023121311155536244_j_jos-2021-0028_ref_008","doi-asserted-by":"crossref","unstructured":"Bhattacharjee, A., and C. Jensen-Butler. 2013. \u201cEstimation of the spatial weights matrix under structural constraints\u201d. Regional Science and Urban Economics 43(4): 617\u2013634. DOI: https:\/\/doi.org\/10.1016\/j.regsciurbeco.2013.03.005.10.1016\/j.regsciurbeco.2013.03.005","DOI":"10.1016\/j.regsciurbeco.2013.03.005"},{"key":"2023121311155536244_j_jos-2021-0028_ref_009","doi-asserted-by":"crossref","unstructured":"Bhattacharjee, A., T. Maiti, and D. Petrie. 2014. \u201cGeneral equilibrium effects of spatial structure: Health outcomes and health behaviours in Scotland\u201d. Regional Science and Urban Economics 49: 286\u2013297. DOI: https:\/\/doi.org\/10.1016\/j.regsciurbeco.2014.10.003.10.1016\/j.regsciurbeco.2014.10.003","DOI":"10.1016\/j.regsciurbeco.2014.10.003"},{"key":"2023121311155536244_j_jos-2021-0028_ref_010","doi-asserted-by":"crossref","unstructured":"Bigotte, J.F., A.P. Antunes, D. Krass, and O. Berman. 2014. \u201cThe relationship between population dynamics and urban hierarchy: Evidence from Portugal\u201d. International Regional Science Review 37(2): 149\u2013171. DOI: https:\/\/doi.org\/10.1177\/0160017614524226.10.1177\/0160017614524226","DOI":"10.1177\/0160017614524226"},{"key":"2023121311155536244_j_jos-2021-0028_ref_011","doi-asserted-by":"crossref","unstructured":"Billari, F.C., R. Graziani, and E. Melilli. 2012. \u201cStochastic population forecasts based on conditional expert opinions\u201d. Journal of the Royal Statistical Society: Series A (Statistics in Society) 175(2): 491\u2013511. DOI: https:\/\/doi.org\/10.1111\/j.1467-985X.2011.01015.x.10.1111\/j.1467-985X.2011.01015.x341222822879704","DOI":"10.1111\/j.1467-985X.2011.01015.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_012","doi-asserted-by":"crossref","unstructured":"Billari, F.C., R. Graziani, and E. Melilli. 2014. \u201cStochastic population forecasting based on combinations of expert evaluations within the bayesian paradigm\u201d. Demography 51(5): 1933\u20131954. DOI: https:\/\/doi.org\/10.1007\/s13524-014-0318-5.10.1007\/s13524-014-0318-525124024","DOI":"10.1007\/s13524-014-0318-5"},{"key":"2023121311155536244_j_jos-2021-0028_ref_013","unstructured":"Blacker, C.P. 1947. \u201cStages in population growth\u201d. The Eugenics Review 39(3): 88."},{"key":"2023121311155536244_j_jos-2021-0028_ref_014","doi-asserted-by":"crossref","unstructured":"Bongaarts, J., and R.A. Bulatao. 1999. \u201cCompleting the demographic transition\u201d. Population and Development Review 25(3): 515\u2013529. DOI: https:\/\/doi.org\/10.4054\/-DemRes.2003.8.3.","DOI":"10.1111\/j.1728-4457.1999.00515.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_015","doi-asserted-by":"crossref","unstructured":"Borgoni, R., and F.C. Billari. 2003. \u201cBayesian spatial analysis of demographic survey data: An application to contraceptive use at first sexual intercourse\u201d. Demographic Research 8: 61\u201392. DOI: https:\/\/doi.org\/10.4054\/DemRes.2003.8.3.10.4054\/DemRes.2003.8.3","DOI":"10.4054\/DemRes.2003.8.3"},{"key":"2023121311155536244_j_jos-2021-0028_ref_016","doi-asserted-by":"crossref","unstructured":"Brooks, S.P., and A. Gelman. 1998. \u201cGeneral methods for monitoring convergence of iterative simulations\u201d. Journal of computational and graphical statistics 7(4): 434\u2013455. DOI: https:\/\/doi.org\/10.1080\/10618600.1998.10474787.10.1080\/10618600.1998.10474787","DOI":"10.1080\/10618600.1998.10474787"},{"key":"2023121311155536244_j_jos-2021-0028_ref_017","unstructured":"Carlin, B.P. and T.A. Louis. 2010. Bayes and empirical Bayes methods for data analysis. Chapman and Hall\/CRC."},{"key":"2023121311155536244_j_jos-2021-0028_ref_018","unstructured":"Castro, E.A., Z. Zhang, A. Bhattacharjee, J.M. Martins, and T. Maiti. 2015. \u201cRegional fertility data analysis: a small area bayesian approach\u201d. In Current trends in Bayesian methodology with applications, 203\u2013224."},{"key":"2023121311155536244_j_jos-2021-0028_ref_019","unstructured":"Cavenaghi, S., J.E. Potter, C.P. Schmertmann, and R.M. Assun\u00e7\u00e3o. 2016. \u201cEstimating total fertility rates for small areas in Brazil\u201d. Anais, 1\u201328."},{"key":"2023121311155536244_j_jos-2021-0028_ref_020","doi-asserted-by":"crossref","unstructured":"Celeux, G., F. Forbes, C.P. Robert, D.M. Titterington et al. 2006. \u201cDeviance information criteria for missing data models\u201d. Bayesian analysis 1(4): 651\u2013673. DOI: https:\/\/doi.org\/10.1214\/06-BA122.10.1214\/06-BA122","DOI":"10.1214\/06-BA122"},{"key":"2023121311155536244_j_jos-2021-0028_ref_021","doi-asserted-by":"crossref","unstructured":"Ciarleglio, A., and R.T. Ogden. 2016. \u201cWavelet-based scalar-on-function finite mixture regression models\u201d. Computational statistics and data analysis 93: 86\u201396. DOI: https:\/\/doi.org\/10.1016\/j.csda.2014.11.017.10.1016\/j.csda.2014.11.017462008726512156","DOI":"10.1016\/j.csda.2014.11.017"},{"key":"2023121311155536244_j_jos-2021-0028_ref_022","doi-asserted-by":"crossref","unstructured":"Clyde, M., and E.I. George. 2000. \u201cFlexible empirical bayes estimation for wavelets\u201d. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62(4): 681\u2013698. DOI: https:\/\/doi.org\/10.1111\/1467-9868.00257.10.1111\/1467-9868.00257","DOI":"10.1111\/1467-9868.00257"},{"key":"2023121311155536244_j_jos-2021-0028_ref_023","doi-asserted-by":"crossref","unstructured":"Clyde, M., and E.I. George. 2003. \u201cWavelet-based nonparametric modeling of hierarchical functions in colon carcinogenesis [with comment]\u201d. Journal of the American Statistical Association 98(463): 584\u2013585. DOI: https:\/\/doi.org\/10.1198\/016214503000000422.10.1198\/016214503000000422","DOI":"10.1198\/016214503000000422"},{"key":"2023121311155536244_j_jos-2021-0028_ref_024","doi-asserted-by":"crossref","unstructured":"Coale, A.J. 2017. The decline of fertility in Europe. Princeton University Press.10.1515\/9781400886692","DOI":"10.1515\/9781400886692"},{"key":"2023121311155536244_j_jos-2021-0028_ref_025","doi-asserted-by":"crossref","unstructured":"Cressie, N., and N.H. Chan. 1989. \u201cSpatial modeling of regional variables\u201d. Journal of the American Statistical Association 84(406): 393\u2013401. DOI: https:\/\/doi.org\/10.2307\/2289922.10.2307\/2289922","DOI":"10.1080\/01621459.1989.10478783"},{"key":"2023121311155536244_j_jos-2021-0028_ref_026","doi-asserted-by":"crossref","unstructured":"Divino, F., V. Egidi, and M.A. Salvatore. 2009. \u201cGeographical mortality patterns in italy: A bayesian analysis\u201d. Demographic Research 20: 435\u2013466. DOI: https:\/\/doi.org\/10.4054\/DemRes.2009.20.18.10.4054\/DemRes.2009.20.18","DOI":"10.4054\/DemRes.2009.20.18"},{"key":"2023121311155536244_j_jos-2021-0028_ref_027","doi-asserted-by":"crossref","unstructured":"Entwisle, B. 2007. \u201cPutting people into place\u201d. Demography 44(4): 687\u2013703. DOI: https:\/\/doi.org\/10.1353\/dem.2007.0045.10.1353\/dem.2007.004518232206","DOI":"10.1353\/dem.2007.0045"},{"key":"2023121311155536244_j_jos-2021-0028_ref_028","doi-asserted-by":"crossref","unstructured":"Feng, W., C.Y. Lim, T. Maiti, and Z. Zhang. 2016. \u201cSpatial regression and estimation of disease risks: A clustering-based approach\u201d. Statistical Analysis and Data Mining: The ASA Data Science Journal 9(6): 417\u2013434. DOI: https:\/\/doi.org\/10.1002\/sam.11314.10.1002\/sam.11314","DOI":"10.1002\/sam.11314"},{"key":"2023121311155536244_j_jos-2021-0028_ref_029","doi-asserted-by":"crossref","unstructured":"Ferguson, T.S. 1973. \u201cA bayesian analysis of some nonparametric problems\u201d. The annals of statistics 1 (2): 209\u2013230. DOI: https:\/\/doi.org\/10.1214\/aos\/1176342360.10.1214\/aos\/1176342360","DOI":"10.1214\/aos\/1176342360"},{"key":"2023121311155536244_j_jos-2021-0028_ref_030","unstructured":"Festy, P., F. Prioux, N. Unies. 2020. An evaluation of the Fertility and Family Surveys project. UN."},{"key":"2023121311155536244_j_jos-2021-0028_ref_031","unstructured":"Gomes, M.C.S., C.J. Silva, E.A.d. Castro, and J.L. Marques. 2016. \u201cEvolu\u00e7\u00e3ao da fecundidade em portugal: uma perspetiva sobre a diversidade regional\u201d. An\u00e1lise Social (218): 36\u201370. DOI: https:\/\/doi.org\/ https:\/\/www.jstor.org\/stable\/43755168."},{"key":"2023121311155536244_j_jos-2021-0028_ref_032","doi-asserted-by":"crossref","unstructured":"Green, P.J. 1995. \u201cReversible jump markov chain monte carlo computation and bayesian model determination\u201d. Biometrika 82(4): 711\u2013732. DOI: https:\/\/doi.org\/10.1093\/biomet\/82.4.711.10.1093\/biomet\/82.4.711","DOI":"10.1093\/biomet\/82.4.711"},{"key":"2023121311155536244_j_jos-2021-0028_ref_033","doi-asserted-by":"crossref","unstructured":"Guinnane, T.W. 2011. \u201cThe historical fertility transition: A guide for economists\u201d. Journal of Economic Literature 49(3): 589\u2013614.10.1257\/jel.49.3.589","DOI":"10.1257\/jel.49.3.589"},{"key":"2023121311155536244_j_jos-2021-0028_ref_034","doi-asserted-by":"crossref","unstructured":"Hubert, L., and P. Arabie. 1985. \u201cComparing partitions\u201d. Journal of classification 2(1): 193\u2013218. DOI: https:\/\/doi.org\/10.1007\/BF01908075.10.1007\/BF01908075","DOI":"10.1007\/BF01908075"},{"key":"2023121311155536244_j_jos-2021-0028_ref_035","unstructured":"INE (2011)\u201d. Nados-vivos por local de resid\u00eancia da m\u00e3ae, grupo et\u00e1ario da m\u00e3ae, sexo e filia\u00e7\u00e3ao. Recenseamento Geral da Popula\u00e7\u00e3ao (Censos de 1991 a 2011), Lisboa. Available at: https:\/\/www.pordata.pt\/Municipios\/Nados+vivos+de+m%C3%A3es+residentes+em+Portugal+total+e+por+grupo+et%C3%A1rio+da+m%C3%A3e-104."},{"key":"2023121311155536244_j_jos-2021-0028_ref_036","doi-asserted-by":"crossref","unstructured":"Knorr-Held, L., and G. Ra\u00dfer. 2000. \u201cBayesian detection of clusters and discontinuities in disease maps\u201d. Biometrics 56(1): 13\u201321.10.1111\/j.0006-341X.2000.00013.x10783772","DOI":"10.1111\/j.0006-341X.2000.00013.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_037","doi-asserted-by":"crossref","unstructured":"Lam, D.A., and J.A. Miron. 1991. \u201cSeasonality of births in human populations\u201d. Social biology 38(1\u20132): 51\u201378. DOI: https:\/\/doi.org\/10.1111\/j.0006-341x.2000.00013.x.10.1111\/j.0006-341X.2000.00013.x","DOI":"10.1080\/19485565.1991.9988772"},{"key":"2023121311155536244_j_jos-2021-0028_ref_038","unstructured":"Mendes, M.F., C. Rego, and A. Caleiro. 2006. \u201cEduca\u00e7\u00e3ao e fecundidade em Portugal: As diferen\u00e7as nos n\u00edveis de educa\u00e7\u00e3ao influenciam as taxas de fecundidade?\u201d DOI: https:\/\/doi.org\/10.13140\/RG.2.1.2449.1764."},{"key":"2023121311155536244_j_jos-2021-0028_ref_039","doi-asserted-by":"crossref","unstructured":"Morris, J.S., C. Arroyo, B.A. Coull, L.M. Ryan, R. Herrick, and S.L. Gortmaker. 2006. \u201cUsing wavelet-based functional mixed models to characterize population heterogeneity in accelerometer profiles: a case study\u201d. Journal of the American Statistical Association 101(476): 1352\u20131364. DOI: https:\/\/doi.org\/10.1198\/016214506000000465.10.1198\/016214506000000465263018919169424","DOI":"10.1198\/016214506000000465"},{"key":"2023121311155536244_j_jos-2021-0028_ref_040","doi-asserted-by":"crossref","unstructured":"Morris, J.S., and R.J. Carroll. 2006. \u201cWavelet-based functional mixed models\u201d. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68(2): 179\u2013199. DOI: https:\/\/doi.org\/10.1111\/j.1467-9868.2006.00539.x.10.1111\/j.1467-9868.2006.00539.x274410519759841","DOI":"10.1111\/j.1467-9868.2006.00539.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_041","unstructured":"Notestein, F.W. 1945. \u201cPopulation-the long view\u201d. In Food for the World, edited by Theodor Schultz, 36\u201357. Chicago: University of Chicago Press."},{"key":"2023121311155536244_j_jos-2021-0028_ref_042","doi-asserted-by":"crossref","unstructured":"Park, T., and G. Casella. 2008. \u201cThe bayesian lasso\u201d. Journal of the American Statistical Association 103(482): 681\u2013686. DOI: https:\/\/doi.org\/10.1198\/016214508000000337.10.1198\/016214508000000337","DOI":"10.1198\/016214508000000337"},{"key":"2023121311155536244_j_jos-2021-0028_ref_043","doi-asserted-by":"crossref","unstructured":"Potter, J.E., C.P. Schmertmann, R.M. Assun\u00e7\u00e3ao, and S.M. Cavenaghi. 2010. \u201cMapping the timing, pace, and scale of the fertility transition in Brazil\u201d. Population and development review 36(2): 283\u2013307.10.1111\/j.1728-4457.2010.00330.x356235620734553","DOI":"10.1111\/j.1728-4457.2010.00330.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_044","doi-asserted-by":"crossref","unstructured":"Potter, J.E., C.P. Schmertmann, and S.M. Cavenaghi. 2002. \u201cFertility and development: evidence from Brazil\u201d. Demography 39(4): 739\u2013761. DOI: https:\/\/doi.org\/10.1111\/j.1728-4457.2010.00330.x.10.1111\/j.1728-4457.2010.00330.x","DOI":"10.1353\/dem.2002.0039"},{"key":"2023121311155536244_j_jos-2021-0028_ref_045","doi-asserted-by":"crossref","unstructured":"Raftery, A.E. 1995. \u201cBayesian model selection in social research\u201d. Sociological methodology 25 (1995): 111\u2013163. DOI: https:\/\/doi.org\/10.2307\/271063.10.2307\/271063","DOI":"10.2307\/271063"},{"key":"2023121311155536244_j_jos-2021-0028_ref_046","doi-asserted-by":"crossref","unstructured":"Raftery, A.E., D. Madigan, and J.A. Hoeting. 1997. \u201cBayesian model averaging for linear regression models\u201d. Journal of the American Statistical Association 92(437): 179\u2013191. DOI: https:\/\/doi.org\/10.1080\/01621459.1997.10473615.10.1080\/01621459.1997.10473615","DOI":"10.1080\/01621459.1997.10473615"},{"key":"2023121311155536244_j_jos-2021-0028_ref_047","doi-asserted-by":"crossref","unstructured":"Ray, S., and B. Mallick. 2006. \u201cFunctional clustering by bayesian wavelet methods\u201d. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68(2): 305\u2013332. DOI: https:\/\/doi.org\/10.1111\/j.1467-9868.2006.00545.x.10.1111\/j.1467-9868.2006.00545.x","DOI":"10.1111\/j.1467-9868.2006.00545.x"},{"key":"2023121311155536244_j_jos-2021-0028_ref_048","doi-asserted-by":"crossref","unstructured":"Retherford, R., N. Ogawa, R. Matsukura, and H. Eini-Zinab. 2010. \u201cMultivariate analysis of parity progression\u2013based measures of the total fertility rate and its components\u201d. Demography 47(1): 97\u2013124. DOI: https:\/\/doi.org\/10.1353\/dem.0.0087.10.1353\/dem.0.0087300001620355686","DOI":"10.1353\/dem.0.0087"},{"key":"2023121311155536244_j_jos-2021-0028_ref_049","doi-asserted-by":"crossref","unstructured":"Ritter, C., and M.A. Tanner. 1992. \u201cFacilitating the Gibbs sampler: the Gibbs stopper and the Griddy-Gibbs sampler\u201d. Journal of the American Statistical Association 87(419): 861\u2013868. DOI: https:\/\/doi.org\/10.2307\/2290225.10.2307\/2290225","DOI":"10.1080\/01621459.1992.10475289"},{"key":"2023121311155536244_j_jos-2021-0028_ref_050","doi-asserted-by":"crossref","unstructured":"Sampson, R.J., J.D. Morenoff, and T. Gannon-Rowley. 2002. \u201cAssessing \u201cneighborhood effects\u201d: Social processes and new directions in research\u201d. Annual review of sociology 28(1): 443\u2013478. DOI: https:\/\/doi.org\/10.1146\/annurev.soc.28.110601.141114.10.1146\/annurev.soc.28.110601.141114","DOI":"10.1146\/annurev.soc.28.110601.141114"},{"key":"2023121311155536244_j_jos-2021-0028_ref_051","doi-asserted-by":"crossref","unstructured":"Seiver, D.A. 1985. \u201cTrend and variation in the seasonality of us fertility, 1947\u20131976\u201d. Demography 22(1): 89\u2013100. DOI: https:\/\/doi.org\/10.2307\/2060988.10.2307\/2060988","DOI":"10.2307\/2060988"},{"key":"2023121311155536244_j_jos-2021-0028_ref_052","unstructured":"Silva, C., C. Gomes, M. Pinto, J. Marques and E. Castro. 2011. \u201cIguais mas diferentes: a import\u00e2ncia em regionalizar os modelos de projec\u00e7\u00e3o da popula\u00e7\u00e3o portuguesa.\u201d XVII Congresso Nacional da APDR. 29 de Junho a 01 de Julho 2011; Bragan\u00e7a e Zamora-Portugal e Espanha): 275\u2013289."},{"key":"2023121311155536244_j_jos-2021-0028_ref_053","doi-asserted-by":"crossref","unstructured":"Smith, S.K., and T. Sincich. 1988. \u201cStability over time in the distribution of population forecast errors\u201d. Demography 25(3): 461\u2013474. DOI: https:\/\/doi.org\/10.2307\/2061544.10.2307\/2061544","DOI":"10.2307\/2061544"},{"key":"2023121311155536244_j_jos-2021-0028_ref_054","doi-asserted-by":"crossref","unstructured":"Thompson, W.C. 1929. \u201cPopulation\u201d. American Journal of Sociology 34: 959\u2013975. DOI: https:\/\/doi.org\/10.1086\/214874.10.1086\/214874","DOI":"10.1086\/214874"},{"key":"2023121311155536244_j_jos-2021-0028_ref_055","doi-asserted-by":"crossref","unstructured":"Tibshirani, R., G. Walther, and T. Hastie. 2001. \u201cEstimating the number of clusters in a data set via the gap statistic\u201d. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63(2): 411\u2013423. DOI: https:\/\/doi.org\/10.1111\/1467-9868.00293.10.1111\/1467-9868.00293","DOI":"10.1111\/1467-9868.00293"},{"key":"2023121311155536244_j_jos-2021-0028_ref_056","doi-asserted-by":"crossref","unstructured":"Tolnay, S.E. 1995. \u201cThe spatial diffusion of fertility: A cross-sectional analysis of counties in the American South, 1940\u201d. American Sociological Review 60(2): 299\u2013308. DOI: https:\/\/doi.org\/10.2307\/2096388.10.2307\/2096388","DOI":"10.2307\/2096388"},{"key":"2023121311155536244_j_jos-2021-0028_ref_057","doi-asserted-by":"crossref","unstructured":"Voss, P.R. 2007. \u201cDemography as a spatial social science\u201d. Population research and policy review 26(5\u20136): 457\u2013476. DOI: https:\/\/doi.org\/10.1007\/s11113-007-9047-4.10.1007\/s11113-007-9047-4","DOI":"10.1007\/s11113-007-9047-4"},{"key":"2023121311155536244_j_jos-2021-0028_ref_058","doi-asserted-by":"crossref","unstructured":"Wall, M.M. 2004. \u201cA close look at the spatial structure implied by the car and sar models\u201d. Journal of statistical planning and inference 121 (2): 311\u2013324. DOI: https:\/\/doi.org\/10.1016\/S0378-3758(03)00111-3.10.1016\/S0378-3758(03)00111-3","DOI":"10.1016\/S0378-3758(03)00111-3"},{"key":"2023121311155536244_j_jos-2021-0028_ref_059","doi-asserted-by":"crossref","unstructured":"Waller, L.A. 2015. \u201cDiscussion: statistical cluster detection, epidemiologic interpretation, and public health policy\u201d. Statistics and Public Policy 2(1): 1\u20138. DOI: https:\/\/doi.org\/10.1080\/2330443X.2015.1026621.10.1080\/2330443X.2015.1026621","DOI":"10.1080\/2330443X.2015.1026621"},{"key":"2023121311155536244_j_jos-2021-0028_ref_060","doi-asserted-by":"crossref","unstructured":"Weeks, J.R. 2004. \u201cThe role of spatial analysis in demographic research\u201d. In Spatially integrated social science, edited by M.F. Goodchild, and D.G. Janelle, 381\u2013399.","DOI":"10.1093\/oso\/9780195152708.003.0019"},{"key":"2023121311155536244_j_jos-2021-0028_ref_061","doi-asserted-by":"crossref","unstructured":"Weeks, J.R., M.S. Gadalla, T. Rashed, J. Stanforth, and A.G. Hill. 2000. \u201cSpatial variability in fertility in menoufia, Egypt, assessed through the application of remote-sensing and gis technologies\u201d. Environment and Planning A 32(4): 695\u2013714. DOI: https:\/\/doi.org\/10.1068\/a3286.10.1068\/a3286","DOI":"10.1068\/a3286"},{"key":"2023121311155536244_j_jos-2021-0028_ref_062","doi-asserted-by":"crossref","unstructured":"Whittle, P. 1954. \u201cOn stationary processes in the plane\u201d. Biometrika 41 (3\/4): 434\u2013449. DOI: https:\/\/doi.org\/10.2307\/2332724.10.2307\/2332724","DOI":"10.1093\/biomet\/41.3-4.434"},{"key":"2023121311155536244_j_jos-2021-0028_ref_063","doi-asserted-by":"crossref","unstructured":"Zhang, Z., C.Y. Lim, and T. Maiti. 2014. \u201cAnalyzing 2000\u20132010 childhood age-adjusted cancer rates in Florida: A spatial clustering approach\u201d. Statistics and Public Policy 1(1): 120\u2013128. DOI: https:\/\/doi.org\/10.1080\/2330443X.2014.979962.10.1080\/2330443X.2014.979962","DOI":"10.1080\/2330443X.2014.979962"},{"key":"2023121311155536244_j_jos-2021-0028_ref_064","doi-asserted-by":"crossref","unstructured":"Zhao, Z., and B. Guo. 2012. \u201cAn algorithm for determination of age-specific fertility rate from initial age structure and total population\u201d. Journal of Systems Science and Complexity 25(5): 833\u2013844. DOI: https:\/\/doi.org\/10.1007\/s11424-012-1039-8.10.1007\/s11424-012-1039-8","DOI":"10.1007\/s11424-012-1039-8"}],"container-title":["Journal of Official Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/jos-2021-0028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:24Z","timestamp":1777507224000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.2478\/jos-2021-0028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,1]]},"references-count":64,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9,13]]},"published-print":{"date-parts":[[2021,9,1]]}},"alternative-id":["10.2478\/jos-2021-0028"],"URL":"https:\/\/doi.org\/10.2478\/jos-2021-0028","relation":{},"ISSN":["2001-7367"],"issn-type":[{"value":"2001-7367","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,1]]}}}